{"id":463533,"date":"2025-06-16T15:01:10","date_gmt":"2025-06-16T15:01:10","guid":{"rendered":"http:\/\/savepearlharbor.com\/?p=463533"},"modified":"-0001-11-30T00:00:00","modified_gmt":"-0001-11-29T21:00:00","slug":"","status":"publish","type":"post","link":"https:\/\/savepearlharbor.com\/?p=463533","title":{"rendered":"<span>\u041e\u0441\u043e\u0431\u0435\u043d\u043d\u043e\u0441\u0442\u044c \u0434\u0438\u0441\u043a\u0440\u0435\u0442\u043d\u043e\u0433\u043e \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u0430 \u2014&gt; \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0431\u044d\u043a\u0434\u043e\u0440 \u0432 \u043f\u0440\u043e\u0442\u043e\u043a\u043e\u043b\u0435 \u0414\u0438\u0444\u0444\u0438 \u2014 \u0425\u0435\u043b\u043b\u043c\u0430\u043d\u0430<\/span>"},"content":{"rendered":"<div><!--[--><!--]--><\/div>\n<div id=\"post-content-body\">\n<div>\n<div class=\"article-formatted-body article-formatted-body article-formatted-body_version-2\">\n<div xmlns=\"http:\/\/www.w3.org\/1999\/xhtml\">\n<figure class=\"full-width\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/upload_files\/52d\/971\/ce5\/52d971ce548bcc0fd1896c8c9756cac0.png\" width=\"780\" height=\"440\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/upload_files\/52d\/971\/ce5\/52d971ce548bcc0fd1896c8c9756cac0.png 780w,&#10; 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      https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/25\/258\/258043ada64cb9d1e310789e7ae04bde.svg 781w\" loading=\"lazy\" decode=\"async\"\/><br \/> <img decoding=\"async\" class=\"formula inline\" source=\"3^5 \\equiv 5 \\pmod 7\" alt=\"3^5 \\equiv 5 \\pmod 7\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a3\/a33\/a33f0d5d1f8e4496f2c0b4b6276ee720.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a3\/a33\/a33f0d5d1f8e4496f2c0b4b6276ee720.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a3\/a33\/a33f0d5d1f8e4496f2c0b4b6276ee720.svg 781w\" loading=\"lazy\" decode=\"async\"\/><br \/> <img decoding=\"async\" class=\"formula inline\" source=\"3^6 \\equiv 1 \\pmod 7\" alt=\"3^6 \\equiv 1 \\pmod 7\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ae\/ae9\/ae9126c8a84cdd130b0e27cefc93cf61.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ae\/ae9\/ae9126c8a84cdd130b0e27cefc93cf61.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ae\/ae9\/ae9126c8a84cdd130b0e27cefc93cf61.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041e\u0431\u0440\u0430\u0449\u0430\u0435\u043c \u0432\u043d\u0438\u043c\u0430\u043d\u0438\u0435 \u043d\u0430 \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u044e\u044e \u0441\u0442\u0440\u043e\u043a\u0443, \u0442.\u0435. \u0435\u0441\u043b\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"a = 1\" alt=\"a = 1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fd\/fd3\/fd352b68bf83391284e044021cab0339.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fd\/fd3\/fd352b68bf83391284e044021cab0339.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fd\/fd3\/fd352b68bf83391284e044021cab0339.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0442\u043e <img decoding=\"async\" class=\"formula inline\" source=\"x = 0\" alt=\"x = 0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3d\/3da\/3dad28281778d5ef4b7a78c7bc7a6b09.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3d\/3da\/3dad28281778d5ef4b7a78c7bc7a6b09.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3d\/3da\/3dad28281778d5ef4b7a78c7bc7a6b09.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438\u043b\u0438 <img decoding=\"async\" class=\"formula inline\" source=\"x = p-1\" alt=\"x = p-1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c9\/c9b\/c9b883d44e08dfd7336c500a1fbc8526.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c9\/c9b\/c9b883d44e08dfd7336c500a1fbc8526.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c9\/c9b\/c9b883d44e08dfd7336c500a1fbc8526.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0418\u0442\u0430\u043a, \u0443 \u043d\u0430\u0441 \u0435\u0441\u0442\u044c \u0443\u0436\u0435 \u0442\u0440\u0438 \u0441\u043b\u0443\u0447\u0430\u044f, \u043a\u043e\u0433\u0434\u0430 \u043f\u043e\u0438\u0441\u043a <img decoding=\"async\" class=\"formula inline\" source=\"x\" alt=\"x\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0442\u0440\u0438\u0432\u0438\u0430\u043b\u0435\u043d:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"x  \\in \\{ 0, 1, p-1\\}\" alt=\"x  \\in \\{ 0, 1, p-1\\}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/7c6\/176\/2db\/7c61762dbe8797a8040c03da1d95d8b5.svg\" width=\"131\" height=\"22\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/7c6\/176\/2db\/7c61762dbe8797a8040c03da1d95d8b5.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/7c6\/176\/2db\/7c61762dbe8797a8040c03da1d95d8b5.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041a\u0430\u043a \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u0434\u043b\u044f \u0430\u043d\u0430\u043b\u0438\u0437\u0430 DLOG \u0441\u0442\u0440\u043e\u044f\u0442 \u0442\u0430\u0431\u043b\u0438\u0446\u0443 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u043e\u0432:<\/p>\n<figure class=\"\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/upload_files\/bee\/a4c\/980\/beea4c98069d3686f4e63e51bc9929a2.png\" alt=\"\u0422\u0430\u0431\u043b\u0438\u0446\u0430 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u043e\u0432 \u0434\u043b\u044f  (\u043d\u0443\u043b\u0435\u0432\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435  \u043e\u0431\u044b\u0447\u043d\u043e \u043e\u043f\u0443\u0441\u043a\u0430\u044e\u0442)\" title=\"\u0422\u0430\u0431\u043b\u0438\u0446\u0430 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u043e\u0432 \u0434\u043b\u044f  (\u043d\u0443\u043b\u0435\u0432\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435  \u043e\u0431\u044b\u0447\u043d\u043e \u043e\u043f\u0443\u0441\u043a\u0430\u044e\u0442)\" width=\"436\" height=\"107\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/upload_files\/bee\/a4c\/980\/beea4c98069d3686f4e63e51bc9929a2.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/upload_files\/bee\/a4c\/980\/beea4c98069d3686f4e63e51bc9929a2.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0422\u0430\u0431\u043b\u0438\u0446\u0430 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u043e\u0432 \u0434\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"GF(7), \\ g = 3\" alt=\"GF(7), \\ g = 3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e7\/e72\/e72318bf9c31fbcaa91e31fbf451e4d4.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e7\/e72\/e72318bf9c31fbcaa91e31fbf451e4d4.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e7\/e72\/e72318bf9c31fbcaa91e31fbf451e4d4.svg 781w\" loading=\"lazy\" decode=\"async\"\/> (\u043d\u0443\u043b\u0435\u0432\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"x\" alt=\"x\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043e\u0431\u044b\u0447\u043d\u043e \u043e\u043f\u0443\u0441\u043a\u0430\u044e\u0442)<\/figcaption><\/div>\n<\/figure>\n<p>\u041f\u043e \u0442\u0430\u0431\u043b\u0438\u0446\u0435 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u043e\u0432 \u043d\u0430\u0440\u0438\u0441\u0443\u0435\u043c \u0433\u0440\u0430\u0444\u0438\u043a:<\/p>\n<figure class=\"full-width\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/upload_files\/872\/48b\/e24\/87248be24efd09dd3514725a02df0fc2.png\" alt=\"\u0413\u0440\u0430\u0444\u0438\u043a \u0442\u0430\u0431\u043b\u0438\u0446\u044b \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u043e\u0432 \u0434\u043b\u044f \" title=\"\u0413\u0440\u0430\u0444\u0438\u043a \u0442\u0430\u0431\u043b\u0438\u0446\u044b \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u043e\u0432 \u0434\u043b\u044f \" width=\"1280\" height=\"750\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/upload_files\/872\/48b\/e24\/87248be24efd09dd3514725a02df0fc2.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/upload_files\/872\/48b\/e24\/87248be24efd09dd3514725a02df0fc2.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0413\u0440\u0430\u0444\u0438\u043a \u0442\u0430\u0431\u043b\u0438\u0446\u044b \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u043e\u0432 \u0434\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"GF(7), \\ g = 3\" alt=\"GF(7), \\ g = 3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e7\/e72\/e72318bf9c31fbcaa91e31fbf451e4d4.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e7\/e72\/e72318bf9c31fbcaa91e31fbf451e4d4.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e7\/e72\/e72318bf9c31fbcaa91e31fbf451e4d4.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/figcaption><\/div>\n<\/figure>\n<p>\u041d\u0430 \u0433\u0440\u0430\u0444\u0438\u043a\u0435 \u043d\u0438\u0447\u0435\u0433\u043e \u0438\u043d\u0442\u0435\u0440\u0435\u0441\u043d\u043e\u0433\u043e, \u0442\u043e\u043b\u044c\u043a\u043e \u0445\u0430\u043e\u0442\u0438\u0447\u043d\u043e\u0435 \u0438\u0437\u043c\u0435\u043d\u0435\u043d\u0438\u0435 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"x\" alt=\"x\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041a\u0440\u0438\u043f\u0442\u043e\u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u043f\u0440\u043e\u0442\u043e\u043a\u043e\u043b DH \u043f\u043e\u0441\u0442\u0440\u043e\u0435\u043d \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0435 DLOG <a href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%9F%D1%80%D0%BE%D1%82%D0%BE%D0%BA%D0%BE%D0%BB_%D0%94%D0%B8%D1%84%D1%84%D0%B8_%E2%80%94_%D0%A5%D0%B5%D0%BB%D0%BB%D0%BC%D0%B0%D0%BD%D0%B0\" rel=\"noopener noreferrer nofollow\">https:\/\/ru.wikipedia.org\/wiki\/\u041f\u0440\u043e\u0442\u043e\u043a\u043e\u043b_\u0414\u0438\u0444\u0444\u0438_\u2014_\u0425\u0435\u043b\u043b\u043c\u0430\u043d\u0430<\/a><\/p>\n<p>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043f\u0440\u0438\u043c\u0435\u0440 \u043f\u0440\u044f\u043c\u043e \u0438\u0437 \u0432\u0438\u043a\u0438:<\/p>\n<figure class=\"full-width\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/upload_files\/744\/3f5\/35c\/7443f535cdfcb5daf95adde9c426623c.png\" alt=\"\u0421\u043a\u0440\u0438\u043d \u0438\u0437 \u0432\u0438\u043a\u0438\u0441\u0442\u0430\u0442\u044c\u0438 \u041f\u0440\u043e\u0442\u043e\u043a\u043e\u043b \u0414\u0438\u0444\u0444\u0438 \u2014 \u0425\u0435\u043b\u043b\u043c\u0430\u043d\u0430\" title=\"\u0421\u043a\u0440\u0438\u043d \u0438\u0437 \u0432\u0438\u043a\u0438\u0441\u0442\u0430\u0442\u044c\u0438 \u041f\u0440\u043e\u0442\u043e\u043a\u043e\u043b \u0414\u0438\u0444\u0444\u0438 \u2014 \u0425\u0435\u043b\u043b\u043c\u0430\u043d\u0430\" width=\"1027\" height=\"712\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/upload_files\/744\/3f5\/35c\/7443f535cdfcb5daf95adde9c426623c.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/upload_files\/744\/3f5\/35c\/7443f535cdfcb5daf95adde9c426623c.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0421\u043a\u0440\u0438\u043d \u0438\u0437 \u0432\u0438\u043a\u0438\u0441\u0442\u0430\u0442\u044c\u0438 \u041f\u0440\u043e\u0442\u043e\u043a\u043e\u043b \u0414\u0438\u0444\u0444\u0438 \u2014 \u0425\u0435\u043b\u043b\u043c\u0430\u043d\u0430<\/figcaption><\/div>\n<\/figure>\n<p>\u041d\u0438\u0447\u0435\u0433\u043e \u0441\u043b\u043e\u0436\u043d\u043e\u0433\u043e.<\/p>\n<p>\u0414\u0430\u043b\u0435\u0435 \u043f\u043e\u0439\u0434\u0435\u0442 \u043d\u043e\u0432\u0430\u044f \u0438\u043b\u0438 \u043d\u0435\u043f\u0443\u0431\u043b\u0438\u0447\u043d\u0430\u044f \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u044f.<\/p>\n<h2>\u041e\u0441\u043d\u043e\u0432\u043d\u0430\u044f \u0447\u0430\u0441\u0442\u044c<\/h2>\n<p>\u0411\u0443\u0434\u0435\u043c \u0430\u043d\u0430\u043b\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u0442\u044c DLOG \u043a\u0430\u043a \u0442\u0430\u0431\u043b\u0438\u0446\u0443 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439. \u0422\u0430\u0431\u043b\u0438\u0446\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 \u044d\u0442\u043e \u043f\u0435\u0440\u0435\u0432\u0435\u0440\u043d\u0443\u0442\u0430\u044f \u0442\u0430\u0431\u043b\u0438\u0446\u0430 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u043e\u0432 (\u0441\u043c. \u0440\u0438\u0441. \u043d\u0438\u0436\u0435), \u0441\u043b\u0435\u0432\u0430 \u2014 \u0442\u0430\u0431\u043b\u0438\u0446\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439, \u0441\u043f\u0440\u0430\u0432\u0430 \u2014 \u0442\u0430\u0431\u043b\u0438\u0446\u0430 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u043e\u0432. \u041e\u0431 \u044d\u0442\u043e\u043c \u044f \u043f\u0438\u0441\u0430\u043b \u0432 \u0441\u0442\u0430\u0442\u044c\u0435 &#171;\u041a\u0430\u043a \u0441\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u043f\u043e\u0440\u043e\u0436\u0434\u0430\u044e\u0449\u0438\u0435 \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u044b \u0434\u043b\u044f \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0445 \u043f\u043e\u043b\u0435\u0439.&#187; <a href=\"https:\/\/habr.com\/ru\/articles\/844300\" rel=\"noopener noreferrer nofollow\">https:\/\/habr.com\/ru\/articles\/844300<\/a><\/p>\n<figure class=\"full-width\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/upload_files\/0c3\/001\/3ec\/0c30013ec11e5da5b2a076edca51fa14.png\" alt=\"\u0422\u0430\u0431\u043b\u0438\u0446\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 \u0438 \u0442\u0430\u0431\u043b\u0438\u0446\u0430 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u043e\u0432 \u0434\u043b\u044f \" title=\"\u0422\u0430\u0431\u043b\u0438\u0446\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 \u0438 \u0442\u0430\u0431\u043b\u0438\u0446\u0430 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u043e\u0432 \u0434\u043b\u044f \" width=\"600\" height=\"254\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/upload_files\/0c3\/001\/3ec\/0c30013ec11e5da5b2a076edca51fa14.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/upload_files\/0c3\/001\/3ec\/0c30013ec11e5da5b2a076edca51fa14.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0422\u0430\u0431\u043b\u0438\u0446\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 \u0438 \u0442\u0430\u0431\u043b\u0438\u0446\u0430 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u043e\u0432 \u0434\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"GF(7)\" alt=\"GF(7)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8c\/8c1\/8c1c5330d79255ea6deb9d2586c2bc07.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8c\/8c1\/8c1c5330d79255ea6deb9d2586c2bc07.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8c\/8c1\/8c1c5330d79255ea6deb9d2586c2bc07.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/figcaption><\/div>\n<\/figure>\n<p>\u0422\u0430\u0431\u043b\u0438\u0446\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 \u0443\u0434\u043e\u0431\u043d\u0435\u0435, \u0442\u0430\u043a \u043a\u0430\u043a \u043c\u043e\u0436\u043d\u043e \u043d\u0430\u0431\u043b\u044e\u0434\u0430\u0442\u044c \u0441\u0440\u0430\u0437\u0443 \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043f\u0440\u0438\u043c\u0438\u0442\u0438\u0432\u043e\u0432 (<img decoding=\"async\" class=\"formula inline\" source=\"g\" alt=\"g\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b2\/b2f\/b2f5ff47436671b6e533d8dc3614845d.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b2\/b2f\/b2f5ff47436671b6e533d8dc3614845d.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b2\/b2f\/b2f5ff47436671b6e533d8dc3614845d.svg 781w\" loading=\"lazy\" decode=\"async\"\/>), \u0441\u0438\u043d\u0438\u043c \u043f\u043e\u0434\u0447\u0435\u0440\u043a\u043d\u0443\u0442\u0430 \u0441\u0442\u0440\u043e\u043a\u0430 \u0434\u043b\u044f \u043f\u0440\u0438\u043c\u0438\u0442\u0438\u0432\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"g = 3\" alt=\"g = 3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/40\/40a\/40afdce0f67dba365f6b571d11f866c5.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/40\/40a\/40afdce0f67dba365f6b571d11f866c5.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/40\/40a\/40afdce0f67dba365f6b571d11f866c5.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043a\u043e\u043b\u043e\u043d\u043a\u0430 \u0434\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"x = 0\" alt=\"x = 0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3d\/3da\/3dad28281778d5ef4b7a78c7bc7a6b09.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3d\/3da\/3dad28281778d5ef4b7a78c7bc7a6b09.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3d\/3da\/3dad28281778d5ef4b7a78c7bc7a6b09.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043d\u0435 \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0435\u043d\u0430.<\/p>\n<p>\u0414\u0430\u043b\u0435\u0435 \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0442\u0430\u0431\u043b\u0438\u0446 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 \u0438 \u043e\u0431\u0440\u0430\u0442\u0438\u043c \u0432\u043d\u0438\u043c\u0430\u043d\u0438\u0435 \u043d\u0430 \u0441\u0440\u0435\u0434\u043d\u044e\u044e \u043a\u043e\u043b\u043e\u043d\u043a\u0443 <img decoding=\"async\" class=\"formula inline\" source=\"x = (p-1)\/2\" alt=\"x = (p-1)\/2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1d\/1d3\/1d361e2cb708642c28db329e7806b717.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1d\/1d3\/1d361e2cb708642c28db329e7806b717.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1d\/1d3\/1d361e2cb708642c28db329e7806b717.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<figure class=\"full-width\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/upload_files\/f7f\/6ea\/17a\/f7f6ea17af134fd6a9cd1795544f4839.png\" alt=\"\u041d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0442\u0430\u0431\u043b\u0438\u0446 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439\" title=\"\u041d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0442\u0430\u0431\u043b\u0438\u0446 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439\" width=\"1360\" height=\"1100\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/upload_files\/f7f\/6ea\/17a\/f7f6ea17af134fd6a9cd1795544f4839.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/upload_files\/f7f\/6ea\/17a\/f7f6ea17af134fd6a9cd1795544f4839.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u041d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0442\u0430\u0431\u043b\u0438\u0446 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439<\/figcaption><\/div>\n<\/figure>\n<p>\u0418\u043c\u0435\u044f \u0432\u0432\u0438\u0434\u0443 \u044d\u043a\u0441\u0442\u0440\u0430\u043f\u043e\u043b\u044f\u0446\u0438\u044e, \u043c\u043e\u0436\u043d\u043e \u043f\u0440\u0435\u0434\u043f\u043e\u043b\u043e\u0436\u0438\u0442\u044c, \u0447\u0442\u043e \u0434\u0430\u043d\u043d\u0430\u044f \u043e\u0441\u043e\u0431\u0435\u043d\u043d\u043e\u0441\u0442\u044c \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u044f\u0435\u0442\u0441\u044f \u043d\u0430 \u0432\u0441\u0435 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u043e \u0442\u0430\u0431\u043b\u0438\u0446 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 <img decoding=\"async\" class=\"formula inline\" source=\"GF(p)\" alt=\"GF(p)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/13\/13d\/13d7f9f1f837dd8322d8dc16e9a699c0.