A Symmetric Cryptoalgorithm Based on a Hierarchical Residue Number System
Ihor Yakymenko, Mykhailo M. Kasianchuk, Olesia Martyniuk, Serhii Martyniuk · International Journal of Computing · 2025
The paper develops a symmetric cryptoalgorithm based on a hierarchical system of remainder classes that allows to efficiently encrypt text messages using the remainders from dividing the numerical form of the plaintext into the corresponding modules. The peculiarity of this algorithm is its stepwise structure, which allows to gradually reduce the bit depth of modules and operands at each level. The software implementation and relevant experimental studies have shown that the abovementioned algorithm is highly resistant to cryptanalytic attacks due to the multi-level encryption structure and the use of large primes as modules at the first levels. It is established that the cryptographic strength increases with the number of modules, their bit depth, and hierarchical levels. A comparative analysis of the stability of the proposed algorithm and the AES-256 algorithm is carried out. It is determined at which values of the input parameters (bit depth of the modules, number of modules and hierarchy levels) the proposed algorithm demonstrates stability comparable to AES-256, while providing greater flexibility of settings and computational efficiency. The proposed methodology allows changing the number and bit depth of modules, the number of hierarchy levels, and other parameters to achieve the required degree of protection, making the algorithm versatile for different attacks and computing resources. This allows you to adaptively adjust the system parameters to achieve the optimal ratio between the level of cryptographic strength and the speed of computation.