DOI
10.34229/KCA2522-9664.25.5.2
UDC 51.681.3
S. Kryvyi
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine,
sl.krivoi@gmail.com
INFORMATION EXCHANGE SYSTEM BASED ON MAPS OF RINGS
Abstract. A cryptosystem for information exchange between subscribers based on surjective mappings of finite associative commutative rings with unity and systems of linear congruences over such rings is proposed. Algorithms for constructing surjective mappings of rings are presented, as well as a protocol for information exchange and the computational features of the means for implementing the protocol. The system does not require cumbersome calculations and construction of ring operation tables, and its stability is based on the combinatorial complexity of the set of surjective mappings and isomorphisms between finite rings of relatively small orders. The algorithms for solving systems of linear congruences that appear in the information exchange protocol are used to encrypt messages and have polynomial complexity. The operation of the cryptosystem is demonstrated with examples.
Keywords: cryptography, symmetric cryptosystem, finite rings, isomorphism, system of linear congruences.
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