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/13\/13d\/13d7f9f1f837dd8322d8dc16e9a699c0.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/13\/13d\/13d7f9f1f837dd8322d8dc16e9a699c0.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<p>\u0412 \u0441\u0440\u0435\u0434\u043d\u0435\u0439 \u043a\u043e\u043b\u043e\u043d\u043a\u0435 \u0447\u0438\u0441\u043b\u043e <img decoding=\"async\" class=\"formula inline\" source=\"p-1\" alt=\"p-1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/70\/70f\/70ff83728fb2701cbc52fac8df762bf1.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/70\/70f\/70ff83728fb2701cbc52fac8df762bf1.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/70\/70f\/70ff83728fb2701cbc52fac8df762bf1.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043f\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442 \u0441\u0442\u0440\u043e\u043a\u0438 \u0441 \u0443\u043d\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u043c\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u043c\u0438, \u0437\u043d\u0430\u0447\u0438\u0442 \u0432 \u043d\u0430\u0447\u0430\u043b\u0435 \u0441\u0442\u0440\u043e\u043a\u0438 &#8212; \u043f\u0440\u0438\u043c\u0438\u0442\u0438\u0432, \u043d\u0430\u0431\u043b\u044e\u0434\u0430\u0435\u043c \u0442\u0430\u043a\u0436\u0435:<\/p>\n<ul>\n<li>\n<p>\u043d\u0435 \u043a\u0430\u0441\u0430\u0435\u0442\u0441\u044f \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0435\u0439 \u0441\u0442\u0440\u043e\u043a\u0438, \u0442\u0430\u043c <img decoding=\"async\" class=\"formula inline\" source=\"\\{1, (p-1), 1, (p-1), \\cdots \\}\" alt=\"\\{1, (p-1), 1, (p-1), \\cdots \\}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/71\/711\/71142bc7776d89497538a70582a859b8.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/71\/711\/71142bc7776d89497538a70582a859b8.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/71\/711\/71142bc7776d89497538a70582a859b8.svg 781w\" loading=\"lazy\" decode=\"async\"\/>;<\/p>\n<\/li>\n<li>\n<p><img decoding=\"async\" class=\"formula inline\" source=\"(p-1)\/2\" alt=\"(p-1)\/2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1a\/1a6\/1a6beb77bddb2f66cf392e0dbd85aa69.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1a\/1a6\/1a6beb77bddb2f66cf392e0dbd85aa69.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1a\/1a6\/1a6beb77bddb2f66cf392e0dbd85aa69.svg 781w\" loading=\"lazy\" decode=\"async\"\/> &#8212; \u043f\u0440\u043e\u0441\u0442\u043e\u0435 \u0447\u0438\u0441\u043b\u043e, \u0438\u043d\u0430\u0447\u0435, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440 \u0434\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"GF(13) \\ \\Longrightarrow \\ (p-1)\/2 = 6\" alt=\"GF(13) \\ \\Longrightarrow \\ (p-1)\/2 = 6\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c0\/c06\/c06af8084619135095aaab6aecffaac2.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c0\/c06\/c06af8084619135095aaab6aecffaac2.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c0\/c06\/c06af8084619135095aaab6aecffaac2.svg 781w\" loading=\"lazy\" decode=\"async\"\/> &#8212; \u043d\u0435\u043f\u0440\u043e\u0441\u0442\u043e\u0435, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0431\u0443\u0434\u0443\u0442 &#171;\u043b\u0438\u0448\u043d\u0438\u0435&#187; \u0441\u0442\u0440\u043e\u043a\u0438: <img decoding=\"async\" class=\"formula inline\" source=\"\\{5, 8\\}\" alt=\"\\{5, 8\\}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/40\/40e\/40ebca2b86c15378c5dcc1894391b66f.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/40\/40e\/40ebca2b86c15378c5dcc1894391b66f.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/40\/40e\/40ebca2b86c15378c5dcc1894391b66f.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<\/li>\n<\/ul>\n<p>\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u044d\u0442\u043e \u0432\u044b\u0433\u043b\u044f\u0434\u0438\u0442 \u0442\u0430\u043a:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"g^{(p-1)\/2} \\equiv p-1\\ |\\ 1 \\pmod p \\quad  (1)\" alt=\"g^{(p-1)\/2} \\equiv p-1\\ |\\ 1 \\pmod p \\quad  (1)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/6cd\/c64\/bc8\/6cdc64bc8836a601222a67b59053acf5.svg\" width=\"283\" height=\"25\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/6cd\/c64\/bc8\/6cdc64bc8836a601222a67b59053acf5.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/6cd\/c64\/bc8\/6cdc64bc8836a601222a67b59053acf5.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438 \u0437\u043d\u0430\u043a\u043e\u043c\u044b\u0435 \u0441 \u043a\u0440\u0438\u0442\u0435\u0440\u0438\u044f\u043c\u0438 \u042d\u0439\u043b\u0435\u0440\u0430 <a href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%9A%D1%80%D0%B8%D1%82%D0%B5%D1%80%D0%B8%D0%B9_%D0%AD%D0%B9%D0%BB%D0%B5%D1%80%D0%B0\" rel=\"noopener noreferrer nofollow\">https:\/\/ru.wikipedia.org\/wiki\/\u041a\u0440\u0438\u0442\u0435\u0440\u0438\u0439_\u042d\u0439\u043b\u0435\u0440\u0430<\/a> \u0438 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u044b\u043c \u0432\u044b\u0447\u0435\u0442\u043e\u043c <a href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%9A%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D0%B8%D1%87%D0%BD%D1%8B%D0%B9_%D0%B2%D1%8B%D1%87%D0%B5%D1%82\" rel=\"noopener noreferrer nofollow\">https:\/\/ru.wikipedia.org\/wiki\/\u041a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u044b\u0439_\u0432\u044b\u0447\u0435\u0442<\/a> \u0443\u0432\u0438\u0434\u044f\u0442 \u0437\u043d\u0430\u043a\u043e\u043c\u043e\u0435:<\/p>\n<ul>\n<li>\n<p><img decoding=\"async\" class=\"formula inline\" source=\"a^{(p-1)\/2}\\equiv 1 \\pmod p\" alt=\"a^{(p-1)\/2}\\equiv 1 \\pmod p\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/09\/09f\/09f080f22e418d94716c35fa45dda5b8.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/09\/09f\/09f080f22e418d94716c35fa45dda5b8.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/09\/09f\/09f080f22e418d94716c35fa45dda5b8.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p><img decoding=\"async\" class=\"formula inline\" source=\"a^{(p-1)\/2}\\equiv -1 \\pmod p\" alt=\"a^{(p-1)\/2}\\equiv -1 \\pmod p\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/72\/72d\/72daa0c78a7c1db1a0d07aadd0cb520f.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/72\/72d\/72daa0c78a7c1db1a0d07aadd0cb520f.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/72\/72d\/72daa0c78a7c1db1a0d07aadd0cb520f.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<\/ul>\n<p>\u043d\u043e \u0437\u0434\u0435\u0441\u044c \u0432\u043c\u0435\u0441\u0442\u043e <img decoding=\"async\" class=\"formula inline\" source=\"(p-1)\" alt=\"(p-1)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fc\/fc8\/fc86261874dd92078554f3ac92efbca8.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fc\/fc8\/fc86261874dd92078554f3ac92efbca8.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fc\/fc8\/fc86261874dd92078554f3ac92efbca8.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0443\u0441\u0442\u0430\u043d\u043e\u0432\u043b\u0435\u043d\u043e <img decoding=\"async\" class=\"formula inline\" source=\"(-1)\" alt=\"(-1)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7d\/7d6\/7d6774ade191488268831fe319436d4f.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7d\/7d6\/7d6774ade191488268831fe319436d4f.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7d\/7d6\/7d6774ade191488268831fe319436d4f.svg 781w\" loading=\"lazy\" decode=\"async\"\/> !<\/p>\n<p>\u041d\u0430\u0434\u043e \u0432\u0441\u043f\u043e\u043c\u043d\u0438\u0442\u044c \u043c\u043e\u0434\u0443\u043b\u044f\u0440\u043d\u0443\u044e \u0430\u0440\u0438\u0444\u043c\u0435\u0442\u0438\u043a\u0443 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Modular_arithmetic\" rel=\"noopener noreferrer nofollow\">https:\/\/en.wikipedia.org\/wiki\/Modular_arithmetic<\/a> (\u0441\u0442\u0430\u0442\u044c\u044f \u0432 en-\u0432\u0438\u043a\u0438 \u0431\u043e\u043b\u0435\u0435 \u043f\u043e\u043d\u044f\u0442\u043d\u0430), \u0444\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0432 \u0434\u0430\u043d\u043d\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"(-1) = (p-1)\" alt=\"(-1) = (p-1)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/ba\/ba3\/ba368b1ae3809c08a0d2ef573400b024.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/ba\/ba3\/ba368b1ae3809c08a0d2ef573400b024.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/ba\/ba3\/ba368b1ae3809c08a0d2ef573400b024.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0432\u0435\u0440\u043d\u0435\u0435 \u0442\u0430\u043a:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"(-1) \\pmod p = (p-1) \\pmod p\" alt=\"(-1) \\pmod p = (p-1) \\pmod p\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8f\/8fd\/8fdb72400650034cc3dd32875fe8c165.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8f\/8fd\/8fdb72400650034cc3dd32875fe8c165.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8f\/8fd\/8fdb72400650034cc3dd32875fe8c165.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0418\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0432\u044b\u0448\u0435\u0441\u043a\u0430\u0437\u0430\u043d\u043d\u043e\u0435, \u043c\u043e\u0436\u043d\u043e \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u044c \u0432\u0441\u0435 \u043f\u0440\u0438\u043c\u0438\u0442\u0438\u0432\u044b \u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0433\u043e \u043f\u043e\u043b\u044f:<\/p>\n<figure class=\"full-width\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/upload_files\/395\/d38\/143\/395d381437db7dd8c58dfe22f1a46f20.png\" alt=\"\u0422\u0430\u0431\u043b\u0438\u0446\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 \" title=\"\u0422\u0430\u0431\u043b\u0438\u0446\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 \" width=\"605\" height=\"419\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/upload_files\/395\/d38\/143\/395d381437db7dd8c58dfe22f1a46f20.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/upload_files\/395\/d38\/143\/395d381437db7dd8c58dfe22f1a46f20.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0422\u0430\u0431\u043b\u0438\u0446\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 <img decoding=\"async\" class=\"formula inline\" source=\"GF(11)\" alt=\"GF(11)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/37\/37f\/37fb3af305a64c2e0ee30b50f57da2a2.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/37\/37f\/37fb3af305a64c2e0ee30b50f57da2a2.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/37\/37f\/37fb3af305a64c2e0ee30b50f57da2a2.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/figcaption><\/div>\n<\/figure>\n<p>\u041e\u0431\u0449\u0435\u0435 \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u043f\u0440\u0438\u043c\u0438\u0442\u0438\u0432\u043e\u0432 \u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0433\u043e \u043f\u043e\u043b\u044f \u0440\u0430\u0432\u043d\u043e <img decoding=\"async\" class=\"formula inline\" source=\"\\varphi(p-1)\" alt=\"\\varphi(p-1)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/51\/513\/513926fd2b05997471e54adbba0f7c99.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/51\/513\/513926fd2b05997471e54adbba0f7c99.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/51\/513\/513926fd2b05997471e54adbba0f7c99.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0433\u0434\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"\\varphi\" alt=\"\\varphi\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/87\/875\/87567e37a1fe699fe1c5d3a79325da6f.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/87\/875\/87567e37a1fe699fe1c5d3a79325da6f.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/87\/875\/87567e37a1fe699fe1c5d3a79325da6f.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u2014 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u042d\u0439\u043b\u0435\u0440\u0430 totient <a href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F_%D0%AD%D0%B9%D0%BB%D0%B5%D1%80%D0%B0\" rel=\"noopener noreferrer nofollow\">https:\/\/ru.wikipedia.org\/wiki\/\u0424\u0443\u043d\u043a\u0446\u0438\u044f_\u042d\u0439\u043b\u0435\u0440\u0430<\/a><\/p>\n<p>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043d\u0430 \u0442\u0430\u0431\u043b\u0438\u0446\u0443 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 <img decoding=\"async\" class=\"formula inline\" source=\"GF(11)\" alt=\"GF(11)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/37\/37f\/37fb3af305a64c2e0ee30b50f57da2a2.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/37\/37f\/37fb3af305a64c2e0ee30b50f57da2a2.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/37\/37f\/37fb3af305a64c2e0ee30b50f57da2a2.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0432 \u0432\u0438\u0434\u0435 \u0433\u0440\u0430\u0444\u0438\u043a\u0430, \u0434\u043e\u0431\u0430\u0432\u0438\u043b \u043d\u0443\u043b\u0435\u0432\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 <img decoding=\"async\" class=\"formula inline\" source=\"x\" alt=\"x\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9dd\/9dd4e461268c8034f5c8564e155c67a6.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0434\u043b\u044f \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u043e\u0441\u0442\u0438, \u043f\u043e\u0445\u043e\u0436 \u043d\u0430 &#171;\u043f\u0430\u0443\u043a\u0430&#187;:<\/p>\n<figure class=\"full-width\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/upload_files\/d8b\/290\/67c\/d8b29067c73f93a75bc899b4cec4a357.png\" alt=\"\u0422\u0430\u0431\u043b\u0438\u0446\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439  \u0432 \u0432\u0438\u0434\u0435 \u0433\u0440\u0430\u0444\u0438\u043a\u0430\" title=\"\u0422\u0430\u0431\u043b\u0438\u0446\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439  \u0432 \u0432\u0438\u0434\u0435 \u0433\u0440\u0430\u0444\u0438\u043a\u0430\" width=\"1119\" height=\"550\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/upload_files\/d8b\/290\/67c\/d8b29067c73f93a75bc899b4cec4a357.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/upload_files\/d8b\/290\/67c\/d8b29067c73f93a75bc899b4cec4a357.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0422\u0430\u0431\u043b\u0438\u0446\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 <img decoding=\"async\" class=\"formula inline\" source=\"GF(11)\" alt=\"GF(11)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/37\/37f\/37fb3af305a64c2e0ee30b50f57da2a2.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/37\/37f\/37fb3af305a64c2e0ee30b50f57da2a2.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/37\/37f\/37fb3af305a64c2e0ee30b50f57da2a2.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0432 \u0432\u0438\u0434\u0435 \u0433\u0440\u0430\u0444\u0438\u043a\u0430<\/figcaption><\/div>\n<\/figure>\n<p>\u0412\u0435\u0440\u043d\u0435\u043c\u0441\u044f \u0432 \u043f\u0440\u043e\u0442\u043e\u043a\u043e\u043b\u0443 DH, \u0438\u0437\u043c\u0435\u043d\u0438\u043c \u043d\u0430\u0438\u043c\u0435\u043d\u043e\u0432\u0430\u043d\u0438\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445:<\/p>\n<p>\u0434\u043b\u044f \u0410\u043b\u0438\u0441\u044b:<img decoding=\"async\" class=\"formula inline\" source=\"A=g^a \\bmod {p}\" alt=\"A=g^a \\bmod {p}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/54\/540\/54009970ac789284764cc499e3cd3610.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/54\/540\/54009970ac789284764cc499e3cd3610.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/54\/540\/54009970ac789284764cc499e3cd3610.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, <img decoding=\"async\" class=\"formula inline\" source=\"A\" alt=\"A\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7f\/7fc\/7fc56270e7a70fa81a5935b72eacbe29.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7f\/7fc\/7fc56270e7a70fa81a5935b72eacbe29.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7f\/7fc\/7fc56270e7a70fa81a5935b72eacbe29.svg 781w\" loading=\"lazy\" decode=\"async\"\/> &#8212; \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447, <img decoding=\"async\" class=\"formula inline\" source=\"a\" alt=\"a\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0c\/0cc\/0cc175b9c0f1b6a831c399e269772661.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0c\/0cc\/0cc175b9c0f1b6a831c399e269772661.svg 780w,&#10; 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      https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9d\/9d5\/9d5ed678fe57bcca610140957afab571.svg 781w\" loading=\"lazy\" decode=\"async\"\/> &#8212; \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447, <img decoding=\"async\" class=\"formula inline\" source=\"b\" alt=\"b\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/92\/92e\/92eb5ffee6ae2fec3ad71c777531578f.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/92\/92e\/92eb5ffee6ae2fec3ad71c777531578f.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/92\/92e\/92eb5ffee6ae2fec3ad71c777531578f.svg 781w\" loading=\"lazy\" decode=\"async\"\/> &#8212; \u0437\u0430\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447.<\/p>\n<p><img decoding=\"async\" class=\"formula inline\" source=\"S\" alt=\"S\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5d\/5db\/5dbc98dcc983a70728bd082d1a47546e.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5d\/5db\/5dbc98dcc983a70728bd082d1a47546e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5d\/5db\/5dbc98dcc983a70728bd082d1a47546e.svg 781w\" loading=\"lazy\" decode=\"async\"\/> &#8212; \u043e\u0431\u0449\u0438\u0439 \u0441\u0435\u043a\u0440\u0435\u0442\u043d\u044b\u0439 \u043a\u043b\u044e\u0447, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0434\u043b\u044f \u0448\u0438\u0444\u0440\u043e\u0432\u043a\u0438 &#8212; \u0440\u0430\u0441\u0448\u0438\u0444\u0440\u043e\u0432\u043a\u0438 \u0441\u043e\u043e\u0431\u0449\u0435\u043d\u0438\u0439.<\/p>\n<p>\u0410\u043b\u0438\u0441\u0430 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442 <img decoding=\"async\" class=\"formula inline\" source=\"S_{alice} = B^a  \\bmod {p}\" alt=\"S_{alice} = B^a  \\bmod {p}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/39\/39a\/39a9009cff66831e03f56585dc920149.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/39\/39a\/39a9009cff66831e03f56585dc920149.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/39\/39a\/39a9009cff66831e03f56585dc920149.