{"id":402160,"date":"2024-06-29T16:19:42","date_gmt":"2024-06-29T16:19:42","guid":{"rendered":"http:\/\/savepearlharbor.com\/?p=402160"},"modified":"-0001-11-30T00:00:00","modified_gmt":"-0001-11-29T21:00:00","slug":"","status":"publish","type":"post","link":"https:\/\/savepearlharbor.com\/?p=402160","title":{"rendered":"Instant Digital Signature Mode<\/span>"},"content":{"rendered":"
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We adhere to established tradition and continue to present the latest findings. In this note, we discuss the Instant Digital Signature (IDS) mode, which was announced earlier<\/u><\/a>. While the main content of the IDS mode was already disclosed in a previous publication<\/u><\/a>, we believe that additional specifications will improve understanding.<\/p>\n

It should be emphasized that the IDS is not a distinct type of signature, but rather a special mode in which any known digital signature (DS) scheme can be used. In other words, we do not take responsibility for developing a new scheme, but rather propose a practical way to apply existing schemes.<\/p>\n

As the name suggests, the IDS mode operates in real-time, specifically, at the moment of signature generation. This means that the mode is used to certify data that is directly associated with an identifying entity, as confirmed in a previously presented proof. Such proof can be obtained through executing an interactive identification protocol, which is necessary for justifying the IDS mode. When discussing this combination, we assume that certain unique variables from the current identification session are used in generating the signature. It is important to understand that these variables are ephemeral by design and only have an effect within the current session.<\/p>\n

It should be noted that in this publication<\/u><\/a>, we use personal data assurance as an example, which is perhaps the most natural application for the IDS mode.<\/p>\n

We demonstrate that the IDS mode is compatible with any known DS scheme. However, it is an open question whether this mode can be used with arbitrary identification protocols. On the other hand, the IDS mode is easily combined with an interactive identification protocol that enables the generation of a shared secret session key, which was created in the development of the protocol presented in this note<\/u><\/a>.<\/p>\n

We do not provide formal proofs in this text, but rather present examples to convey the essence of our findings. Unfortunately, we could not avoid using formal notation, but we hope that it will not pose any difficulties, as all necessary notation was introduced in our earlier publication<\/u><\/a>. Additionally, we use standard mathematical notation adopted in specialized literature, such as [Cohen_etc._2006].<\/p>\n

Interactive Identification Protocol<\/strong><\/p>\n

First of all, let us recall what an interactive identification protocol is. In fact, this is a game of two participants<\/u>, each of which is endowed with its own role. To avoid unnecessary complications, we will deliberately limit the number of subjects of interaction.<\/p>\n

There are two distinct roles: \"P\" (Prover) and \"V\" (Verifier). \"P\" provides proof of knowledge, such as a secret, which \"V\" then verifies using a decision rule. The verdict can be positive (evidence accepted), negative (evidence rejected), or indeterminate. Typically, upon acceptance or rejection of the evidence, a specific action is initiated. For example, a common scenario is when \"P\" requests access to a resource, which is granted if \"V\" accepts the proof. There are other applications for this protocol as well.<\/p>\n

Identification protocols belong to a more general class of \"\\hbox{$\\Sigma$-protocols}\", which were first introduced in [Cramer_1996]. \"P\" and \"V\" are modeled using a probabilistic interactive Turing machine, and the \"\\hbox{$\\Sigma$-protocols}\" itself is an interactive proof scheme based on Arthur-Merlin game style [Babai_Moran_1988], in which \"V\" always chooses some variable with a random distribution.<\/p>\n

Let’s focus on identification protocols that rely on asymmetric cryptography.\u00a0<\/p>\n

The interactive identification protocol can be represented by the following diagram:<\/p>\n

\"P<\/p>\n

It is clear that three messages are transmitted during the protocol: witness, challenge, <\/em>and response<\/em>. In this case, \"P\" transmits two messages (witness<\/em> and response<\/em>), and \"V\" transmits only one message (challenge<\/em>). The purpose of each message is clear from its name.\u00a0<\/p>\n

Let’s call the independent variables with a random distribution that change from one protocol session to another as the ephemeris<\/em>. In cryptographic terms, ephemeris is equivalent to secret keys. To reveal an unknown ephemeris, it is necessary to find a solution to some computational complexity problem or to undertake a brute force attack.<\/p>\n

It is assumed that each participant has a pair of unique keys: a secret key and a public key. Additionally, proper certificates have been issued for the public keys.<\/p>\n

The parties do the following:<\/p>\n