Symmetric System for Exchange Information on the Base of Surjective Isomorphism of Rings
Sergiy Kryvyi, Volodymyr Opanasenko, Olena Grinenko, Yulia Nortman · 2022
The paper focuses on the building of a cryptosystem by using finite associative-commutative rings with unity. The algorithms for constructing such rings and exchanging information between subscribers on the basis of a special case of isomorphisms (surjective isomorphisms) are described. Encryption and decryption processes in ring Gkof order$k$are reduced to computation over ring Zk(residues modulo$k$) by using the linear Diophantine equations over ring ZkThe complexity of computations in cryptosystems is relatively simple but using surjective isomorphism, all computations are performed over an area that is inaccessible to hackers. The advantages of the system are that: a) the method of frequency analysis is not applicable to it. b) we avoid building tables of ring operations by using surjective isomorphism; c) the rings can be chosen with relatively small orders, which simplifies calculations during encryption and decryption; and d) the solution algorithm of system linear Diophantine equations is polynomial. The disadvantage of our system is that the length of the encryption text is twice as large as the length of the message.