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0411\u043e\u0431 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442 <img decoding=\"async\" class=\"formula inline\" source=\"S_{bob} = A^b  \\bmod {p}\" alt=\"S_{bob} = A^b  \\bmod {p}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3a\/3af\/3afe2815ddd6a85ee4999c629663db6b.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3a\/3af\/3afe2815ddd6a85ee4999c629663db6b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3a\/3af\/3afe2815ddd6a85ee4999c629663db6b.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043a\u0430\u043d\u043e\u043d\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u043f\u0440\u0438\u043c\u0435\u0440:<\/p>\n<ol>\n<li>\n<p><img decoding=\"async\" class=\"formula inline\" source=\"p=11, g = 2\" alt=\"p=11, g = 2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b8\/b8d\/b8df77ad16f1974a7ef81e7f5b211560.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b8\/b8d\/b8df77ad16f1974a7ef81e7f5b211560.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b8\/b8d\/b8df77ad16f1974a7ef81e7f5b211560.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0410\u043b\u0438\u0441\u0430 \u0432\u044b\u0431\u0438\u0440\u0430\u0435\u0442 \u0437\u0430\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447 <img decoding=\"async\" class=\"formula inline\" source=\"a=3\" alt=\"a=3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3d\/3d7\/3d7b566aaed7713dfc5583dfc4b9c386.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3d\/3d7\/3d7b566aaed7713dfc5583dfc4b9c386.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3d\/3d7\/3d7b566aaed7713dfc5583dfc4b9c386.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0411\u043e\u0431 \u0432\u044b\u0431\u0438\u0440\u0430\u0435\u0442 \u0437\u0430\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447 <img decoding=\"async\" class=\"formula inline\" source=\"b=9\" alt=\"b=9\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/26\/262\/262fd0431f12265576c923b3c1524cd5.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/26\/262\/262fd0431f12265576c923b3c1524cd5.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/26\/262\/262fd0431f12265576c923b3c1524cd5.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0410\u043b\u0438\u0441\u0430 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442 \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447 <img decoding=\"async\" class=\"formula inline\" source=\"A = 2^3 \\bmod 11 = 8\" alt=\"A = 2^3 \\bmod 11 = 8\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/70\/704\/70444cf72eb4475fa14becd1e1123a46.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/70\/704\/70444cf72eb4475fa14becd1e1123a46.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/70\/704\/70444cf72eb4475fa14becd1e1123a46.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0411\u043e\u0431 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442 \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447 <img decoding=\"async\" class=\"formula inline\" source=\"B = 2^9 \\bmod 11 = 6\" alt=\"B = 2^9 \\bmod 11 = 6\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ad\/ad0\/ad02d4672a52cc6cb1c94fd9cee28e27.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ad\/ad0\/ad02d4672a52cc6cb1c94fd9cee28e27.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ad\/ad0\/ad02d4672a52cc6cb1c94fd9cee28e27.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0410\u043b\u0438\u0441\u0430 \u0438 \u0411\u043e\u0431 \u043e\u0431\u043c\u0435\u043d\u0438\u0432\u0430\u044e\u0442\u0441\u044f \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u043c\u0438 \u043a\u043b\u044e\u0447\u0430\u043c\u0438<\/p>\n<\/li>\n<li>\n<p>\u0410\u043b\u0438\u0441\u0430 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442 \u043e\u0431\u0449\u0438\u0439 \u0441\u0435\u043a\u0440\u0435\u0442\u043d\u044b\u0439 \u043a\u043b\u044e\u0447 <img decoding=\"async\" class=\"formula inline\" source=\"S_{alice} = 6^3  \\bmod 11 = 7\" alt=\"S_{alice} = 6^3  \\bmod 11 = 7\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/90\/90e\/90e47f92888a196b6fe53e00aa707642.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/90\/90e\/90e47f92888a196b6fe53e00aa707642.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/90\/90e\/90e47f92888a196b6fe53e00aa707642.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0411\u043e\u0431 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442 \u043e\u0431\u0449\u0438\u0439 \u0441\u0435\u043a\u0440\u0435\u0442\u043d\u044b\u0439 \u043a\u043b\u044e\u0447 <img decoding=\"async\" class=\"formula inline\" source=\"S_{bob} = 8^9  \\bmod 11 = 7\" alt=\"S_{bob} = 8^9  \\bmod 11 = 7\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/bf\/bfe\/bfe49d10348d10958b262702239a72cd.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/bf\/bfe\/bfe49d10348d10958b262702239a72cd.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/bf\/bfe\/bfe49d10348d10958b262702239a72cd.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0410\u043b\u0438\u0441\u0430 \u0438 \u0411\u043e\u0431 \u043f\u043e\u043b\u0443\u0447\u0438\u043b\u0438 \u043e\u0434\u0438\u043d \u0438 \u0442\u043e\u0442-\u0436\u0435 \u0441\u0435\u043a\u0440\u0435\u0442\u043d\u044b\u0439 \u043a\u043b\u044e\u0447 <img decoding=\"async\" class=\"formula inline\" source=\"S\" alt=\"S\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5d\/5db\/5dbc98dcc983a70728bd082d1a47546e.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5d\/5db\/5dbc98dcc983a70728bd082d1a47546e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5d\/5db\/5dbc98dcc983a70728bd082d1a47546e.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043d\u0435 \u043f\u0435\u0440\u0435\u0434\u0430\u0432\u0430\u044f \u0435\u0433\u043e \u043f\u043e \u0441\u0435\u0442\u0438.<\/p>\n<\/li>\n<\/ol>\n<p>\u0422\u0435\u043f\u0435\u0440\u044c \u043f\u0440\u0438\u043c\u0435\u0440, \u043a\u043e\u0433\u0434\u0430 \u0437\u0430\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447 \u0440\u0430\u0432\u0435\u043d <img decoding=\"async\" class=\"formula inline\" source=\"(p-1)\/2\" alt=\"(p-1)\/2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1a\/1a6\/1a6beb77bddb2f66cf392e0dbd85aa69.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1a\/1a6\/1a6beb77bddb2f66cf392e0dbd85aa69.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1a\/1a6\/1a6beb77bddb2f66cf392e0dbd85aa69.svg 781w\" loading=\"lazy\" decode=\"async\"\/>:<\/p>\n<ol>\n<li>\n<p><img decoding=\"async\" class=\"formula inline\" source=\"p=11, g = 2\" alt=\"p=11, g = 2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b8\/b8d\/b8df77ad16f1974a7ef81e7f5b211560.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b8\/b8d\/b8df77ad16f1974a7ef81e7f5b211560.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b8\/b8d\/b8df77ad16f1974a7ef81e7f5b211560.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0410\u043b\u0438\u0441\u0430 \u0432\u044b\u0431\u0438\u0440\u0430\u0435\u0442 \u0437\u0430\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447 <img decoding=\"async\" class=\"formula inline\" source=\"a=5 = (p-1)\/2\" alt=\"a=5 = (p-1)\/2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cc\/cca\/cca5c86d77a73b721574bcc43237b194.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cc\/cca\/cca5c86d77a73b721574bcc43237b194.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cc\/cca\/cca5c86d77a73b721574bcc43237b194.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0411\u043e\u0431 \u0432\u044b\u0431\u0438\u0440\u0430\u0435\u0442 \u0437\u0430\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447 <img decoding=\"async\" class=\"formula inline\" source=\"b=9\" alt=\"b=9\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/26\/262\/262fd0431f12265576c923b3c1524cd5.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/26\/262\/262fd0431f12265576c923b3c1524cd5.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/26\/262\/262fd0431f12265576c923b3c1524cd5.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0410\u043b\u0438\u0441\u0430 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442 \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447 <img decoding=\"async\" class=\"formula inline\" source=\"A = 2^5 \\bmod 11 = 10\" alt=\"A = 2^5 \\bmod 11 = 10\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/4a\/4a0\/4a0745ce1f1ba95ee7a2f6e761e86591.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/4a\/4a0\/4a0745ce1f1ba95ee7a2f6e761e86591.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/4a\/4a0\/4a0745ce1f1ba95ee7a2f6e761e86591.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0411\u043e\u0431 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442 \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447 <img decoding=\"async\" class=\"formula inline\" source=\"B = 2^9 \\bmod 11 = 6\" alt=\"B = 2^9 \\bmod 11 = 6\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ad\/ad0\/ad02d4672a52cc6cb1c94fd9cee28e27.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ad\/ad0\/ad02d4672a52cc6cb1c94fd9cee28e27.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ad\/ad0\/ad02d4672a52cc6cb1c94fd9cee28e27.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0410\u043b\u0438\u0441\u0430 \u0438 \u0411\u043e\u0431 \u043e\u0431\u043c\u0435\u043d\u0438\u0432\u0430\u044e\u0442\u0441\u044f \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u043c\u0438 \u043a\u043b\u044e\u0447\u0430\u043c\u0438<\/p>\n<\/li>\n<li>\n<p>\u0410\u043b\u0438\u0441\u0430 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442 \u043e\u0431\u0449\u0438\u0439 \u0441\u0435\u043a\u0440\u0435\u0442\u043d\u044b\u0439 \u043a\u043b\u044e\u0447 <img decoding=\"async\" class=\"formula inline\" source=\"S_{alice} = 6^5  \\bmod 11 = 10\" alt=\"S_{alice} = 6^5  \\bmod 11 = 10\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/78\/78c\/78cabc5eaece02bf4785eb2158351316.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/78\/78c\/78cabc5eaece02bf4785eb2158351316.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/78\/78c\/78cabc5eaece02bf4785eb2158351316.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0411\u043e\u0431 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442 \u043e\u0431\u0449\u0438\u0439 \u0441\u0435\u043a\u0440\u0435\u0442\u043d\u044b\u0439 \u043a\u043b\u044e\u0447 <img decoding=\"async\" class=\"formula inline\" source=\"S_{bob} = 10^9  \\bmod 11 = 10\" alt=\"S_{bob} = 10^9  \\bmod 11 = 10\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b0\/b0e\/b0ebe41a18950539a642e3aa49c11414.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b0\/b0e\/b0ebe41a18950539a642e3aa49c11414.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b0\/b0e\/b0ebe41a18950539a642e3aa49c11414.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<\/ol>\n<p>\u0417\u043b\u043e\u0443\u043c\u044b\u0448\u043b\u0435\u043d\u043d\u0438\u043a \u043f\u0435\u0440\u0435\u0445\u0432\u0430\u0442\u0438\u043b \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447 <img decoding=\"async\" class=\"formula inline\" source=\"A = (p-1) = 10\" alt=\"A = (p-1) = 10\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fb\/fbb\/fbb0209bf4f6d5c0e83dc28660ff4abd.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fb\/fbb\/fbb0209bf4f6d5c0e83dc28660ff4abd.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fb\/fbb\/fbb0209bf4f6d5c0e83dc28660ff4abd.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442 \u0437\u0430\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447 \u0442\u043e\u0439-\u0436\u0435 \u0410\u043b\u0438\u0441\u044b \u043f\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435 (1): <img decoding=\"async\" class=\"formula inline\" source=\"(p-1) = 10 \\Longrightarrow a = (p-1)\/2 = (11-1)\/2 = 5\" alt=\"(p-1) = 10 \\Longrightarrow a = (p-1)\/2 = (11-1)\/2 = 5\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/38\/386\/38683c36ba441663e5ae0a0cd8dbb6e7.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/38\/386\/38683c36ba441663e5ae0a0cd8dbb6e7.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/38\/386\/38683c36ba441663e5ae0a0cd8dbb6e7.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0414\u0430\u043b\u0435\u0435, \u0434\u043b\u044f \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u044f \u0441\u0435\u043a\u0440\u0435\u0442\u043d\u043e\u0433\u043e \u043a\u043b\u044e\u0447\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"S\" alt=\"S\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5d\/5db\/5dbc98dcc983a70728bd082d1a47546e.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5d\/5db\/5dbc98dcc983a70728bd082d1a47546e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/5\/5d\/5db\/5dbc98dcc983a70728bd082d1a47546e.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0435\u0441\u0442\u044c \u0434\u0432\u0430 \u0441\u043f\u043e\u0441\u043e\u0431\u0430:<\/p>\n<p>1 \u0441\u043f\u043e\u0441\u043e\u0431. \u0421 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043e\u0442\u043a\u0440\u044b\u0442\u043e\u0433\u043e \u043a\u043b\u044e\u0447\u0430 \u0411\u043e\u0431\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"B = 6\" alt=\"B = 6\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f9\/f9d\/f9d6eea13c0e725a715babf233e31e4c.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f9\/f9d\/f9d6eea13c0e725a715babf233e31e4c.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f9\/f9d\/f9d6eea13c0e725a715babf233e31e4c.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p><img decoding=\"async\" class=\"formula inline\" source=\"S_{alice} = 6^5  \\bmod 11 = 10\" alt=\"S_{alice} = 6^5  \\bmod 11 = 10\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/78\/78c\/78cabc5eaece02bf4785eb2158351316.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/78\/78c\/78cabc5eaece02bf4785eb2158351316.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/78\/78c\/78cabc5eaece02bf4785eb2158351316.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>2 \u0441\u043f\u043e\u0441\u043e\u0431. \u0421\u0440\u0430\u0437\u0443, \u0435\u0441\u043b\u0438 \u0445\u043e\u0442\u044f \u0431\u044b \u043e\u0434\u0438\u043d \u0438\u0437 \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u0445 \u043a\u043b\u044e\u0447\u0435\u0439 \u0440\u0430\u0432\u0435\u043d <img decoding=\"async\" class=\"formula inline\" source=\"(p-1)\" alt=\"(p-1)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fc\/fc8\/fc86261874dd92078554f3ac92efbca8.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fc\/fc8\/fc86261874dd92078554f3ac92efbca8.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/fc\/fc8\/fc86261874dd92078554f3ac92efbca8.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0442\u043e <img decoding=\"async\" class=\"formula inline\" source=\"S = (p-1)\" alt=\"S = (p-1)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0b\/0bf\/0bfe9c004b2d7332fe7b407131ea85e8.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0b\/0bf\/0bfe9c004b2d7332fe7b407131ea85e8.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0b\/0bf\/0bfe9c004b2d7332fe7b407131ea85e8.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0438\u043b\u0438 <img decoding=\"async\" src=\"\" class=\"formula inline\"\/>, \u043f\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"S = (p-1)^n \\bmod p = (p-1)\\ |\\ 1, \\mbox{ \u0433\u0434\u0435 } n - \\mbox{ \u043b\u044e\u0431\u043e\u0439 \u044d\u043b\u0435\u043c\u0435\u043d\u0442 \u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0433\u043e \u043f\u043e\u043b\u044f } GF(p)\" alt=\"S = (p-1)^n \\bmod p = (p-1)\\ |\\ 1, \\mbox{ \u0433\u0434\u0435 } n - \\mbox{ \u043b\u044e\u0431\u043e\u0439 \u044d\u043b\u0435\u043c\u0435\u043d\u0442 \u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0433\u043e \u043f\u043e\u043b\u044f } GF(p)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/70\/70d\/70d1800b3d195d81eb8641595c2f86db.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/70\/70d\/70d1800b3d195d81eb8641595c2f86db.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/70\/70d\/70d1800b3d195d81eb8641595c2f86db.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0412\u043d\u0438\u043c\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u0442\u0435 \u043d\u0430 \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u044e\u044e \u0441\u0442\u0440\u043e\u043a\u0443 \u043b\u044e\u0431\u043e\u0433\u043e <img decoding=\"async\" class=\"formula inline\" source=\"GF\" alt=\"GF\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c0\/c07\/c07b0b4d7660314f711a68fc47c4ab38.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c0\/c07\/c07b0b4d7660314f711a68fc47c4ab38.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c0\/c07\/c07b0b4d7660314f711a68fc47c4ab38.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440 \u0441\u043c. \u0440\u0438\u0441. \u0432\u044b\u0448\u0435 &#171;\u041d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0442\u0430\u0431\u043b\u0438\u0446 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439&#187;.<\/p>\n<p>\u042f \u043d\u0435 \u043d\u0430\u0448\u0435\u043b \u0432 \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u0445 \u0438\u0441\u0442\u043e\u0447\u043d\u0438\u043a\u0430\u0445 \u0437\u0430\u043f\u0440\u0435\u0442\u0430 \u043d\u0430 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u0435 \u0432 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435 \u0437\u0430\u043a\u0440\u044b\u0442\u043e\u0433\u043e \u043a\u043b\u044e\u0447\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"(p-1)\/2\" alt=\"(p-1)\/2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1a\/1a6\/1a6beb77bddb2f66cf392e0dbd85aa69.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1a\/1a6\/1a6beb77bddb2f66cf392e0dbd85aa69.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1a\/1a6\/1a6beb77bddb2f66cf392e0dbd85aa69.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<p>\u0414\u0430\u043d\u043d\u043e\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0443\u043f\u043e\u043c\u0438\u043d\u0430\u0435\u0442\u0441\u044f \u0432 \u0441\u0442\u0430\u0442\u044c\u0435: S. C. Pohlig and M. E. Hellman, &#171;An improved algorithm for computing logarithms in GF(p) and its cryptographic significance.&#187; <a href=\"https:\/\/ee.stanford.edu\/~hellman\/publications\/28.pdf\" rel=\"noopener noreferrer nofollow\">https:\/\/ee.stanford.edu\/~hellman\/publications\/28.pdf<\/a>, IEEE Trans. Info. Theory 24 (1978), 106\u2013111.<\/p>\n<p>\u0412 \u0441\u0442\u0430\u0442\u044c\u0435 \u0443\u043a\u0430\u0437\u0430\u043d\u043e \u0447\u0442\u043e <img decoding=\"async\" class=\"formula inline\" source=\"(p-1)\/2\" alt=\"(p-1)\/2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1a\/1a6\/1a6beb77bddb2f66cf392e0dbd85aa69.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1a\/1a6\/1a6beb77bddb2f66cf392e0dbd85aa69.