Paper 2020/589

Developing Symmetric Encryption Methods Based On Residue Number System And Investigating Their Cryptosecurity

Mykhailo Kasianchuk, Mikolaj Karpinski, Roman Kochan, Volodymyr Karpinskyi, Grzegorz Litawa, Inna Shylinska, and Igor Yakymenko

Abstract

This paper proposes new symmetric cryptoalgorithms of Residue Number System and its Modified Perfect Form. According to the first method, ciphertext is regarded as a set of residues to the corresponding sets of modules (keys) and decryption or decimal number recovery from its residues takes place according to the Chinese remainder theorem. To simplify the calculations, it is proposed to use a Modified Perfect Form of Residue Number System, which leads to a decrease in the number of arithmetic operations (in particular, finding the inverse and multiplying by it) during the decryption process. Another method of symmetric encryption based on the Chinese remainder theorem can be applied when fast decryption is required. In this algorithm, the plaintext block is divided into sub-blocks that are smaller than the corresponding module and serve as remainders on dividing some number, which is a ciphertext, by these modules. Plaintext recovery is based on finding the ciphertext remainders to the corresponding modules. Examples of cryptoalgorithms implementation and their encryption schemes are given. Cryptosecurity of the proposed methods is estimated on the basis of the Prime number theorem and the Euler function. It is investigated which bitness and a number of modules are required for the developed symmetric security systems to ensure the same security level as the largest length key of the AES algorithm does. It is found that as the number of modules increases, their bitness decreases. Graphical dependencies of cryptoanalysis complexity on bitness and a number of modules are built. It is shown that with the increase of specified parameters, the cryptosecurity of the developed methods also increases.