The use of mathematical linguistic methods in creating secret sharing threshold algorithms

This publication discusses new opportunities for creating threshold schemes for secret sharing arising from the use of mathematical linguistic formalisms. Such methods are based on known threshold schemes of information splitting extended by adding an extra stage at which bit blocks of the shared information are coded using suitably defined context-free grammars. In practice, this will help with developing new algorithms, which besides allowing information sharing will also make it possible to obtain protocols for the confidential exchange of this information with or without involving a trusted instance. Such protocols will contribute to the development of modern cryptographic techniques and future computer science

1. Introduction

One interesting subject associated with modern cryptography is the development of algorithms and protocols for splitting and sharing information. Such algorithms were developed as early as the, but the increased demand for new solutions has meant that scientific circles have kept looking for newer methods of ensuring the confidentiality of information which is shared between the authorised group of participants in a given protocol. Known secret sharing methods have very good mathematical properties and meet all requirements concerning the security of individual components of the shared secret. However, it is worth noting that new areas for using such information splitting techniques have appeared now. Such new areas include, for example, the possibilities of intelligently splitting or managing the components of a secret in state administration institutions, military formations or even industrial entities. In such cases, there is often a need to create new protocols enabling the information to be intelligently split and then distributed between authorised users. This tasks should frequently be performed taking into account the hierarchical management structure and access to confidential data.

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