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1a\/1a6\/1a6beb77bddb2f66cf392e0dbd85aa69.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0434\u043e\u043b\u0436\u043d\u043e \u0431\u044b\u0442\u044c \u043f\u0440\u043e\u0441\u0442\u044b\u043c \u0447\u0438\u0441\u043b\u043e\u043c \u0434\u043b\u044f \u043f\u043e\u0432\u044b\u0448\u0435\u043d\u0438\u044f \u0431\u0435\u0437\u043e\u043f\u0430\u0441\u043d\u043e\u0441\u0442\u0438.<\/p>\n<p>\u0415\u0449\u0435 \u0432 \u0441\u0442\u0430\u0442\u044c\u0435 \u043c\u043e\u0436\u043d\u043e \u0432\u0441\u0442\u0440\u0435\u0442\u0438\u0442\u044c \u0443\u043f\u043e\u043c\u0438\u043d\u0430\u043d\u0438\u0435 \u0442\u0440\u0438\u0432\u0438\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0441\u043b\u0443\u0447\u0430\u044f <img decoding=\"async\" src=\"\" class=\"formula inline\"\/>: &#171;<em>Also, restrictions might be imposed on K (e.g., <img decoding=\"async\" class=\"formula inline\" source=\"K \\ne 1\" alt=\"K \\ne 1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/07\/077\/07706b2b5fed091d8bd4b06c53ecced0.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/07\/077\/07706b2b5fed091d8bd4b06c53ecced0.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/07\/077\/07706b2b5fed091d8bd4b06c53ecced0.svg 781w\" loading=\"lazy\" decode=\"async\"\/>) to avoid simple but improbable transformations.<\/em>&#187; \u0412 \u043f\u0435\u0440\u0435\u0432\u043e\u0434\u0435: &#171;<em>\u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u043d\u0430 K \u043c\u043e\u0433\u0443\u0442 \u0431\u044b\u0442\u044c \u043d\u0430\u043b\u043e\u0436\u0435\u043d\u044b \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0438\u044f (\u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, <img decoding=\"async\" class=\"formula inline\" source=\"K \\ne 1\" alt=\"K \\ne 1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/07\/077\/07706b2b5fed091d8bd4b06c53ecced0.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/07\/077\/07706b2b5fed091d8bd4b06c53ecced0.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/07\/077\/07706b2b5fed091d8bd4b06c53ecced0.svg 781w\" loading=\"lazy\" decode=\"async\"\/>), \u0447\u0442\u043e\u0431\u044b \u0438\u0437\u0431\u0435\u0436\u0430\u0442\u044c \u043f\u0440\u043e\u0441\u0442\u044b\u0445, \u043d\u043e \u043c\u0430\u043b\u043e\u0432\u0435\u0440\u043e\u044f\u0442\u043d\u044b\u0445 \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0439.<\/em>&#187; (<img decoding=\"async\" class=\"formula inline\" source=\"K\" alt=\"K\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a5\/a5f\/a5f3c6a11b03839d46af9fb43c97c188.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a5\/a5f\/a5f3c6a11b03839d46af9fb43c97c188.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a5\/a5f\/a5f3c6a11b03839d46af9fb43c97c188.svg 781w\" loading=\"lazy\" decode=\"async\"\/> &#8212; \u043a\u043b\u044e\u0447).<\/p>\n<p>\u0420\u0435\u0448\u0435\u043d\u0438\u0435: \u0437\u0430\u043f\u0440\u0435\u0442\u0438\u0442\u044c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0432 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435 \u0437\u0430\u043a\u0440\u044b\u0442\u043e\u0433\u043e \u043a\u043b\u044e\u0447\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"(p-1)\/2\" alt=\"(p-1)\/2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1a\/1a6\/1a6beb77bddb2f66cf392e0dbd85aa69.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1a\/1a6\/1a6beb77bddb2f66cf392e0dbd85aa69.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/1a\/1a6\/1a6beb77bddb2f66cf392e0dbd85aa69.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0434\u043e\u043f\u043e\u043b\u043d\u044f\u0435\u043c \u0441\u043f\u0438\u0441\u043e\u043a \u0442\u0440\u0438\u0432\u0438\u0430\u043b\u044c\u043d\u044b\u0445 \u0441\u043b\u0443\u0447\u0430\u0435\u0432:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"x \\in  \\{0, 1, (p-1)\/2, p-1\\}\" alt=\"x \\in  \\{0, 1, (p-1)\/2, p-1\\}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/3e8\/048\/03c\/3e804803c0d96dd8f70d9689078cc955.svg\" width=\"216\" height=\"22\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/3e8\/048\/03c\/3e804803c0d96dd8f70d9689078cc955.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/3e8\/048\/03c\/3e804803c0d96dd8f70d9689078cc955.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041c\u043e\u0436\u043d\u043e \u043d\u0430\u0439\u0442\u0438 \u0435\u0449\u0435? \u041f\u043e\u043f\u0440\u043e\u0431\u0443\u0435\u043c.<\/p>\n<p>\u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0432\u043d\u0438\u043c\u0430\u0442\u0435\u043b\u044c\u043d\u043e &#171;\u043f\u0430\u0443\u043a\u0430&#187;, \u0441\u043c. \u0440\u0438\u0441. \u0432\u044b\u0448\u0435, \u043f\u043e\u0447\u0435\u043c\u0443 \u043e\u043d \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u043d?<\/p>\n<p>\u041f\u0440\u0438\u043c\u0438\u0442\u0438\u0432\u044b \u0441\u0433\u0440\u0443\u043f\u043f\u0438\u0440\u043e\u0432\u0430\u043d\u044b \u043f\u0430\u0440\u0430\u043c\u0438:<\/p>\n<figure class=\"\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/upload_files\/52d\/b8b\/64e\/52db8b64e1fd1e7c0ee35860ed969598.png\" alt=\"\u041f\u0430\u0440\u043d\u044b\u0435 \u043f\u0440\u0438\u043c\u0438\u0442\u0438\u0432\u044b \" title=\"\u041f\u0430\u0440\u043d\u044b\u0435 \u043f\u0440\u0438\u043c\u0438\u0442\u0438\u0432\u044b \" width=\"389\" height=\"346\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/upload_files\/52d\/b8b\/64e\/52db8b64e1fd1e7c0ee35860ed969598.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/upload_files\/52d\/b8b\/64e\/52db8b64e1fd1e7c0ee35860ed969598.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u041f\u0430\u0440\u043d\u044b\u0435 \u043f\u0440\u0438\u043c\u0438\u0442\u0438\u0432\u044b <img decoding=\"async\" class=\"formula inline\" source=\"GF(11)\" alt=\"GF(11)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/37\/37f\/37fb3af305a64c2e0ee30b50f57da2a2.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/37\/37f\/37fb3af305a64c2e0ee30b50f57da2a2.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/37\/37f\/37fb3af305a64c2e0ee30b50f57da2a2.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/figcaption><\/div>\n<\/figure>\n<p>\u041a\u043e\u0433\u0434\u0430-\u0442\u043e \u044f \u043d\u0435\u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u043e \u043f\u0440\u0435\u0434\u043f\u043e\u043b\u043e\u0436\u0438\u043b, \u0447\u0442\u043e \u044d\u0442\u0438 \u043f\u0430\u0440\u044b \u0432\u0437\u0430\u0438\u043c\u043d\u043e \u043f\u0440\u043e\u0441\u0442\u044b\u0435, \u043d\u0430 \u0441\u0430\u043c\u043e\u043c \u0434\u0435\u043b\u0435 \u043e\u043d\u0438 \u043c\u0443\u043b\u044c\u0442\u0438\u043f\u043b\u0438\u043a\u0430\u0442\u0438\u0432\u043d\u043e \u043e\u0431\u0440\u0430\u0442\u043d\u044b \u043f\u043e \u043c\u043e\u0434\u0443\u043b\u044e <a href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%9E%D0%B1%D1%80%D0%B0%D1%82%D0%BD%D0%BE%D0%B5_%D0%BF%D0%BE_%D0%BC%D0%BE%D0%B4%D1%83%D0%BB%D1%8E_%D1%87%D0%B8%D1%81%D0%BB%D0%BE\" rel=\"noopener noreferrer nofollow\">https:\/\/ru.wikipedia.org\/wiki\/\u041e\u0431\u0440\u0430\u0442\u043d\u043e\u0435_\u043f\u043e_\u043c\u043e\u0434\u0443\u043b\u044e_\u0447\u0438\u0441\u043b\u043e<\/a><\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"g \\times g' \\equiv 1 \\pmod p\" alt=\"g \\times g' \\equiv 1 \\pmod p\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/eac\/eacc06b6e03da34a2168393448ef6406.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/eac\/eacc06b6e03da34a2168393448ef6406.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ea\/eac\/eacc06b6e03da34a2168393448ef6406.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u041f\u0440\u043e\u0432\u0435\u0440\u0438\u043c:<\/p>\n<ul>\n<li>\n<p><img decoding=\"async\" class=\"formula inline\" source=\"2 \\times 6 \\equiv 1 \\pmod {11}\" alt=\"2 \\times 6 \\equiv 1 \\pmod {11}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ee\/ee5\/ee57b97a92d437b006f2b451e681e21a.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ee\/ee5\/ee57b97a92d437b006f2b451e681e21a.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ee\/ee5\/ee57b97a92d437b006f2b451e681e21a.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p><img decoding=\"async\" class=\"formula inline\" source=\"7 \\times 8 \\equiv 1 \\pmod {11}\" alt=\"7 \\times 8 \\equiv 1 \\pmod {11}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/949\/949473e0c0bef528ea1d6d0f964384db.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/949\/949473e0c0bef528ea1d6d0f964384db.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/94\/949\/949473e0c0bef528ea1d6d0f964384db.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<\/ul>\n<p>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0433\u0440\u0430\u0444\u0438\u043a \u043f\u0435\u0440\u0432\u043e\u0439 \u043f\u0430\u0440\u044b <img decoding=\"async\" class=\"formula inline\" source=\"\\{2, 6\\}\" alt=\"\\{2, 6\\}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/31\/31a\/31a706ac50f21e1121352569076d7848.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/31\/31a\/31a706ac50f21e1121352569076d7848.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/31\/31a\/31a706ac50f21e1121352569076d7848.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<figure class=\"full-width\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/upload_files\/c6d\/615\/81c\/c6d61581c769bfe17ddda993da265b84.png\" alt=\"\u0422\u0430\u0431\u043b\u0438\u0446\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439  \u0432 \u0432\u0438\u0434\u0435 \u0433\u0440\u0430\u0444\u0438\u043a\u0430 \u0434\u043b\u044f \u043f\u0430\u0440\u044b \u043f\u0440\u0438\u043c\u0438\u0442\u0438\u0432\u043e\u0432 \" title=\"\u0422\u0430\u0431\u043b\u0438\u0446\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439  \u0432 \u0432\u0438\u0434\u0435 \u0433\u0440\u0430\u0444\u0438\u043a\u0430 \u0434\u043b\u044f \u043f\u0430\u0440\u044b \u043f\u0440\u0438\u043c\u0438\u0442\u0438\u0432\u043e\u0432 \" width=\"1054\" height=\"600\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/upload_files\/c6d\/615\/81c\/c6d61581c769bfe17ddda993da265b84.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/upload_files\/c6d\/615\/81c\/c6d61581c769bfe17ddda993da265b84.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0422\u0430\u0431\u043b\u0438\u0446\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 <img decoding=\"async\" class=\"formula inline\" source=\"GF(11)\" alt=\"GF(11)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/37\/37f\/37fb3af305a64c2e0ee30b50f57da2a2.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/37\/37f\/37fb3af305a64c2e0ee30b50f57da2a2.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/37\/37f\/37fb3af305a64c2e0ee30b50f57da2a2.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0432 \u0432\u0438\u0434\u0435 \u0433\u0440\u0430\u0444\u0438\u043a\u0430 \u0434\u043b\u044f \u043f\u0430\u0440\u044b \u043f\u0440\u0438\u043c\u0438\u0442\u0438\u0432\u043e\u0432 <img decoding=\"async\" class=\"formula inline\" source=\"\\{2,6\\}\" alt=\"\\{2,6\\}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ae\/ae4\/ae42bd2359a9a6ef112b7e7419794250.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ae\/ae4\/ae42bd2359a9a6ef112b7e7419794250.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ae\/ae4\/ae42bd2359a9a6ef112b7e7419794250.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/figcaption><\/div>\n<\/figure>\n<p>\u0421\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u043e, \u043d\u0435 \u043f\u0440\u0430\u0432\u0434\u0430 \u043b\u0438? \u0438 \u0432 \u0442\u0430\u0431\u043b\u0438\u0447\u043d\u043e\u043c \u0432\u0438\u0434\u0435:<\/p>\n<figure class=\"\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/upload_files\/ee2\/e4b\/47a\/ee2e4b47a58abdc66666253a4117e65c.png\" alt=\"\u0422\u0430\u0431\u043b\u0438\u0446\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439  \u0434\u043b\u044f \u043f\u0440\u0438\u043c\u0438\u0442\u0438\u0432\u043e\u0432 \" title=\"\u0422\u0430\u0431\u043b\u0438\u0446\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439  \u0434\u043b\u044f \u043f\u0440\u0438\u043c\u0438\u0442\u0438\u0432\u043e\u0432 \" width=\"400\" height=\"90\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/upload_files\/ee2\/e4b\/47a\/ee2e4b47a58abdc66666253a4117e65c.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/upload_files\/ee2\/e4b\/47a\/ee2e4b47a58abdc66666253a4117e65c.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0422\u0430\u0431\u043b\u0438\u0446\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 <img decoding=\"async\" class=\"formula inline\" source=\"GF(11)\" alt=\"GF(11)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/37\/37f\/37fb3af305a64c2e0ee30b50f57da2a2.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/37\/37f\/37fb3af305a64c2e0ee30b50f57da2a2.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/37\/37f\/37fb3af305a64c2e0ee30b50f57da2a2.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0434\u043b\u044f \u043f\u0440\u0438\u043c\u0438\u0442\u0438\u0432\u043e\u0432 <img decoding=\"async\" class=\"formula inline\" source=\"\\{2,6\\}\" alt=\"\\{2,6\\}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ae\/ae4\/ae42bd2359a9a6ef112b7e7419794250.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ae\/ae4\/ae42bd2359a9a6ef112b7e7419794250.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ae\/ae4\/ae42bd2359a9a6ef112b7e7419794250.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/figcaption><\/div>\n<\/figure>\n<p>\u041c\u044b \u0432\u044b\u044f\u0441\u043d\u0438\u043b\u0438 \u0432\u044b\u0448\u0435, \u0447\u0442\u043e <img decoding=\"async\" class=\"formula inline\" source=\"\\{2,6\\}\" alt=\"\\{2,6\\}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ae\/ae4\/ae42bd2359a9a6ef112b7e7419794250.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ae\/ae4\/ae42bd2359a9a6ef112b7e7419794250.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ae\/ae4\/ae42bd2359a9a6ef112b7e7419794250.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043c\u0443\u043b\u044c\u0442\u0438\u043f\u043b\u0438\u043a\u0430\u0442\u0438\u0432\u043d\u043e \u043e\u0431\u0440\u0430\u0442\u043d\u044b, \u043f\u0440\u043e\u0432\u0435\u0440\u0438\u043c \u043e\u0441\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u043f\u0430\u0440\u044b:<\/p>\n<ul>\n<li>\n<p><img decoding=\"async\" class=\"formula inline\" source=\"1 \\times 1 \\equiv 1 \\pmod {11}\" alt=\"1 \\times 1 \\equiv 1 \\pmod {11}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/00\/000\/00071fdacf4f4171d1d050d12fa52f9e.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/00\/000\/00071fdacf4f4171d1d050d12fa52f9e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/00\/000\/00071fdacf4f4171d1d050d12fa52f9e.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p><img decoding=\"async\" class=\"formula inline\" source=\"4 \\times 3 \\equiv 1 \\pmod {11}\" alt=\"4 \\times 3 \\equiv 1 \\pmod {11}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a9\/a94\/a94b5c30285c313fbf503a4492ff20d6.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a9\/a94\/a94b5c30285c313fbf503a4492ff20d6.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a9\/a94\/a94b5c30285c313fbf503a4492ff20d6.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p><img decoding=\"async\" class=\"formula inline\" source=\"8 \\times 7 \\equiv 1 \\pmod {11}\" alt=\"8 \\times 7 \\equiv 1 \\pmod {11}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/08\/084\/084e4279d97dc93a6da560af0e61c4d7.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/08\/084\/084e4279d97dc93a6da560af0e61c4d7.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/08\/084\/084e4279d97dc93a6da560af0e61c4d7.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p><img decoding=\"async\" class=\"formula inline\" source=\"5 \\times 9 \\equiv 1 \\pmod {11}\" alt=\"5 \\times 9 \\equiv 1 \\pmod {11}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0e\/0e0\/0e0dedddb801f74c4060df091764a11e.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0e\/0e0\/0e0dedddb801f74c4060df091764a11e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/0\/0e\/0e0\/0e0dedddb801f74c4060df091764a11e.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p><img decoding=\"async\" class=\"formula inline\" source=\"10 \\times 10 \\equiv 1 \\pmod {11}\" alt=\"10 \\times 10 \\equiv 1 \\pmod {11}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7b\/7be\/7be37531e392f05ee12ad3e20212945e.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7b\/7be\/7be37531e392f05ee12ad3e20212945e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/7\/7b\/7be\/7be37531e392f05ee12ad3e20212945e.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<\/ul>\n<p>\u0412\u0441\u0435 \u043f\u0430\u0440\u044b \u043c\u0443\u043b\u044c\u0442\u0438\u043f\u043b\u0438\u043a\u0430\u0442\u0438\u0432\u043d\u043e \u043e\u0431\u0440\u0430\u0442\u043d\u044b \u043f\u043e \u043c\u043e\u0434\u0443\u043b\u044e <img decoding=\"async\" class=\"formula inline\" source=\"p\" alt=\"p\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/83\/838\/83878c91171338902e0fe0fb97a8c47a.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/83\/838\/83878c91171338902e0fe0fb97a8c47a.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/83\/838\/83878c91171338902e0fe0fb97a8c47a.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<p>\u0412\u043e\u0437\u0432\u0440\u0430\u0449\u0430\u0435\u043c\u0441\u044f \u043a DH, \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043f\u0440\u0438\u043c\u0435\u0440:<\/p>\n<ol>\n<li>\n<p><img decoding=\"async\" class=\"formula inline\" source=\"p=11, g = 7\" alt=\"p=11, g = 7\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cd\/cdb\/cdbee4d646a42b6b1496211c12216d90.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cd\/cdb\/cdbee4d646a42b6b1496211c12216d90.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/cd\/cdb\/cdbee4d646a42b6b1496211c12216d90.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0410\u043b\u0438\u0441\u0430 \u0432\u044b\u0431\u0438\u0440\u0430\u0435\u0442 \u0437\u0430\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447 <img decoding=\"async\" class=\"formula inline\" source=\"a=4\" alt=\"a=4\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3c\/3c9\/3c9d2347726735da8c5c1ed9a44f5759.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3c\/3c9\/3c9d2347726735da8c5c1ed9a44f5759.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/3c\/3c9\/3c9d2347726735da8c5c1ed9a44f5759.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0411\u043e\u0431 \u0432\u044b\u0431\u0438\u0440\u0430\u0435\u0442 \u0437\u0430\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447 <img decoding=\"async\" class=\"formula inline\" source=\"b=9\" alt=\"b=9\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/26\/262\/262fd0431f12265576c923b3c1524cd5.