A Cryptanalytic Approach to Breaking RSA Encryption Using Public Key, with Proposed Improvement Leveraging Prime Number Distribution Patterns

Abstract

RSA algorithm, a widely used public-key cryptosystem, relies on the difficulty of factoring large composite numbers into their prime factors. However, advancements in computational power and factorization techniques have introduced potential threats to its security. As RSA remains a cornerstone of modern cryptography, the need for improved in its security measures is paramount in the face of evolving computational challenges. This study presents a cryptanalytic examination of the RSA encryption scheme and proposes an improvement that leverages prime number distribution patterns to strengthen data security. Several mathematical methods which involve RSA key generation and its encryption/decryption process, ASCII Table, mapping as well as the Sieve of Eratosthenes were applied in the study. The research analyses how RSA public parameters and encoding methods can reveal structural weaknesses when subjected to mathematical scrutiny. To address these vulnerabilities, a modified scheme is introduced, in which plaintext characters are mapped using prime distribution patterns. This substitution increases ciphertexts randomness and minimizes predictable patterns between plaintexts and ciphertexts. Experimental evaluation demonstrates that the proposed improvement enhances resistance to analytical attacks while maintaining RSA operational compatibility. The study contributes to the on-going development of more secure and efficient public-key cryptographic systems.