Abstract :

Cryptography secures information through encryption, allowing only authorized access. The RSA algorithm, which relies on the difficulty of factoring  where  and  are primes, is a popular public-key cryptosystem. Advances in factorization techniques and computing power necessitate improvements to methods for enhanced security. This study proposes a multi-prime RSA permutation cryptosystem based on the algebraic structure of a clear ring as a modification of RSA. It uses three primes  to form modulus , increasing modulus complexity and thus security. Permutation is applied in binary code form to produce more random ciphertext, alongside the application of a clear ring structure, specifically, the ring of integers modulo 256 with addition and multiplication modulo 256 based on ASCII. This ring allows each element to be expressed as a sum of a unit and a regular unit. The algorithm strengthens key generation and creates varied representations for the same plaintext through unit and regular unit addition, complicating cryptanalysis. Permutation further randomizes ciphertext. However, the method requires careful implementation to avoid errors. This innovation supports digital security.

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Keywords :

Clear Ring, Cryptography, Permutation, Ring, RSA, RSA Multi-Prime.

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