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/26\/262\/262fd0431f12265576c923b3c1524cd5.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/26\/262\/262fd0431f12265576c923b3c1524cd5.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0410\u043b\u0438\u0441\u0430 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442 \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447 <img decoding=\"async\" class=\"formula inline\" source=\"A = 7^4 \\bmod 11 = 3\" alt=\"A = 7^4 \\bmod 11 = 3\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/32\/32c\/32ce774a33b1e466e3b03fb817d0f28e.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/32\/32c\/32ce774a33b1e466e3b03fb817d0f28e.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/3\/32\/32c\/32ce774a33b1e466e3b03fb817d0f28e.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0411\u043e\u0431 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442 \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447 <img decoding=\"async\" class=\"formula inline\" source=\"B = 7^9 \\bmod 11 = 8\" alt=\"B = 7^9 \\bmod 11 = 8\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b7\/b71\/b71b5e46891cb4fbd32e057ecc583bee.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b7\/b71\/b71b5e46891cb4fbd32e057ecc583bee.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b7\/b71\/b71b5e46891cb4fbd32e057ecc583bee.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0410\u043b\u0438\u0441\u0430 \u0438 \u0411\u043e\u0431 \u043e\u0431\u043c\u0435\u043d\u0438\u0432\u0430\u044e\u0442\u0441\u044f \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u043c\u0438 \u043a\u043b\u044e\u0447\u0430\u043c\u0438<\/p>\n<\/li>\n<li>\n<p>\u0410\u043b\u0438\u0441\u0430 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442 \u043e\u0431\u0449\u0438\u0439 \u0441\u0435\u043a\u0440\u0435\u0442\u043d\u044b\u0439 \u043a\u043b\u044e\u0447 <img decoding=\"async\" class=\"formula inline\" source=\"S_{alice} = 8^4  \\bmod 11 = 4\" alt=\"S_{alice} = 8^4  \\bmod 11 = 4\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c6\/c69\/c69cd8d7a6e0668eb3819d5c8203d650.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c6\/c69\/c69cd8d7a6e0668eb3819d5c8203d650.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c6\/c69\/c69cd8d7a6e0668eb3819d5c8203d650.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p>\u0411\u043e\u0431 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442 \u043e\u0431\u0449\u0438\u0439 \u0441\u0435\u043a\u0440\u0435\u0442\u043d\u044b\u0439 \u043a\u043b\u044e\u0447 <img decoding=\"async\" class=\"formula inline\" source=\"S_{bob} = 3^9  \\bmod 11 = 4\" alt=\"S_{bob} = 3^9  \\bmod 11 = 4\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ac\/acf\/acf721dd3264ad6763fe1d2dee908620.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ac\/acf\/acf721dd3264ad6763fe1d2dee908620.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/ac\/acf\/acf721dd3264ad6763fe1d2dee908620.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<\/ol>\n<p>\u0412\u0440\u043e\u0434\u0435 \u0432\u0441\u0435 \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e, \u043d\u043e!<\/p>\n<ol>\n<li>\n<p>\u041d\u0430\u043c \u0438\u0437\u0432\u0435\u0441\u0442\u0435\u043d \u043f\u0440\u0438\u043c\u0438\u0442\u0438\u0432 <img decoding=\"async\" class=\"formula inline\" source=\"g = 7\" alt=\"g = 7\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9e\/9ee\/9eed67db41da95ceb9344fafbff5208c.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9e\/9ee\/9eed67db41da95ceb9344fafbff5208c.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9e\/9ee\/9eed67db41da95ceb9344fafbff5208c.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u043c\u0443\u043b\u044c\u0442\u0438\u043f\u043b\u0438\u043a\u0430\u0442\u0438\u0432\u043d\u043e \u043e\u0431\u0440\u0430\u0442\u043d\u044b\u0439 <img decoding=\"async\" class=\"formula inline\" source=\"g' = 8\" alt=\"g' = 8\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/20\/20b\/20b10d82d951cc4c52cbb051c416e45b.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/20\/20b\/20b10d82d951cc4c52cbb051c416e45b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/20\/20b\/20b10d82d951cc4c52cbb051c416e45b.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043f\u0440\u0438 \u043f\u043e\u043c\u043e\u0449\u0438 \u0440\u0430\u0441\u0448\u0438\u0440\u0435\u043d\u043d\u043e\u0433\u043e \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0430 \u0415\u0432\u043a\u043b\u0438\u0434\u0430 <a href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%A0%D0%B0%D1%81%D1%88%D0%B8%D1%80%D0%B5%D0%BD%D0%BD%D1%8B%D0%B9_%D0%B0%D0%BB%D0%B3%D0%BE%D1%80%D0%B8%D1%82%D0%BC_%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4%D0%B0\" rel=\"noopener noreferrer nofollow\">https:\/\/ru.wikipedia.org\/wiki\/\u0420\u0430\u0441\u0448\u0438\u0440\u0435\u043d\u043d\u044b\u0439_\u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c_\u0415\u0432\u043a\u043b\u0438\u0434\u0430<\/a><\/p>\n<\/li>\n<li>\n<p>\u0421\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u0435\u043c <img decoding=\"async\" class=\"formula inline\" source=\"g' = 8\" alt=\"g' = 8\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/20\/20b\/20b10d82d951cc4c52cbb051c416e45b.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/20\/20b\/20b10d82d951cc4c52cbb051c416e45b.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/20\/20b\/20b10d82d951cc4c52cbb051c416e45b.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u0441 \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u043c\u0438 \u043a\u043b\u044e\u0447\u0430\u043c\u0438, \u0443 \u0411\u043e\u0431\u0430 \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447 <img decoding=\"async\" class=\"formula inline\" source=\"B = 8\" alt=\"B = 8\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/97\/97f\/97f51400775e422380f3b6ef85889c7a.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/97\/97f\/97f51400775e422380f3b6ef85889c7a.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/97\/97f\/97f51400775e422380f3b6ef85889c7a.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0437\u043d\u0430\u0447\u0438\u0442 \u0437\u0430\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447 \u0411\u043e\u0431\u0430 \u0440\u0430\u0432\u0435\u043d <img decoding=\"async\" class=\"formula inline\" source=\"b = (p-2) = 9\" alt=\"b = (p-2) = 9\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a1\/a1e\/a1ea17401461e5df16cc2874aac67039.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a1\/a1e\/a1ea17401461e5df16cc2874aac67039.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a1\/a1e\/a1ea17401461e5df16cc2874aac67039.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u0441\u043c. \u0440\u0438\u0441. \u043d\u0438\u0436\u0435<\/p>\n<\/li>\n<li>\n<p>\u0412\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u0441\u0435\u043a\u0440\u0435\u0442\u043d\u044b\u0439 \u043a\u043b\u044e\u0447 <img decoding=\"async\" class=\"formula inline\" source=\"S_b = A^b  \\bmod 11 = 3^9  \\bmod 11 = 4\" alt=\"S_b = A^b  \\bmod 11 = 3^9  \\bmod 11 = 4\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a2\/a2e\/a2ef2d313fa4d2ca5605b69248c60020.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a2\/a2e\/a2ef2d313fa4d2ca5605b69248c60020.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/a\/a2\/a2e\/a2ef2d313fa4d2ca5605b69248c60020.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<\/ol>\n<figure class=\"\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/upload_files\/023\/b4d\/140\/023b4d1406171ede08a1ba5f8ed4808c.png\" alt=\"\u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0437\u0430\u043a\u0440\u044b\u0442\u043e\u0433\u043e \u043a\u043b\u044e\u0447\u0430  \u043f\u043e \" title=\"\u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0437\u0430\u043a\u0440\u044b\u0442\u043e\u0433\u043e \u043a\u043b\u044e\u0447\u0430  \u043f\u043e \" width=\"379\" height=\"309\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/upload_files\/023\/b4d\/140\/023b4d1406171ede08a1ba5f8ed4808c.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/upload_files\/023\/b4d\/140\/023b4d1406171ede08a1ba5f8ed4808c.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0437\u0430\u043a\u0440\u044b\u0442\u043e\u0433\u043e \u043a\u043b\u044e\u0447\u0430 <img decoding=\"async\" class=\"formula inline\" source=\"(p-2)\" alt=\"(p-2)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/47\/478\/478ce8c2163d42657f51ff351cd43873.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/47\/478\/478ce8c2163d42657f51ff351cd43873.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/4\/47\/478\/478ce8c2163d42657f51ff351cd43873.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043f\u043e <img decoding=\"async\" class=\"formula inline\" source=\"g'\" alt=\"g'\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/24\/243\/2434102e9be337298e17c9e419643480.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/24\/243\/2434102e9be337298e17c9e419643480.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/24\/243\/2434102e9be337298e17c9e419643480.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/figcaption><\/div>\n<\/figure>\n<p>\u0411\u0438\u043d\u0433\u043e &#8212; \u0432\u043e\u0442 \u0432\u0442\u043e\u0440\u0430\u044f &#171;\u0434\u044b\u0440\u043a\u0430&#187;, \u0441\u043e\u0433\u043b\u0430\u0441\u043d\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"g^{(p-2)} \\equiv g' \\pmod p\" alt=\"g^{(p-2)} \\equiv g' \\pmod p\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/68\/688\/68815f782713f1eaba5dd6917db042cd.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/68\/688\/68815f782713f1eaba5dd6917db042cd.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/68\/688\/68815f782713f1eaba5dd6917db042cd.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u042d\u0442\u0443 \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u043c\u043e\u0436\u043d\u043e \u0432\u044b\u0432\u0435\u0441\u0442\u0438 \u0438\u0437 \u041c\u0430\u043b\u043e\u0439 \u0442\u0435\u043e\u0440\u0435\u043c\u044b \u0424\u0435\u0440\u043c\u0430 <a href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%9C%D0%B0%D0%BB%D0%B0%D1%8F_%D1%82%D0%B5%D0%BE%D1%80%D0%B5%D0%BC%D0%B0_%D0%A4%D0%B5%D1%80%D0%BC%D0%B0\" rel=\"noopener noreferrer nofollow\">https:\/\/ru.wikipedia.org\/wiki\/\u041c\u0430\u043b\u0430\u044f_\u0442\u0435\u043e\u0440\u0435\u043c\u0430_\u0424\u0435\u0440\u043c\u0430<\/a><\/p>\n<ol>\n<li>\n<p><img decoding=\"async\" class=\"formula inline\" source=\"g^{(p-1)} \\equiv 1 \\pmod p\" alt=\"g^{(p-1)} \\equiv 1 \\pmod p\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9f\/9f3\/9f358d84dd8908f65c62842675acc6e1.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9f\/9f3\/9f358d84dd8908f65c62842675acc6e1.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9f\/9f3\/9f358d84dd8908f65c62842675acc6e1.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p><img decoding=\"async\" class=\"formula inline\" source=\"g * g^{(p-2)} \\equiv 1 \\pmod p\" alt=\"g * g^{(p-2)} \\equiv 1 \\pmod p\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c6\/c69\/c69bcadd3bc4772285ba99620a918726.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c6\/c69\/c69bcadd3bc4772285ba99620a918726.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/c\/c6\/c69\/c69bcadd3bc4772285ba99620a918726.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<li>\n<p><img decoding=\"async\" class=\"formula inline\" source=\"g^{(p-2)} \\equiv g^{-1} \\pmod p\" alt=\"g^{(p-2)} \\equiv g^{-1} \\pmod p\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8a\/8a1\/8a13b1cb33c38ca57b8eb93ad47a25ca.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8a\/8a1\/8a13b1cb33c38ca57b8eb93ad47a25ca.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/8\/8a\/8a1\/8a13b1cb33c38ca57b8eb93ad47a25ca.svg 781w\" loading=\"lazy\" decode=\"async\"\/>.<\/p>\n<\/li>\n<li>\n<p><img decoding=\"async\" class=\"formula inline\" source=\"g^{-1}\" alt=\"g^{-1}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b2\/b23\/b23e589fe6c12931d7d6fbd0e0d092f6.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b2\/b23\/b23e589fe6c12931d7d6fbd0e0d092f6.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/b2\/b23\/b23e589fe6c12931d7d6fbd0e0d092f6.svg 781w\" loading=\"lazy\" decode=\"async\"\/> &#8212; \u044d\u0442\u043e \u0438 \u0435\u0441\u0442\u044c \u043e\u0431\u0440\u0430\u0442\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e &#8212; <img decoding=\"async\" class=\"formula inline\" source=\"g'\" alt=\"g'\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/24\/243\/2434102e9be337298e17c9e419643480.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/24\/243\/2434102e9be337298e17c9e419643480.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/2\/24\/243\/2434102e9be337298e17c9e419643480.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<\/li>\n<\/ol>\n<p>\u0414\u043e\u043f\u043e\u043b\u043d\u044f\u0435\u043c \u0441\u043f\u0438\u0441\u043e\u043a \u0442\u0440\u0438\u0432\u0438\u0430\u043b\u044c\u043d\u044b\u0445 \u0441\u043b\u0443\u0447\u0430\u0435\u0432:<\/p>\n<p><img decoding=\"async\" class=\"formula\" source=\"x \\in  \\{ 0, 1, (p-1)\/2, p-2, p-1\\}\" alt=\"x \\in  \\{ 0, 1, (p-1)\/2, p-2, p-1\\}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e1\/e10\/e10d15a4ee3a4a052c82a4677d311c04.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e1\/e10\/e10d15a4ee3a4a052c82a4677d311c04.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/e1\/e10\/e10d15a4ee3a4a052c82a4677d311c04.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<p>\u0411\u043e\u043b\u044c\u0448\u0435 \u0443\u044f\u0437\u0432\u0438\u043c\u043e\u0441\u0442\u0435\u0439 \u043f\u043e\u043a\u0430 \u043d\u0435 \u043d\u0430\u0448\u0435\u043b.<\/p>\n<p>\u041c\u043e\u0436\u043d\u043e \u0435\u0449\u0435 \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0433\u0440\u0430\u0444\u0438\u043a \u043f\u043e\u043b\u044f <img decoding=\"async\" class=\"formula inline\" source=\"GF(47)\" alt=\"GF(47)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ed\/ed5\/ed540fd4b2cbb3a0af4cbb3b4bdef675.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ed\/ed5\/ed540fd4b2cbb3a0af4cbb3b4bdef675.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ed\/ed5\/ed540fd4b2cbb3a0af4cbb3b4bdef675.svg 781w\" loading=\"lazy\" decode=\"async\"\/> (\u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u043e\u0441\u0442\u044c \u0442\u0430\u043a\u0436\u0435 \u0432\u0438\u0434\u043d\u0430) \u0438 \u0442\u0430\u0431\u043b\u0438\u0446\u0443, \u0441\u043c. \u0440\u0438\u0441\u0443\u043d\u043a\u0438 \u043d\u0438\u0436\u0435:<\/p>\n<figure class=\"full-width\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/upload_files\/ee0\/a56\/c1f\/ee0a56c1fef1767984f92efe09e992b2.png\" alt=\"\u0413\u0440\u0430\u0444\u0438\u043a  \u043f\u043e \u0434\u0432\u0443\u043c \u043f\u0430\u0440\u0430\u043c \u043f\u0440\u0438\u043c\u0438\u0442\u0438\u0432\u043e\u0432: \" title=\"\u0413\u0440\u0430\u0444\u0438\u043a  \u043f\u043e \u0434\u0432\u0443\u043c \u043f\u0430\u0440\u0430\u043c \u043f\u0440\u0438\u043c\u0438\u0442\u0438\u0432\u043e\u0432: \" width=\"1617\" height=\"860\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/upload_files\/ee0\/a56\/c1f\/ee0a56c1fef1767984f92efe09e992b2.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/upload_files\/ee0\/a56\/c1f\/ee0a56c1fef1767984f92efe09e992b2.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0413\u0440\u0430\u0444\u0438\u043a <img decoding=\"async\" class=\"formula inline\" source=\"GF(47)\" alt=\"GF(47)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ed\/ed5\/ed540fd4b2cbb3a0af4cbb3b4bdef675.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ed\/ed5\/ed540fd4b2cbb3a0af4cbb3b4bdef675.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ed\/ed5\/ed540fd4b2cbb3a0af4cbb3b4bdef675.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043f\u043e \u0434\u0432\u0443\u043c \u043f\u0430\u0440\u0430\u043c \u043f\u0440\u0438\u043c\u0438\u0442\u0438\u0432\u043e\u0432: <img decoding=\"async\" class=\"formula inline\" source=\"\\{5, 19\\}, \\{10, 33\\}\" alt=\"\\{5, 19\\}, \\{10, 33\\}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f6\/f67\/f676e680b19ecbba8194ed8591c07d5f.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f6\/f67\/f676e680b19ecbba8194ed8591c07d5f.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/f\/f6\/f67\/f676e680b19ecbba8194ed8591c07d5f.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/figcaption><\/div>\n<\/figure>\n<figure class=\"full-width\"><img decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/upload_files\/8fc\/5b1\/f3a\/8fc5b1f3aeb3c890230c0446541efa6e.png\" alt=\"\u0422\u0430\u0431\u043b\u0438\u0446\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 \" title=\"\u0422\u0430\u0431\u043b\u0438\u0446\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 \" width=\"1362\" height=\"1254\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/r\/w780\/getpro\/habr\/upload_files\/8fc\/5b1\/f3a\/8fc5b1f3aeb3c890230c0446541efa6e.png 780w,&#10;       https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/upload_files\/8fc\/5b1\/f3a\/8fc5b1f3aeb3c890230c0446541efa6e.png 781w\" loading=\"lazy\" decode=\"async\"\/><\/p>\n<div><figcaption>\u0422\u0430\u0431\u043b\u0438\u0446\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 <img decoding=\"async\" class=\"formula inline\" source=\"GF(47)\" alt=\"GF(47)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ed\/ed5\/ed540fd4b2cbb3a0af4cbb3b4bdef675.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ed\/ed5\/ed540fd4b2cbb3a0af4cbb3b4bdef675.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/e\/ed\/ed5\/ed540fd4b2cbb3a0af4cbb3b4bdef675.svg 781w\" loading=\"lazy\" decode=\"async\"\/><\/figcaption><\/div>\n<\/figure>\n<h2>\u0417\u0430\u043a\u043b\u044e\u0447\u0435\u043d\u0438\u0435<\/h2>\n<p>\u041f\u0440\u0435\u0434\u0443\u043f\u0440\u0435\u0436\u0434\u0435\u043d\u0438\u044f \u043e \u043f\u0440\u0435\u0434\u043f\u043e\u043b\u0430\u0433\u0430\u0435\u043c\u043e\u0439 \u0441\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 DLOG, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440:<\/p>\n<ul>\n<li>\n<p>&#171;<em>\u041a\u0440\u0438\u043f\u0442\u043e\u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0441\u0442\u043e\u0439\u043a\u043e\u0441\u0442\u044c \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0430 \u0414\u0438\u0444\u0444\u0438 \u2014 \u0425\u0435\u043b\u043b\u043c\u0430\u043d\u0430 (\u0442\u043e \u0435\u0441\u0442\u044c \u0441\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u044c \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f <img decoding=\"async\" class=\"formula inline\" source=\"K=g^{ab} \\bmod {p}\" alt=\"K=g^{ab} \\bmod {p}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/bb\/bb3\/bb3550cdb4396ccd6aaa98772a56b3c2.