Residue Number System Asymmetric Cryptoalgorithms

Theoretical foundations of asymmetric encryption based on the residue number system and its modified perfect form are developed. The moduli of the residue number system are considered to be secret keys. When recovering a number from its residues, multiplication by arbitrarily selected coefficients (public keys) takes place. It is established that cryptostability of the proposed algorithms is based on solving the problem of factorization or exhaustive search of sets of moduli. The developed approaches allow us to increase the block of plaintext almost indefinitely, eliminating the need to use different encryption modes.