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/bb\/bb3\/bb3550cdb4396ccd6aaa98772a56b3c2.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/b\/bb\/bb3\/bb3550cdb4396ccd6aaa98772a56b3c2.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043f\u043e \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u043c <img decoding=\"async\" class=\"formula inline\" source=\"p, g, A=g^{a} \\bmod {p} \\mbox{ \u0438 }  B=g^{b} \\bmod {p}\" alt=\"p, g, A=g^{a} \\bmod {p} \\mbox{ \u0438 }  B=g^{b} \\bmod {p}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9b\/9be\/9be17923b094c0618c404d566f226da0.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9b\/9be\/9be17923b094c0618c404d566f226da0.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/9\/9b\/9be\/9be17923b094c0618c404d566f226da0.svg 781w\" loading=\"lazy\" decode=\"async\"\/>) \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0430 \u043d\u0430 <\/em><strong><em>\u043f\u0440\u0435\u0434\u043f\u043e\u043b\u0430\u0433\u0430\u0435\u043c\u043e\u0439<\/em><\/strong><em> \u0441\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u0434\u0438\u0441\u043a\u0440\u0435\u0442\u043d\u043e\u0433\u043e \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f.<\/em>&#187;  \u0424\u043e\u0440\u043c\u0430\u0442\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435 \u0441\u043e\u0445\u0440\u0430\u043d\u0435\u043d\u043e, \u0438\u0441\u0442\u043e\u0447\u043d\u0438\u043a: <a href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%9F%D1%80%D0%BE%D1%82%D0%BE%D0%BA%D0%BE%D0%BB_%D0%94%D0%B8%D1%84%D1%84%D0%B8_%E2%80%94_%D0%A5%D0%B5%D0%BB%D0%BB%D0%BC%D0%B0%D0%BD%D0%B0#%D0%9A%D1%80%D0%B8%D0%BF%D1%82%D0%BE%D0%B3%D1%80%D0%B0%D1%84%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0%D1%8F_%D1%81%D1%82%D0%BE%D0%B9%D0%BA%D0%BE%D1%81%D1%82%D1%8C\" rel=\"noopener noreferrer nofollow\">https:\/\/ru.wikipedia.org\/wiki\/\u041f\u0440\u043e\u0442\u043e\u043a\u043e\u043b_\u0414\u0438\u0444\u0444\u0438_\u2014_\u0425\u0435\u043b\u043b\u043c\u0430\u043d\u0430#\u041a\u0440\u0438\u043f\u0442\u043e\u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u0430\u044f_\u0441\u0442\u043e\u0439\u043a\u043e\u0441\u0442\u044c<\/a><\/p>\n<\/li>\n<li>\n<p>&#171;<em>A cryptographic system is described which is secure if and only if computing logarithms over <img decoding=\"async\" class=\"formula inline\" source=\"GF(p)\" alt=\"GF(p)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/13\/13d\/13d7f9f1f837dd8322d8dc16e9a699c0.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/13\/13d\/13d7f9f1f837dd8322d8dc16e9a699c0.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/13\/13d\/13d7f9f1f837dd8322d8dc16e9a699c0.svg 781w\" loading=\"lazy\" decode=\"async\"\/> is infeasible.<\/em>&#187; (\u043c\u043e\u0439 \u043f\u0435\u0440\u0435\u0432\u043e\u0434: &#171;<em>\u041e\u043f\u0438\u0441\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u043a\u0440\u0438\u043f\u0442\u043e\u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0441\u0438\u0441\u0442\u0435\u043c\u0430, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0431\u0435\u0437\u043e\u043f\u0430\u0441\u043d\u043e\u0439 \u0442\u043e\u0433\u0434\u0430 \u0438 \u0442\u043e\u043b\u044c\u043a\u043e \u0442\u043e\u0433\u0434\u0430, \u043a\u043e\u0433\u0434\u0430 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u043e\u0432 \u043f\u043e <img decoding=\"async\" class=\"formula inline\" source=\"GF(p)\" alt=\"GF(p)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/13\/13d\/13d7f9f1f837dd8322d8dc16e9a699c0.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/13\/13d\/13d7f9f1f837dd8322d8dc16e9a699c0.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/1\/13\/13d\/13d7f9f1f837dd8322d8dc16e9a699c0.svg 781w\" loading=\"lazy\" decode=\"async\"\/> \u043d\u0435\u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e.<\/em>&#171;) \u0418\u0441\u0442\u043e\u0447\u043d\u0438\u043a: S. C. Pohlig and M. E. Hellman, &#171;<em>An improved algorithm for computing logarithms in GF(p) and its cryptographic significance.<\/em>&#187; <a href=\"https:\/\/ee.stanford.edu\/~hellman\/publications\/28.pdf\" rel=\"noopener noreferrer nofollow\">https:\/\/ee.stanford.edu\/~hellman\/publications\/28.pdf<\/a> IEEE Trans. Info. Theory 24 (1978), 106\u2013111.<\/p>\n<\/li>\n<\/ul>\n<p>\u0427\u0442\u043e \u043a\u0430\u0441\u0430\u0435\u0442\u0441\u044f \u043e\u043f\u0438\u0441\u0430\u043d\u043d\u044b\u0445 \u0432 \u0434\u0430\u043d\u043d\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u0443\u044f\u0437\u0432\u0438\u043c\u043e\u0441\u0442\u044f\u0445, \u0442\u043e \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u043d\u0435 \u0442\u0430\u043a\u0438\u0435 \u0431\u043e\u043b\u044c\u0448\u0438\u0435. \u041d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0432 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u043d\u043e\u0435 \u043e\u0431\u0435\u0441\u043f\u0435\u0447\u0435\u043d\u0438\u0435, \u0433\u0435\u043d\u0435\u0440\u0438\u0440\u0443\u044e\u0449\u0435\u0435 \u0437\u0430\u043a\u0440\u044b\u0442\u044b\u0435 \u043a\u043b\u044e\u0447\u0438, \u0434\u043e\u0431\u0430\u0432\u0438\u0442\u044c \u0438\u0441\u043a\u043b\u044e\u0447\u0435\u043d\u0438\u044f: <img decoding=\"async\" class=\"formula inline\" source=\"\\{(p-1)\/2, \\ p-2\\}\" alt=\"\\{(p-1)\/2, \\ p-2\\}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/68\/68c\/68c665a24d1a3fbdd4518d28a7036543.svg\" width=\"auto\" height=\"auto\" sizes=\"auto, (max-width: 780px) 100vw, 50vw\" srcset=\"https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/68\/68c\/68c665a24d1a3fbdd4518d28a7036543.svg 780w,&#10;       https:\/\/habrastorage.org\/getpro\/habr\/formulas\/6\/68\/68c\/68c665a24d1a3fbdd4518d28a7036543.svg 781w\" loading=\"lazy\" decode=\"async\"\/>, \u043e\u0441\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u0431\u044b\u043b\u0438 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b \u0438 \u0440\u0430\u043d\u0435\u0435.<\/p>\n<p>\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0443\u044f\u0437\u0432\u0438\u043c\u043e\u0441\u0442\u0438 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0442 \u0438 \u0434\u043e\u043b\u0436\u043d\u044b \u0431\u044b\u0442\u044c \u043e\u0431\u0449\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b.<\/p>\n<p>\u0415\u0441\u043b\u0438 \u043d\u0430\u0448\u043b\u0438 \u043e\u0448\u0438\u0431\u043a\u0438, \u043f\u0438\u0448\u0438\u0442\u0435 \u043a\u0430\u043c\u043c\u0435\u043d\u0442\u044b.<\/p>\n<p>&#171;\u041f\u043e\u0438\u0433\u0440\u0430\u0442\u044c\u0441\u044f&#187; \u0441 \u0442\u0430\u0431\u043b\u0438\u0446\u0430\u043c\u0438 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 \u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u043f\u0440\u0438\u043c\u0438\u0442\u0438\u0432\u044b \u043c\u043e\u0436\u043d\u043e \u0432 \u0441\u0435\u0440\u0432\u0438\u0441\u0435 <a href=\"https:\/\/dlog.vladlin.ru\/\" rel=\"noopener noreferrer nofollow\">https:\/\/dlog.vladlin.ru\/<\/a> (AS IS)<\/p>\n<p>\u041d\u0430 \u0437\u0430\u0434\u0430\u0447\u0435 DLOG, \u043a\u0440\u043e\u043c\u0435 \u043f\u0440\u043e\u0442\u043e\u043a\u043e\u043b\u0430 \u0414\u0438\u0444\u0444\u0438-\u0425\u0435\u043b\u043b\u043c\u0430\u043d\u0430, \u0431\u0430\u0437\u0438\u0440\u0443\u044e\u0442\u0441\u044f \u0438 \u0434\u0440\u0443\u0433\u0438\u0435, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440:<\/p>\n<ul>\n<li>\n<p>\u0421\u0445\u0435\u043c\u0430 \u042d\u043b\u044c-\u0413\u0430\u043c\u0430\u043b\u044f <a href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%A1%D1%85%D0%B5%D0%BC%D0%B0_%D0%AD%D0%BB%D1%8C-%D0%93%D0%B0%D0%BC%D0%B0%D0%BB%D1%8F\" rel=\"noopener noreferrer nofollow\">https:\/\/ru.wikipedia.org\/wiki\/\u0421\u0445\u0435\u043c\u0430_\u042d\u043b\u044c-\u0413\u0430\u043c\u0430\u043b\u044f<\/a><\/p>\n<\/li>\n<li>\n<p>\u041a\u0440\u0438\u043f\u0442\u043e\u0441\u0438\u0441\u0442\u0435\u043c\u0430 \u041c\u044d\u0441\u0441\u0438 \u2014 \u041e\u043c\u0443\u0440\u044b <a href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%9A%D1%80%D0%B8%D0%BF%D1%82%D0%BE%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B0_%D0%9C%D1%8D%D1%81%D1%81%D0%B8_%E2%80%94_%D0%9E%D0%BC%D1%83%D1%80%D1%8B\" rel=\"noopener noreferrer nofollow\">https:\/\/ru.wikipedia.org\/wiki\/\u041a\u0440\u0438\u043f\u0442\u043e\u0441\u0438\u0441\u0442\u0435\u043c\u0430_\u041c\u044d\u0441\u0441\u0438_\u2014_\u041e\u043c\u0443\u0440\u044b<\/a><\/p>\n<\/li>\n<li>\n<p>Digital Signature Algorithm <a href=\"https:\/\/ru.wikipedia.org\/wiki\/DSA\" rel=\"noopener noreferrer nofollow\">https:\/\/ru.wikipedia.org\/wiki\/DSA<\/a><\/p>\n<\/li>\n<\/ul>\n<p>\u041d\u0430\u0434\u043e \u043f\u0440\u043e\u0432\u0435\u0440\u0438\u0442\u044c \ud83d\ude42<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p><!----><!----><\/div>\n<p><!----><!----><br \/> \u0441\u0441\u044b\u043b\u043a\u0430 \u043d\u0430 \u043e\u0440\u0438\u0433\u0438\u043d\u0430\u043b \u0441\u0442\u0430\u0442\u044c\u0438 <a href=\"https:\/\/habr.com\/ru\/articles\/918742\/\"> https:\/\/habr.com\/ru\/articles\/918742\/<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<div><!--[--><!--]--><\/div>\n<div id=\"post-content-body\">\n<div>\n<div class=\"article-formatted-body article-formatted-body article-formatted-body_version-2\">\n<div xmlns=\"http:\/\/www.w3.org\/1999\/xhtml\">\n<figure class=\"full-width\"><\/figure>\n<p>\u041f\u0440\u043e\u0434\u043e\u043b\u0436\u0430\u044e \u0438\u0437\u0443\u0447\u0430\u0442\u044c \u043a\u0440\u0438\u043f\u0442\u043e\u0433\u0440\u0430\u0444\u0438\u044e, \u0434\u0435\u043b\u044e\u0441\u044c \u043e\u043f\u044b\u0442\u043e\u043c. \u041d\u0430\u0448\u0435\u043b \u0438\u043d\u0442\u0435\u0440\u0435\u0441\u043d\u0443\u044e \u043e\u0441\u043e\u0431\u0435\u043d\u043d\u043e\u0441\u0442\u044c \u0434\u0438\u0441\u043a\u0440\u0435\u0442\u043d\u043e\u0433\u043e \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u0430, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043f\u0440\u0435\u0432\u0440\u0430\u0449\u0430\u0435\u0442\u0441\u044f \u0432 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0431\u044d\u043a\u0434\u043e\u0440 \u043f\u0440\u043e\u0442\u043e\u043a\u043e\u043b\u0430 \u0414\u0438\u0444\u0444\u0438 \u2014 \u0425\u0435\u043b\u043b\u043c\u0430\u043d\u0430  (\u0434\u0430\u043b\u0435\u0435 DH).<\/p>\n<h2>\u041f\u0440\u043e\u0431\u0435\u0436\u0438\u043c\u0441\u044f \u043f\u043e \u0442\u0435\u043e\u0440\u0438\u0438<\/h2>\n<p>\u0412\u0441\u043f\u043e\u043c\u043d\u0438\u043c \u0434\u0438\u0441\u043a\u0440\u0435\u0442\u043d\u044b\u0439 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c (\u0434\u0430\u043b\u0435\u0435 DLOG) <a href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%94%D0%B8%D1%81%D0%BA%D1%80%D0%B5%D1%82%D0%BD%D0%BE%D0%B5_%D0%BB%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D0%B5\" rel=\"noopener noreferrer nofollow\">https:\/\/ru.wikipedia.org\/wiki\/\u0414\u0438\u0441\u043a\u0440\u0435\u0442\u043d\u043e\u0435_\u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435<\/a><\/p>\n<p>\u041d\u0430\u043c \u043d\u0443\u0436\u0435\u043d \u0432\u0430\u0440\u0438\u0430\u043d\u0442 DLOG \u0432 \u043a\u043e\u043d\u0435\u0447\u043d\u043e\u043c \u043f\u043e\u043b\u0435 , \u0433\u0434\u0435 p &#8212; \u043f\u0440\u043e\u0441\u0442\u043e\u0435 \u0447\u0438\u0441\u043b\u043e <a href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%9A%D0%BE%D0%BD%D0%B5%D1%87%D0%BD%D0%BE%D0%B5_%D0%BF%D0%BE%D0%BB%D0%B5\" rel=\"noopener noreferrer nofollow\">https:\/\/ru.wikipedia.org\/wiki\/\u041a\u043e\u043d\u0435\u0447\u043d\u043e\u0435_\u043f\u043e\u043b\u0435<\/a><\/p>\n<\/p>\n<p>\u041e\u0431\u0449\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e \u0447\u0442\u043e \u0437\u0430\u0434\u0430\u0447\u0430 DLOG \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043e\u0434\u043d\u043e\u0441\u0442\u043e\u0440\u043e\u043d\u043d\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439 <a href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%9E%D0%B4%D0%BD%D0%BE%D1%81%D1%82%D0%BE%D1%80%D0%BE%D0%BD%D0%BD%D1%8F%D1%8F_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F\" rel=\"noopener noreferrer nofollow\">https:\/\/ru.wikipedia.org\/wiki\/\u041e\u0434\u043d\u043e\u0441\u0442\u043e\u0440\u043e\u043d\u043d\u044f\u044f_\u0444\u0443\u043d\u043a\u0446\u0438\u044f<\/a> \u0442.\u0435. \u043f\u043e\u0438\u0441\u043a  \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0442\u0440\u0443\u0434\u043d\u043e\u0439 \u0437\u0430\u0434\u0430\u0447\u0435\u0439.<\/p>\n<p>\u041a\u0440\u043e\u043c\u0435 \u043f\u043e\u043b\u043d\u043e\u0433\u043e \u043f\u0435\u0440\u0435\u0431\u043e\u0440\u0430, \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u043c\u043d\u043e\u0433\u043e \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u043e\u0432 \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0434\u0430\u043d\u043d\u043e\u0439 \u0437\u0430\u0434\u0430\u0447\u0438 <a href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%94%D0%B8%D1%81%D0%BA%D1%80%D0%B5%D1%82%D0%BD%D0%BE%D0%B5_%D0%BB%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D0%B5#%D0%90%D0%BB%D0%B3%D0%BE%D1%80%D0%B8%D1%82%D0%BC%D1%8B_%D1%80%D0%B5%D1%88%D0%B5%D0%BD%D0%B8%D1%8F\" rel=\"noopener noreferrer nofollow\">https:\/\/ru.wikipedia.org\/wiki\/\u0414\u0438\u0441\u043a\u0440\u0435\u0442\u043d\u043e\u0435_\u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435#\u0410\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u044b_\u0440\u0435\u0448\u0435\u043d\u0438\u044f<\/a> (\u043d\u0435 \u0431\u0443\u0434\u0435\u043c \u0438\u0445 \u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u0442\u044c).<\/p>\n<p>\u0418\u043d\u043e\u0433\u0434\u0430 \u043f\u043e\u0438\u0441\u043a  \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0442\u0440\u0438\u0432\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0437\u0430\u0434\u0430\u0447\u0435\u0439, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440:<\/p>\n<p>\u0435\u0441\u043b\u0438 , \u0442\u043e <\/p>\n<p>\u0435\u0441\u043b\u0438 , \u0442\u043e <\/p>\n<p>\u0421\u043b\u0435\u0434\u0443\u0435\u0442 \u0441\u043a\u0430\u0437\u0430\u0442\u044c \u0447\u0442\u043e  \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043f\u0435\u0440\u0432\u043e\u043e\u0431\u0440\u0430\u0437\u043d\u044b\u043c \u043a\u043e\u0440\u043d\u0435\u043c \u0438\u043b\u0438 \u043f\u0440\u0438\u043c\u0438\u0442\u0438\u0432\u043e\u043c <a href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%9F%D0%B5%D1%80%D0%B2%D0%BE%D0%BE%D0%B1%D1%80%D0%B0%D0%B7%D0%BD%D1%8B%D0%B9_%D0%BA%D0%BE%D1%80%D0%B5%D0%BD%D1%8C_(%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F_%D1%87%D0%B8%D1%81%D0%B5%D0%BB)\" rel=\"noopener noreferrer nofollow\">https:\/\/ru.wikipedia.org\/wiki\/\u041f\u0435\u0440\u0432\u043e\u043e\u0431\u0440\u0430\u0437\u043d\u044b\u0439_\u043a\u043e\u0440\u0435\u043d\u044c_(\u0442\u0435\u043e\u0440\u0438\u044f_\u0447\u0438\u0441\u0435\u043b)<\/a><\/p>\n<p>\u0414\u043b\u044f  \u043f\u0440\u0438\u043c\u0438\u0442\u0438\u0432 , \u043f\u0440\u043e\u0432\u0435\u0440\u0438\u043c:<\/p>\n<\/p>\n<p>\u041e\u0431\u0440\u0430\u0449\u0430\u0435\u043c \u0432\u043d\u0438\u043c\u0430\u043d\u0438\u0435 \u043d\u0430 \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u044e\u044e \u0441\u0442\u0440\u043e\u043a\u0443, \u0442.\u0435. \u0435\u0441\u043b\u0438 , \u0442\u043e  \u0438\u043b\u0438 <\/p>\n<p>\u0418\u0442\u0430\u043a, \u0443 \u043d\u0430\u0441 \u0435\u0441\u0442\u044c \u0443\u0436\u0435 \u0442\u0440\u0438 \u0441\u043b\u0443\u0447\u0430\u044f, \u043a\u043e\u0433\u0434\u0430 \u043f\u043e\u0438\u0441\u043a  \u0442\u0440\u0438\u0432\u0438\u0430\u043b\u0435\u043d:<\/p>\n<p>\u041a\u0430\u043a \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u0434\u043b\u044f \u0430\u043d\u0430\u043b\u0438\u0437\u0430 DLOG \u0441\u0442\u0440\u043e\u044f\u0442 \u0442\u0430\u0431\u043b\u0438\u0446\u0443 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u043e\u0432:<\/p>\n<figure class=\"\">\n<div><figcaption>\u0422\u0430\u0431\u043b\u0438\u0446\u0430 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u043e\u0432 \u0434\u043b\u044f  (\u043d\u0443\u043b\u0435\u0432\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435  \u043e\u0431\u044b\u0447\u043d\u043e \u043e\u043f\u0443\u0441\u043a\u0430\u044e\u0442)<\/figcaption><\/div>\n<\/figure>\n<p>\u041f\u043e \u0442\u0430\u0431\u043b\u0438\u0446\u0435 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u043e\u0432 \u043d\u0430\u0440\u0438\u0441\u0443\u0435\u043c \u0433\u0440\u0430\u0444\u0438\u043a:<\/p>\n<figure class=\"full-width\">\n<div><figcaption>\u0413\u0440\u0430\u0444\u0438\u043a \u0442\u0430\u0431\u043b\u0438\u0446\u044b \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u043e\u0432 \u0434\u043b\u044f <\/figcaption><\/div>\n<\/figure>\n<p>\u041d\u0430 \u0433\u0440\u0430\u0444\u0438\u043a\u0435 \u043d\u0438\u0447\u0435\u0433\u043e \u0438\u043d\u0442\u0435\u0440\u0435\u0441\u043d\u043e\u0433\u043e, \u0442\u043e\u043b\u044c\u043a\u043e \u0445\u0430\u043e\u0442\u0438\u0447\u043d\u043e\u0435 \u0438\u0437\u043c\u0435\u043d\u0435\u043d\u0438\u0435 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044f <\/p>\n<p>\u041a\u0440\u0438\u043f\u0442\u043e\u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u043f\u0440\u043e\u0442\u043e\u043a\u043e\u043b DH \u043f\u043e\u0441\u0442\u0440\u043e\u0435\u043d \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0435 DLOG <a href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%9F%D1%80%D0%BE%D1%82%D0%BE%D0%BA%D0%BE%D0%BB_%D0%94%D0%B8%D1%84%D1%84%D0%B8_%E2%80%94_%D0%A5%D0%B5%D0%BB%D0%BB%D0%BC%D0%B0%D0%BD%D0%B0\" rel=\"noopener noreferrer nofollow\">https:\/\/ru.wikipedia.org\/wiki\/\u041f\u0440\u043e\u0442\u043e\u043a\u043e\u043b_\u0414\u0438\u0444\u0444\u0438_\u2014_\u0425\u0435\u043b\u043b\u043c\u0430\u043d\u0430<\/a><\/p>\n<p>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043f\u0440\u0438\u043c\u0435\u0440 \u043f\u0440\u044f\u043c\u043e \u0438\u0437 \u0432\u0438\u043a\u0438:<\/p>\n<figure class=\"full-width\">\n<div><figcaption>\u0421\u043a\u0440\u0438\u043d \u0438\u0437 \u0432\u0438\u043a\u0438\u0441\u0442\u0430\u0442\u044c\u0438 \u041f\u0440\u043e\u0442\u043e\u043a\u043e\u043b \u0414\u0438\u0444\u0444\u0438 \u2014 \u0425\u0435\u043b\u043b\u043c\u0430\u043d\u0430<\/figcaption><\/div>\n<\/figure>\n<p>\u041d\u0438\u0447\u0435\u0433\u043e \u0441\u043b\u043e\u0436\u043d\u043e\u0433\u043e.<\/p>\n<p>\u0414\u0430\u043b\u0435\u0435 \u043f\u043e\u0439\u0434\u0435\u0442 \u043d\u043e\u0432\u0430\u044f \u0438\u043b\u0438 \u043d\u0435\u043f\u0443\u0431\u043b\u0438\u0447\u043d\u0430\u044f \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u044f.<\/p>\n<h2>\u041e\u0441\u043d\u043e\u0432\u043d\u0430\u044f \u0447\u0430\u0441\u0442\u044c<\/h2>\n<p>\u0411\u0443\u0434\u0435\u043c \u0430\u043d\u0430\u043b\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u0442\u044c DLOG \u043a\u0430\u043a \u0442\u0430\u0431\u043b\u0438\u0446\u0443 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439. \u0422\u0430\u0431\u043b\u0438\u0446\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 \u044d\u0442\u043e \u043f\u0435\u0440\u0435\u0432\u0435\u0440\u043d\u0443\u0442\u0430\u044f \u0442\u0430\u0431\u043b\u0438\u0446\u0430 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u043e\u0432 (\u0441\u043c. \u0440\u0438\u0441. \u043d\u0438\u0436\u0435), \u0441\u043b\u0435\u0432\u0430 \u2014 \u0442\u0430\u0431\u043b\u0438\u0446\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439, \u0441\u043f\u0440\u0430\u0432\u0430 \u2014 \u0442\u0430\u0431\u043b\u0438\u0446\u0430 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u043e\u0432. \u041e\u0431 \u044d\u0442\u043e\u043c \u044f \u043f\u0438\u0441\u0430\u043b \u0432 \u0441\u0442\u0430\u0442\u044c\u0435 &#171;\u041a\u0430\u043a \u0441\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u043f\u043e\u0440\u043e\u0436\u0434\u0430\u044e\u0449\u0438\u0435 \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u044b \u0434\u043b\u044f \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0445 \u043f\u043e\u043b\u0435\u0439.&#187; <a href=\"https:\/\/habr.com\/ru\/articles\/844300\" rel=\"noopener noreferrer nofollow\">https:\/\/habr.com\/ru\/articles\/844300<\/a><\/p>\n<figure class=\"full-width\">\n<div><figcaption>\u0422\u0430\u0431\u043b\u0438\u0446\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 \u0438 \u0442\u0430\u0431\u043b\u0438\u0446\u0430 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u043e\u0432 \u0434\u043b\u044f <\/figcaption><\/div>\n<\/figure>\n<p>\u0422\u0430\u0431\u043b\u0438\u0446\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 \u0443\u0434\u043e\u0431\u043d\u0435\u0435, \u0442\u0430\u043a \u043a\u0430\u043a \u043c\u043e\u0436\u043d\u043e \u043d\u0430\u0431\u043b\u044e\u0434\u0430\u0442\u044c \u0441\u0440\u0430\u0437\u0443 \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043f\u0440\u0438\u043c\u0438\u0442\u0438\u0432\u043e\u0432 (), \u0441\u0438\u043d\u0438\u043c \u043f\u043e\u0434\u0447\u0435\u0440\u043a\u043d\u0443\u0442\u0430 \u0441\u0442\u0440\u043e\u043a\u0430 \u0434\u043b\u044f \u043f\u0440\u0438\u043c\u0438\u0442\u0438\u0432\u0430 , \u043a\u043e\u043b\u043e\u043d\u043a\u0430 \u0434\u043b\u044f  \u043d\u0435 \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0435\u043d\u0430.<\/p>\n<p>\u0414\u0430\u043b\u0435\u0435 \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0442\u0430\u0431\u043b\u0438\u0446 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 \u0438 \u043e\u0431\u0440\u0430\u0442\u0438\u043c \u0432\u043d\u0438\u043c\u0430\u043d\u0438\u0435 \u043d\u0430 \u0441\u0440\u0435\u0434\u043d\u044e\u044e \u043a\u043e\u043b\u043e\u043d\u043a\u0443 <\/p>\n<figure class=\"full-width\">\n<div><figcaption>\u041d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0442\u0430\u0431\u043b\u0438\u0446 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439<\/figcaption><\/div>\n<\/figure>\n<p>\u0418\u043c\u0435\u044f \u0432\u0432\u0438\u0434\u0443 \u044d\u043a\u0441\u0442\u0440\u0430\u043f\u043e\u043b\u044f\u0446\u0438\u044e, \u043c\u043e\u0436\u043d\u043e \u043f\u0440\u0435\u0434\u043f\u043e\u043b\u043e\u0436\u0438\u0442\u044c, \u0447\u0442\u043e \u0434\u0430\u043d\u043d\u0430\u044f \u043e\u0441\u043e\u0431\u0435\u043d\u043d\u043e\u0441\u0442\u044c \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u044f\u0435\u0442\u0441\u044f \u043d\u0430 \u0432\u0441\u0435 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u043e \u0442\u0430\u0431\u043b\u0438\u0446 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 .<\/p>\n<p>\u0412 \u0441\u0440\u0435\u0434\u043d\u0435\u0439 \u043a\u043e\u043b\u043e\u043d\u043a\u0435 \u0447\u0438\u0441\u043b\u043e  \u043f\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442 \u0441\u0442\u0440\u043e\u043a\u0438 \u0441 \u0443\u043d\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u043c\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u043c\u0438, \u0437\u043d\u0430\u0447\u0438\u0442 \u0432 \u043d\u0430\u0447\u0430\u043b\u0435 \u0441\u0442\u0440\u043e\u043a\u0438 &#8212; \u043f\u0440\u0438\u043c\u0438\u0442\u0438\u0432, \u043d\u0430\u0431\u043b\u044e\u0434\u0430\u0435\u043c \u0442\u0430\u043a\u0436\u0435:<\/p>\n<ul>\n<li>\n<p>\u043d\u0435 \u043a\u0430\u0441\u0430\u0435\u0442\u0441\u044f \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0435\u0439 \u0441\u0442\u0440\u043e\u043a\u0438, \u0442\u0430\u043c ;<\/p>\n<\/li>\n<li>\n<p> &#8212; \u043f\u0440\u043e\u0441\u0442\u043e\u0435 \u0447\u0438\u0441\u043b\u043e, \u0438\u043d\u0430\u0447\u0435, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440 \u0434\u043b\u044f  &#8212; \u043d\u0435\u043f\u0440\u043e\u0441\u0442\u043e\u0435, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0431\u0443\u0434\u0443\u0442 &#171;\u043b\u0438\u0448\u043d\u0438\u0435&#187; \u0441\u0442\u0440\u043e\u043a\u0438: .<\/p>\n<\/li>\n<\/ul>\n<p>\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u044d\u0442\u043e \u0432\u044b\u0433\u043b\u044f\u0434\u0438\u0442 \u0442\u0430\u043a:<\/p>\n<p>\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438 \u0437\u043d\u0430\u043a\u043e\u043c\u044b\u0435 \u0441 \u043a\u0440\u0438\u0442\u0435\u0440\u0438\u044f\u043c\u0438 \u042d\u0439\u043b\u0435\u0440\u0430 <a href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%9A%D1%80%D0%B8%D1%82%D0%B5%D1%80%D0%B8%D0%B9_%D0%AD%D0%B9%D0%BB%D0%B5%D1%80%D0%B0\" rel=\"noopener noreferrer nofollow\">https:\/\/ru.wikipedia.org\/wiki\/\u041a\u0440\u0438\u0442\u0435\u0440\u0438\u0439_\u042d\u0439\u043b\u0435\u0440\u0430<\/a> \u0438 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u044b\u043c \u0432\u044b\u0447\u0435\u0442\u043e\u043c <a href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%9A%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D0%B8%D1%87%D0%BD%D1%8B%D0%B9_%D0%B2%D1%8B%D1%87%D0%B5%D1%82\" rel=\"noopener noreferrer nofollow\">https:\/\/ru.wikipedia.org\/wiki\/\u041a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u044b\u0439_\u0432\u044b\u0447\u0435\u0442<\/a> \u0443\u0432\u0438\u0434\u044f\u0442 \u0437\u043d\u0430\u043a\u043e\u043c\u043e\u0435:<\/p>\n<ul>\n<li>\n<\/li>\n<li>\n<\/li>\n<\/ul>\n<p>\u043d\u043e \u0437\u0434\u0435\u0441\u044c \u0432\u043c\u0435\u0441\u0442\u043e  \u0443\u0441\u0442\u0430\u043d\u043e\u0432\u043b\u0435\u043d\u043e  !<\/p>\n<p>\u041d\u0430\u0434\u043e \u0432\u0441\u043f\u043e\u043c\u043d\u0438\u0442\u044c \u043c\u043e\u0434\u0443\u043b\u044f\u0440\u043d\u0443\u044e \u0430\u0440\u0438\u0444\u043c\u0435\u0442\u0438\u043a\u0443 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Modular_arithmetic\" rel=\"noopener noreferrer nofollow\">https:\/\/en.wikipedia.org\/wiki\/Modular_arithmetic<\/a> (\u0441\u0442\u0430\u0442\u044c\u044f \u0432 en-\u0432\u0438\u043a\u0438 \u0431\u043e\u043b\u0435\u0435 \u043f\u043e\u043d\u044f\u0442\u043d\u0430), \u0444\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0432 \u0434\u0430\u043d\u043d\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 , \u0432\u0435\u0440\u043d\u0435\u0435 \u0442\u0430\u043a:<\/p>\n<p>\u0418\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0432\u044b\u0448\u0435\u0441\u043a\u0430\u0437\u0430\u043d\u043d\u043e\u0435, \u043c\u043e\u0436\u043d\u043e \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u044c \u0432\u0441\u0435 \u043f\u0440\u0438\u043c\u0438\u0442\u0438\u0432\u044b \u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0433\u043e \u043f\u043e\u043b\u044f:<\/p>\n<figure class=\"full-width\">\n<div><figcaption>\u0422\u0430\u0431\u043b\u0438\u0446\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 <\/figcaption><\/div>\n<\/figure>\n<p>\u041e\u0431\u0449\u0435\u0435 \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u043f\u0440\u0438\u043c\u0438\u0442\u0438\u0432\u043e\u0432 \u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0433\u043e \u043f\u043e\u043b\u044f \u0440\u0430\u0432\u043d\u043e , \u0433\u0434\u0435  \u2014 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u042d\u0439\u043b\u0435\u0440\u0430 totient <a href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F_%D0%AD%D0%B9%D0%BB%D0%B5%D1%80%D0%B0\" rel=\"noopener noreferrer nofollow\">https:\/\/ru.wikipedia.org\/wiki\/\u0424\u0443\u043d\u043a\u0446\u0438\u044f_\u042d\u0439\u043b\u0435\u0440\u0430<\/a><\/p>\n<p>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043d\u0430 \u0442\u0430\u0431\u043b\u0438\u0446\u0443 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439  \u0432 \u0432\u0438\u0434\u0435 \u0433\u0440\u0430\u0444\u0438\u043a\u0430, \u0434\u043e\u0431\u0430\u0432\u0438\u043b \u043d\u0443\u043b\u0435\u0432\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435  \u0434\u043b\u044f \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u043e\u0441\u0442\u0438, \u043f\u043e\u0445\u043e\u0436 \u043d\u0430 &#171;\u043f\u0430\u0443\u043a\u0430&#187;:<\/p>\n<figure class=\"full-width\">\n<div><figcaption>\u0422\u0430\u0431\u043b\u0438\u0446\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439  \u0432 \u0432\u0438\u0434\u0435 \u0433\u0440\u0430\u0444\u0438\u043a\u0430<\/figcaption><\/div>\n<\/figure>\n<p>\u0412\u0435\u0440\u043d\u0435\u043c\u0441\u044f \u0432 \u043f\u0440\u043e\u0442\u043e\u043a\u043e\u043b\u0443 DH, \u0438\u0437\u043c\u0435\u043d\u0438\u043c \u043d\u0430\u0438\u043c\u0435\u043d\u043e\u0432\u0430\u043d\u0438\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445:<\/p>\n<p>\u0434\u043b\u044f \u0410\u043b\u0438\u0441\u044b:,  &#8212; \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447,  &#8212; \u0437\u0430\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447.<\/p>\n<p>\u0434\u043b\u044f \u0411\u043e\u0431\u0430: ,  &#8212; \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447,  &#8212; \u0437\u0430\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447.<\/p>\n<p> &#8212; \u043e\u0431\u0449\u0438\u0439 \u0441\u0435\u043a\u0440\u0435\u0442\u043d\u044b\u0439 \u043a\u043b\u044e\u0447, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0434\u043b\u044f \u0448\u0438\u0444\u0440\u043e\u0432\u043a\u0438 &#8212; \u0440\u0430\u0441\u0448\u0438\u0444\u0440\u043e\u0432\u043a\u0438 \u0441\u043e\u043e\u0431\u0449\u0435\u043d\u0438\u0439.<\/p>\n<p>\u0410\u043b\u0438\u0441\u0430 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442 <\/p>\n<p>\u0411\u043e\u0431 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442 <\/p>\n<p>\u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043a\u0430\u043d\u043e\u043d\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u043f\u0440\u0438\u043c\u0435\u0440:<\/p>\n<ol>\n<li>\n<\/li>\n<li>\n<p>\u0410\u043b\u0438\u0441\u0430 \u0432\u044b\u0431\u0438\u0440\u0430\u0435\u0442 \u0437\u0430\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447 <\/p>\n<\/li>\n<li>\n<p>\u0411\u043e\u0431 \u0432\u044b\u0431\u0438\u0440\u0430\u0435\u0442 \u0437\u0430\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447 <\/p>\n<\/li>\n<li>\n<p>\u0410\u043b\u0438\u0441\u0430 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442 \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447 <\/p>\n<\/li>\n<li>\n<p>\u0411\u043e\u0431 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442 \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447 <\/p>\n<\/li>\n<li>\n<p>\u0410\u043b\u0438\u0441\u0430 \u0438 \u0411\u043e\u0431 \u043e\u0431\u043c\u0435\u043d\u0438\u0432\u0430\u044e\u0442\u0441\u044f \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u043c\u0438 \u043a\u043b\u044e\u0447\u0430\u043c\u0438<\/p>\n<\/li>\n<li>\n<p>\u0410\u043b\u0438\u0441\u0430 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442 \u043e\u0431\u0449\u0438\u0439 \u0441\u0435\u043a\u0440\u0435\u0442\u043d\u044b\u0439 \u043a\u043b\u044e\u0447 <\/p>\n<\/li>\n<li>\n<p>\u0411\u043e\u0431 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442 \u043e\u0431\u0449\u0438\u0439 \u0441\u0435\u043a\u0440\u0435\u0442\u043d\u044b\u0439 \u043a\u043b\u044e\u0447 <\/p>\n<\/li>\n<li>\n<p>\u0410\u043b\u0438\u0441\u0430 \u0438 \u0411\u043e\u0431 \u043f\u043e\u043b\u0443\u0447\u0438\u043b\u0438 \u043e\u0434\u0438\u043d \u0438 \u0442\u043e\u0442-\u0436\u0435 \u0441\u0435\u043a\u0440\u0435\u0442\u043d\u044b\u0439 \u043a\u043b\u044e\u0447 , \u043d\u0435 \u043f\u0435\u0440\u0435\u0434\u0430\u0432\u0430\u044f \u0435\u0433\u043e \u043f\u043e \u0441\u0435\u0442\u0438.<\/p>\n<\/li>\n<\/ol>\n<p>\u0422\u0435\u043f\u0435\u0440\u044c \u043f\u0440\u0438\u043c\u0435\u0440, \u043a\u043e\u0433\u0434\u0430 \u0437\u0430\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447 \u0440\u0430\u0432\u0435\u043d :<\/p>\n<ol>\n<li>\n<\/li>\n<li>\n<p>\u0410\u043b\u0438\u0441\u0430 \u0432\u044b\u0431\u0438\u0440\u0430\u0435\u0442 \u0437\u0430\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447 <\/p>\n<\/li>\n<li>\n<p>\u0411\u043e\u0431 \u0432\u044b\u0431\u0438\u0440\u0430\u0435\u0442 \u0437\u0430\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447 <\/p>\n<\/li>\n<li>\n<p>\u0410\u043b\u0438\u0441\u0430 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442 \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447 <\/p>\n<\/li>\n<li>\n<p>\u0411\u043e\u0431 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442 \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447 <\/p>\n<\/li>\n<li>\n<p>\u0410\u043b\u0438\u0441\u0430 \u0438 \u0411\u043e\u0431 \u043e\u0431\u043c\u0435\u043d\u0438\u0432\u0430\u044e\u0442\u0441\u044f \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u043c\u0438 \u043a\u043b\u044e\u0447\u0430\u043c\u0438<\/p>\n<\/li>\n<li>\n<p>\u0410\u043b\u0438\u0441\u0430 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442 \u043e\u0431\u0449\u0438\u0439 \u0441\u0435\u043a\u0440\u0435\u0442\u043d\u044b\u0439 \u043a\u043b\u044e\u0447 <\/p>\n<\/li>\n<li>\n<p>\u0411\u043e\u0431 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442 \u043e\u0431\u0449\u0438\u0439 \u0441\u0435\u043a\u0440\u0435\u0442\u043d\u044b\u0439 \u043a\u043b\u044e\u0447 <\/p>\n<\/li>\n<\/ol>\n<p>\u0417\u043b\u043e\u0443\u043c\u044b\u0448\u043b\u0435\u043d\u043d\u0438\u043a \u043f\u0435\u0440\u0435\u0445\u0432\u0430\u0442\u0438\u043b \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447  \u0438 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442 \u0437\u0430\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447 \u0442\u043e\u0439-\u0436\u0435 \u0410\u043b\u0438\u0441\u044b \u043f\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435 (1): <\/p>\n<p>\u0414\u0430\u043b\u0435\u0435, \u0434\u043b\u044f \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u044f \u0441\u0435\u043a\u0440\u0435\u0442\u043d\u043e\u0433\u043e \u043a\u043b\u044e\u0447\u0430  \u0435\u0441\u0442\u044c \u0434\u0432\u0430 \u0441\u043f\u043e\u0441\u043e\u0431\u0430:<\/p>\n<p>1 \u0441\u043f\u043e\u0441\u043e\u0431. \u0421 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043e\u0442\u043a\u0440\u044b\u0442\u043e\u0433\u043e \u043a\u043b\u044e\u0447\u0430 \u0411\u043e\u0431\u0430 <\/p>\n<\/p>\n<p>2 \u0441\u043f\u043e\u0441\u043e\u0431. \u0421\u0440\u0430\u0437\u0443, \u0435\u0441\u043b\u0438 \u0445\u043e\u0442\u044f \u0431\u044b \u043e\u0434\u0438\u043d \u0438\u0437 \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u0445 \u043a\u043b\u044e\u0447\u0435\u0439 \u0440\u0430\u0432\u0435\u043d , \u0442\u043e  \u0438\u043b\u0438 , \u043f\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435:<\/p>\n<p>\u0412\u043d\u0438\u043c\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u0442\u0435 \u043d\u0430 \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u044e\u044e \u0441\u0442\u0440\u043e\u043a\u0443 \u043b\u044e\u0431\u043e\u0433\u043e , \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440 \u0441\u043c. \u0440\u0438\u0441. \u0432\u044b\u0448\u0435 &#171;\u041d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0442\u0430\u0431\u043b\u0438\u0446 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439&#187;.<\/p>\n<p>\u042f \u043d\u0435 \u043d\u0430\u0448\u0435\u043b \u0432 \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u0445 \u0438\u0441\u0442\u043e\u0447\u043d\u0438\u043a\u0430\u0445 \u0437\u0430\u043f\u0440\u0435\u0442\u0430 \u043d\u0430 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u0435 \u0432 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435 \u0437\u0430\u043a\u0440\u044b\u0442\u043e\u0433\u043e \u043a\u043b\u044e\u0447\u0430 .<\/p>\n<p>\u0414\u0430\u043d\u043d\u043e\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0443\u043f\u043e\u043c\u0438\u043d\u0430\u0435\u0442\u0441\u044f \u0432 \u0441\u0442\u0430\u0442\u044c\u0435: S. C. Pohlig and M. E. Hellman, &#171;An improved algorithm for computing logarithms in GF(p) and its cryptographic significance.&#187; <a href=\"https:\/\/ee.stanford.edu\/~hellman\/publications\/28.pdf\" rel=\"noopener noreferrer nofollow\">https:\/\/ee.stanford.edu\/~hellman\/publications\/28.pdf<\/a>, IEEE Trans. Info. Theory 24 (1978), 106\u2013111.<\/p>\n<p>\u0412 \u0441\u0442\u0430\u0442\u044c\u0435 \u0443\u043a\u0430\u0437\u0430\u043d\u043e \u0447\u0442\u043e  \u0434\u043e\u043b\u0436\u043d\u043e \u0431\u044b\u0442\u044c \u043f\u0440\u043e\u0441\u0442\u044b\u043c \u0447\u0438\u0441\u043b\u043e\u043c \u0434\u043b\u044f \u043f\u043e\u0432\u044b\u0448\u0435\u043d\u0438\u044f \u0431\u0435\u0437\u043e\u043f\u0430\u0441\u043d\u043e\u0441\u0442\u0438.<\/p>\n<p>\u0415\u0449\u0435 \u0432 \u0441\u0442\u0430\u0442\u044c\u0435 \u043c\u043e\u0436\u043d\u043e \u0432\u0441\u0442\u0440\u0435\u0442\u0438\u0442\u044c \u0443\u043f\u043e\u043c\u0438\u043d\u0430\u043d\u0438\u0435 \u0442\u0440\u0438\u0432\u0438\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0441\u043b\u0443\u0447\u0430\u044f : &#171;<em>Also, restrictions might be imposed on K (e.g., ) to avoid simple but improbable transformations.<\/em>&#187; \u0412 \u043f\u0435\u0440\u0435\u0432\u043e\u0434\u0435: &#171;<em>\u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u043d\u0430 K \u043c\u043e\u0433\u0443\u0442 \u0431\u044b\u0442\u044c \u043d\u0430\u043b\u043e\u0436\u0435\u043d\u044b \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0438\u044f (\u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, ), \u0447\u0442\u043e\u0431\u044b \u0438\u0437\u0431\u0435\u0436\u0430\u0442\u044c \u043f\u0440\u043e\u0441\u0442\u044b\u0445, \u043d\u043e \u043c\u0430\u043b\u043e\u0432\u0435\u0440\u043e\u044f\u0442\u043d\u044b\u0445 \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0439.<\/em>&#187; ( &#8212; \u043a\u043b\u044e\u0447).<\/p>\n<p>\u0420\u0435\u0448\u0435\u043d\u0438\u0435: \u0437\u0430\u043f\u0440\u0435\u0442\u0438\u0442\u044c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0432 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435 \u0437\u0430\u043a\u0440\u044b\u0442\u043e\u0433\u043e \u043a\u043b\u044e\u0447\u0430 , \u0434\u043e\u043f\u043e\u043b\u043d\u044f\u0435\u043c \u0441\u043f\u0438\u0441\u043e\u043a \u0442\u0440\u0438\u0432\u0438\u0430\u043b\u044c\u043d\u044b\u0445 \u0441\u043b\u0443\u0447\u0430\u0435\u0432:<\/p>\n<p>\u041c\u043e\u0436\u043d\u043e \u043d\u0430\u0439\u0442\u0438 \u0435\u0449\u0435? \u041f\u043e\u043f\u0440\u043e\u0431\u0443\u0435\u043c.<\/p>\n<p>\u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0432\u043d\u0438\u043c\u0430\u0442\u0435\u043b\u044c\u043d\u043e &#171;\u043f\u0430\u0443\u043a\u0430&#187;, \u0441\u043c. \u0440\u0438\u0441. \u0432\u044b\u0448\u0435, \u043f\u043e\u0447\u0435\u043c\u0443 \u043e\u043d \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u043d?<\/p>\n<p>\u041f\u0440\u0438\u043c\u0438\u0442\u0438\u0432\u044b \u0441\u0433\u0440\u0443\u043f\u043f\u0438\u0440\u043e\u0432\u0430\u043d\u044b \u043f\u0430\u0440\u0430\u043c\u0438:<\/p>\n<figure class=\"\">\n<div><figcaption>\u041f\u0430\u0440\u043d\u044b\u0435 \u043f\u0440\u0438\u043c\u0438\u0442\u0438\u0432\u044b <\/figcaption><\/div>\n<\/figure>\n<p>\u041a\u043e\u0433\u0434\u0430-\u0442\u043e \u044f \u043d\u0435\u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u043e \u043f\u0440\u0435\u0434\u043f\u043e\u043b\u043e\u0436\u0438\u043b, \u0447\u0442\u043e \u044d\u0442\u0438 \u043f\u0430\u0440\u044b \u0432\u0437\u0430\u0438\u043c\u043d\u043e \u043f\u0440\u043e\u0441\u0442\u044b\u0435, \u043d\u0430 \u0441\u0430\u043c\u043e\u043c \u0434\u0435\u043b\u0435 \u043e\u043d\u0438 \u043c\u0443\u043b\u044c\u0442\u0438\u043f\u043b\u0438\u043a\u0430\u0442\u0438\u0432\u043d\u043e \u043e\u0431\u0440\u0430\u0442\u043d\u044b \u043f\u043e \u043c\u043e\u0434\u0443\u043b\u044e <a href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%9E%D0%B1%D1%80%D0%B0%D1%82%D0%BD%D0%BE%D0%B5_%D0%BF%D0%BE_%D0%BC%D0%BE%D0%B4%D1%83%D0%BB%D1%8E_%D1%87%D0%B8%D1%81%D0%BB%D0%BE\" rel=\"noopener noreferrer nofollow\">https:\/\/ru.wikipedia.org\/wiki\/\u041e\u0431\u0440\u0430\u0442\u043d\u043e\u0435_\u043f\u043e_\u043c\u043e\u0434\u0443\u043b\u044e_\u0447\u0438\u0441\u043b\u043e<\/a><\/p>\n<p>\u041f\u0440\u043e\u0432\u0435\u0440\u0438\u043c:<\/p>\n<ul>\n<li>\n<\/li>\n<li>\n<\/li>\n<\/ul>\n<p>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0433\u0440\u0430\u0444\u0438\u043a \u043f\u0435\u0440\u0432\u043e\u0439 \u043f\u0430\u0440\u044b <\/p>\n<figure class=\"full-width\">\n<div><figcaption>\u0422\u0430\u0431\u043b\u0438\u0446\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439  \u0432 \u0432\u0438\u0434\u0435 \u0433\u0440\u0430\u0444\u0438\u043a\u0430 \u0434\u043b\u044f \u043f\u0430\u0440\u044b \u043f\u0440\u0438\u043c\u0438\u0442\u0438\u0432\u043e\u0432 <\/figcaption><\/div>\n<\/figure>\n<p>\u0421\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u043e, \u043d\u0435 \u043f\u0440\u0430\u0432\u0434\u0430 \u043b\u0438? \u0438 \u0432 \u0442\u0430\u0431\u043b\u0438\u0447\u043d\u043e\u043c \u0432\u0438\u0434\u0435:<\/p>\n<figure class=\"\">\n<div><figcaption>\u0422\u0430\u0431\u043b\u0438\u0446\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439  \u0434\u043b\u044f \u043f\u0440\u0438\u043c\u0438\u0442\u0438\u0432\u043e\u0432 <\/figcaption><\/div>\n<\/figure>\n<p>\u041c\u044b \u0432\u044b\u044f\u0441\u043d\u0438\u043b\u0438 \u0432\u044b\u0448\u0435, \u0447\u0442\u043e  \u043c\u0443\u043b\u044c\u0442\u0438\u043f\u043b\u0438\u043a\u0430\u0442\u0438\u0432\u043d\u043e \u043e\u0431\u0440\u0430\u0442\u043d\u044b, \u043f\u0440\u043e\u0432\u0435\u0440\u0438\u043c \u043e\u0441\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u043f\u0430\u0440\u044b:<\/p>\n<ul>\n<li>\n<\/li>\n<li>\n<\/li>\n<li>\n<\/li>\n<li>\n<\/li>\n<li>\n<\/li>\n<\/ul>\n<p>\u0412\u0441\u0435 \u043f\u0430\u0440\u044b \u043c\u0443\u043b\u044c\u0442\u0438\u043f\u043b\u0438\u043a\u0430\u0442\u0438\u0432\u043d\u043e \u043e\u0431\u0440\u0430\u0442\u043d\u044b \u043f\u043e \u043c\u043e\u0434\u0443\u043b\u044e .<\/p>\n<p>\u0412\u043e\u0437\u0432\u0440\u0430\u0449\u0430\u0435\u043c\u0441\u044f \u043a DH, \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043f\u0440\u0438\u043c\u0435\u0440:<\/p>\n<ol>\n<li>\n<\/li>\n<li>\n<p>\u0410\u043b\u0438\u0441\u0430 \u0432\u044b\u0431\u0438\u0440\u0430\u0435\u0442 \u0437\u0430\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447 <\/p>\n<\/li>\n<li>\n<p>\u0411\u043e\u0431 \u0432\u044b\u0431\u0438\u0440\u0430\u0435\u0442 \u0437\u0430\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447 <\/p>\n<\/li>\n<li>\n<p>\u0410\u043b\u0438\u0441\u0430 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442 \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447 <\/p>\n<\/li>\n<li>\n<p>\u0411\u043e\u0431 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442 \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447 <\/p>\n<\/li>\n<li>\n<p>\u0410\u043b\u0438\u0441\u0430 \u0438 \u0411\u043e\u0431 \u043e\u0431\u043c\u0435\u043d\u0438\u0432\u0430\u044e\u0442\u0441\u044f \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u043c\u0438 \u043a\u043b\u044e\u0447\u0430\u043c\u0438<\/p>\n<\/li>\n<li>\n<p>\u0410\u043b\u0438\u0441\u0430 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442 \u043e\u0431\u0449\u0438\u0439 \u0441\u0435\u043a\u0440\u0435\u0442\u043d\u044b\u0439 \u043a\u043b\u044e\u0447 <\/p>\n<\/li>\n<li>\n<p>\u0411\u043e\u0431 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442 \u043e\u0431\u0449\u0438\u0439 \u0441\u0435\u043a\u0440\u0435\u0442\u043d\u044b\u0439 \u043a\u043b\u044e\u0447 <\/p>\n<\/li>\n<\/ol>\n<p>\u0412\u0440\u043e\u0434\u0435 \u0432\u0441\u0435 \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e, \u043d\u043e!<\/p>\n<ol>\n<li>\n<p>\u041d\u0430\u043c \u0438\u0437\u0432\u0435\u0441\u0442\u0435\u043d \u043f\u0440\u0438\u043c\u0438\u0442\u0438\u0432 , \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u043c\u0443\u043b\u044c\u0442\u0438\u043f\u043b\u0438\u043a\u0430\u0442\u0438\u0432\u043d\u043e \u043e\u0431\u0440\u0430\u0442\u043d\u044b\u0439  \u043f\u0440\u0438 \u043f\u043e\u043c\u043e\u0449\u0438 \u0440\u0430\u0441\u0448\u0438\u0440\u0435\u043d\u043d\u043e\u0433\u043e \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0430 \u0415\u0432\u043a\u043b\u0438\u0434\u0430 <a href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%A0%D0%B0%D1%81%D1%88%D0%B8%D1%80%D0%B5%D0%BD%D0%BD%D1%8B%D0%B9_%D0%B0%D0%BB%D0%B3%D0%BE%D1%80%D0%B8%D1%82%D0%BC_%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4%D0%B0\" rel=\"noopener noreferrer nofollow\">https:\/\/ru.wikipedia.org\/wiki\/\u0420\u0430\u0441\u0448\u0438\u0440\u0435\u043d\u043d\u044b\u0439_\u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c_\u0415\u0432\u043a\u043b\u0438\u0434\u0430<\/a><\/p>\n<\/li>\n<li>\n<p>\u0421\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u0435\u043c  \u0441 \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u043c\u0438 \u043a\u043b\u044e\u0447\u0430\u043c\u0438, \u0443 \u0411\u043e\u0431\u0430 \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447 , \u0437\u043d\u0430\u0447\u0438\u0442 \u0437\u0430\u043a\u0440\u044b\u0442\u044b\u0439 \u043a\u043b\u044e\u0447 \u0411\u043e\u0431\u0430 \u0440\u0430\u0432\u0435\u043d , \u0441\u043c. \u0440\u0438\u0441. \u043d\u0438\u0436\u0435<\/p>\n<\/li>\n<li>\n<p>\u0412\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u0441\u0435\u043a\u0440\u0435\u0442\u043d\u044b\u0439 \u043a\u043b\u044e\u0447 <\/p>\n<\/li>\n<\/ol>\n<figure class=\"\">\n<div><figcaption>\u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0437\u0430\u043a\u0440\u044b\u0442\u043e\u0433\u043e \u043a\u043b\u044e\u0447\u0430  \u043f\u043e <\/figcaption><\/div>\n<\/figure>\n<p>\u0411\u0438\u043d\u0433\u043e &#8212; \u0432\u043e\u0442 \u0432\u0442\u043e\u0440\u0430\u044f &#171;\u0434\u044b\u0440\u043a\u0430&#187;, \u0441\u043e\u0433\u043b\u0430\u0441\u043d\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435:<\/p>\n<p>\u042d\u0442\u0443 \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u043c\u043e\u0436\u043d\u043e \u0432\u044b\u0432\u0435\u0441\u0442\u0438 \u0438\u0437 \u041c\u0430\u043b\u043e\u0439 \u0442\u0435\u043e\u0440\u0435\u043c\u044b \u0424\u0435\u0440\u043c\u0430 <a href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%9C%D0%B0%D0%BB%D0%B0%D1%8F_%D1%82%D0%B5%D0%BE%D1%80%D0%B5%D0%BC%D0%B0_%D0%A4%D0%B5%D1%80%D0%BC%D0%B0\" rel=\"noopener noreferrer nofollow\">https:\/\/ru.wikipedia.org\/wiki\/\u041c\u0430\u043b\u0430\u044f_\u0442\u0435\u043e\u0440\u0435\u043c\u0430_\u0424\u0435\u0440\u043c\u0430<\/a><\/p>\n<ol>\n<li>\n<\/li>\n<li>\n<\/li>\n<li>\n<p>.<\/p>\n<\/li>\n<li>\n<p> &#8212; \u044d\u0442\u043e \u0438 \u0435\u0441\u0442\u044c \u043e\u0431\u0440\u0430\u0442\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e &#8212; <\/p>\n<\/li>\n<\/ol>\n<p>\u0414\u043e\u043f\u043e\u043b\u043d\u044f\u0435\u043c \u0441\u043f\u0438\u0441\u043e\u043a \u0442\u0440\u0438\u0432\u0438\u0430\u043b\u044c\u043d\u044b\u0445 \u0441\u043b\u0443\u0447\u0430\u0435\u0432:<\/p>\n<p>\u0411\u043e\u043b\u044c\u0448\u0435 \u0443\u044f\u0437\u0432\u0438\u043c\u043e\u0441\u0442\u0435\u0439 \u043f\u043e\u043a\u0430 \u043d\u0435 \u043d\u0430\u0448\u0435\u043b.<\/p>\n<p>\u041c\u043e\u0436\u043d\u043e \u0435\u0449\u0435 \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0433\u0440\u0430\u0444\u0438\u043a \u043f\u043e\u043b\u044f  (\u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u043e\u0441\u0442\u044c \u0442\u0430\u043a\u0436\u0435 \u0432\u0438\u0434\u043d\u0430) \u0438 \u0442\u0430\u0431\u043b\u0438\u0446\u0443, \u0441\u043c. \u0440\u0438\u0441\u0443\u043d\u043a\u0438 \u043d\u0438\u0436\u0435:<\/p>\n<figure class=\"full-width\">\n<div><figcaption>\u0413\u0440\u0430\u0444\u0438\u043a  \u043f\u043e \u0434\u0432\u0443\u043c \u043f\u0430\u0440\u0430\u043c \u043f\u0440\u0438\u043c\u0438\u0442\u0438\u0432\u043e\u0432: <\/figcaption><\/div>\n<\/figure>\n<figure class=\"full-width\">\n<div><figcaption>\u0422\u0430\u0431\u043b\u0438\u0446\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 <\/figcaption><\/div>\n<\/figure>\n<h2>\u0417\u0430\u043a\u043b\u044e\u0447\u0435\u043d\u0438\u0435<\/h2>\n<p>\u041f\u0440\u0435\u0434\u0443\u043f\u0440\u0435\u0436\u0434\u0435\u043d\u0438\u044f \u043e \u043f\u0440\u0435\u0434\u043f\u043e\u043b\u0430\u0433\u0430\u0435\u043c\u043e\u0439 \u0441\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 DLOG, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440:<\/p>\n<ul>\n<li>\n<p>&#171;<em>\u041a\u0440\u0438\u043f\u0442\u043e\u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0441\u0442\u043e\u0439\u043a\u043e\u0441\u0442\u044c \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0430 \u0414\u0438\u0444\u0444\u0438 \u2014 \u0425\u0435\u043b\u043b\u043c\u0430\u043d\u0430 (\u0442\u043e \u0435\u0441\u0442\u044c \u0441\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u044c \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f  \u043f\u043e \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u043c ) \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0430 \u043d\u0430 <\/em><strong><em>\u043f\u0440\u0435\u0434\u043f\u043e\u043b\u0430\u0433\u0430\u0435\u043c\u043e\u0439<\/em><\/strong><em> \u0441\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u0434\u0438\u0441\u043a\u0440\u0435\u0442\u043d\u043e\u0433\u043e \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f.<\/em>&#187;  \u0424\u043e\u0440\u043c\u0430\u0442\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435 \u0441\u043e\u0445\u0440\u0430\u043d\u0435\u043d\u043e, \u0438\u0441\u0442\u043e\u0447\u043d\u0438\u043a: <a href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%9F%D1%80%D0%BE%D1%82%D0%BE%D0%BA%D0%BE%D0%BB_%D0%94%D0%B8%D1%84%D1%84%D0%B8_%E2%80%94_%D0%A5%D0%B5%D0%BB%D0%BB%D0%BC%D0%B0%D0%BD%D0%B0#%D0%9A%D1%80%D0%B8%D0%BF%D1%82%D0%BE%D0%B3%D1%80%D0%B0%D1%84%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0%D1%8F_%D1%81%D1%82%D0%BE%D0%B9%D0%BA%D0%BE%D1%81%D1%82%D1%8C\" rel=\"noopener noreferrer nofollow\">https:\/\/ru.wikipedia.org\/wiki\/\u041f\u0440\u043e\u0442\u043e\u043a\u043e\u043b_\u0414\u0438\u0444\u0444\u0438_\u2014_\u0425\u0435\u043b\u043b\u043c\u0430\u043d\u0430#\u041a\u0440\u0438\u043f\u0442\u043e\u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u0430\u044f_\u0441\u0442\u043e\u0439\u043a\u043e\u0441\u0442\u044c<\/a><\/p>\n<\/li>\n<li>\n<p>&#171;<em>A cryptographic system is described which is secure if and only if computing logarithms over  is infeasible.<\/em>&#187; (\u043c\u043e\u0439 \u043f\u0435\u0440\u0435\u0432\u043e\u0434: &#171;<em>\u041e\u043f\u0438\u0441\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u043a\u0440\u0438\u043f\u0442\u043e\u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0441\u0438\u0441\u0442\u0435\u043c\u0430, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0431\u0435\u0437\u043e\u043f\u0430\u0441\u043d\u043e\u0439 \u0442\u043e\u0433\u0434\u0430 \u0438 \u0442\u043e\u043b\u044c\u043a\u043e \u0442\u043e\u0433\u0434\u0430, \u043a\u043e\u0433\u0434\u0430 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u043e\u0432 \u043f\u043e  \u043d\u0435\u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e.<\/em>&#171;) \u0418\u0441\u0442\u043e\u0447\u043d\u0438\u043a: S. C. Pohlig and M. E. Hellman, &#171;<em>An improved algorithm for computing logarithms in GF(p) and its cryptographic significance.<\/em>&#187; <a href=\"https:\/\/ee.stanford.edu\/~hellman\/publications\/28.pdf\" rel=\"noopener noreferrer nofollow\">https:\/\/ee.stanford.edu\/~hellman\/publications\/28.pdf<\/a> IEEE Trans. Info. Theory 24 (1978), 106\u2013111.<\/p>\n<\/li>\n<\/ul>\n<p>\u0427\u0442\u043e \u043a\u0430\u0441\u0430\u0435\u0442\u0441\u044f \u043e\u043f\u0438\u0441\u0430\u043d\u043d\u044b\u0445 \u0432 \u0434\u0430\u043d\u043d\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u0443\u044f\u0437\u0432\u0438\u043c\u043e\u0441\u0442\u044f\u0445, \u0442\u043e \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u043d\u0435 \u0442\u0430\u043a\u0438\u0435 \u0431\u043e\u043b\u044c\u0448\u0438\u0435. \u041d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0432 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u043d\u043e\u0435 \u043e\u0431\u0435\u0441\u043f\u0435\u0447\u0435\u043d\u0438\u0435, \u0433\u0435\u043d\u0435\u0440\u0438\u0440\u0443\u044e\u0449\u0435\u0435 \u0437\u0430\u043a\u0440\u044b\u0442\u044b\u0435 \u043a\u043b\u044e\u0447\u0438, \u0434\u043e\u0431\u0430\u0432\u0438\u0442\u044c \u0438\u0441\u043a\u043b\u044e\u0447\u0435\u043d\u0438\u044f: , \u043e\u0441\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u0431\u044b\u043b\u0438 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b \u0438 \u0440\u0430\u043d\u0435\u0435.<\/p>\n<p>\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0443\u044f\u0437\u0432\u0438\u043c\u043e\u0441\u0442\u0438 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0442 \u0438 \u0434\u043e\u043b\u0436\u043d\u044b \u0431\u044b\u0442\u044c \u043e\u0431\u0449\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b.<\/p>\n<p>\u0415\u0441\u043b\u0438 \u043d\u0430\u0448\u043b\u0438 \u043e\u0448\u0438\u0431\u043a\u0438, \u043f\u0438\u0448\u0438\u0442\u0435 \u043a\u0430\u043c\u043c\u0435\u043d\u0442\u044b.<\/p>\n<p>&#171;\u041f\u043e\u0438\u0433\u0440\u0430\u0442\u044c\u0441\u044f&#187; \u0441 \u0442\u0430\u0431\u043b\u0438\u0446\u0430\u043c\u0438 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 \u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u043f\u0440\u0438\u043c\u0438\u0442\u0438\u0432\u044b \u043c\u043e\u0436\u043d\u043e \u0432 \u0441\u0435\u0440\u0432\u0438\u0441\u0435 <a href=\"https:\/\/dlog.vladlin.ru\/\" rel=\"noopener noreferrer nofollow\">https:\/\/dlog.vladlin.ru\/<\/a> (AS IS)<\/p>\n<p>\u041d\u0430 \u0437\u0430\u0434\u0430\u0447\u0435 DLOG, \u043a\u0440\u043e\u043c\u0435 \u043f\u0440\u043e\u0442\u043e\u043a\u043e\u043b\u0430 \u0414\u0438\u0444\u0444\u0438-\u0425\u0435\u043b\u043b\u043c\u0430\u043d\u0430, \u0431\u0430\u0437\u0438\u0440\u0443\u044e\u0442\u0441\u044f \u0438 \u0434\u0440\u0443\u0433\u0438\u0435, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440:<\/p>\n<ul>\n<li>\n<p>\u0421\u0445\u0435\u043c\u0430 \u042d\u043b\u044c-\u0413\u0430\u043c\u0430\u043b\u044f <a href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%A1%D1%85%D0%B5%D0%BC%D0%B0_%D0%AD%D0%BB%D1%8C-%D0%93%D0%B0%D0%BC%D0%B0%D0%BB%D1%8F\" rel=\"noopener noreferrer nofollow\">https:\/\/ru.wikipedia.org\/wiki\/\u0421\u0445\u0435\u043c\u0430_\u042d\u043b\u044c-\u0413\u0430\u043c\u0430\u043b\u044f<\/a><\/p>\n<\/li>\n<li>\n<p>\u041a\u0440\u0438\u043f\u0442\u043e\u0441\u0438\u0441\u0442\u0435\u043c\u0430 \u041c\u044d\u0441\u0441\u0438 \u2014 \u041e\u043c\u0443\u0440\u044b <a href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%9A%D1%80%D0%B8%D0%BF%D1%82%D0%BE%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B0_%D0%9C%D1%8D%D1%81%D1%81%D0%B8_%E2%80%94_%D0%9E%D0%BC%D1%83%D1%80%D1%8B\" rel=\"noopener noreferrer nofollow\">https:\/\/ru.wikipedia.org\/wiki\/\u041a\u0440\u0438\u043f\u0442\u043e\u0441\u0438\u0441\u0442\u0435\u043c\u0430_\u041c\u044d\u0441\u0441\u0438_\u2014_\u041e\u043c\u0443\u0440\u044b<\/a><\/p>\n<\/li>\n<li>\n<p>Digital Signature Algorithm <a href=\"https:\/\/ru.wikipedia.org\/wiki\/DSA\" rel=\"noopener noreferrer nofollow\">https:\/\/ru.wikipedia.org\/wiki\/DSA<\/a><\/p>\n<\/li>\n<\/ul>\n<p>\u041d\u0430\u0434\u043e \u043f\u0440\u043e\u0432\u0435\u0440\u0438\u0442\u044c \ud83d\ude42<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p><!----><!----><\/div>\n<p><!----><!----><br \/> \u0441\u0441\u044b\u043b\u043a\u0430 \u043d\u0430 \u043e\u0440\u0438\u0433\u0438\u043d\u0430\u043b \u0441\u0442\u0430\u0442\u044c\u0438 <a href=\"https:\/\/habr.com\/ru\/articles\/918742\/\"> https:\/\/habr.com\/ru\/articles\/918742\/<\/a><br \/><\/br><\/br><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-463533","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=\/wp\/v2\/posts\/463533","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=463533"}],"version-history":[{"count":0,"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=\/wp\/v2\/posts\/463533\/revisions"}],"wp:attachment":[{"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=463533"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=463533"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=463533"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}