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Research Article Open access CC BY 4.0

Factorization Algorithm for Semi-primes and the Cryptanalysis of Rivest-Shamir-Adleman (RSA) Cryptography

Richard Omollo, Arnold Okoth

Asian Journal of Research in Computer Science · pp. 85–95 · Published 18 Apr 2024

10.9734/ajrcos/2024/v17i6458

Abstract

This paper introduces a new factoring algorithm called Anorld’s Factorization Algorithm that utilizes semi-prime numbers and their implications for the cryptanalysis of the Rivest-Shamir-Adleman (RSA) cryptosystem. While using the concepts of number theory and algorithmic design, we advance a novel approach that notably enhances the efficiency of factoring large semi-prime numbers compared to other algorithms that have been developed earlier. In our approach, we propose a three-step algorithm that factorizes relatively large semi-primes in polynomial time. We have introduced factorization up to 12-digit semi-prime using Wolfram|Alpha, a mathematical software suitable for exploring polynomials. Additionally, we have discussed the implications of the new algorithm for the security of RSA-based cryptosystems. In conclusion, our research work emphasizes the important role of factoring algorithms in the cryptanalysis of RSA cryptosystems and proposes a novel approach that bolsters the efficiency and effectiveness of semi-prime factorization, thereby informing the development of more powerful cryptographic protocols.

Arnold’s Factorization Algorithm (A.F.A.) modular factorial euclidean algorithm RSA cryptography

References (8)

  1. 1 The Physics of Quantum Information [DOI]
  2. 2 Origins of the analysis of the Euclidean algorithm [DOI]
  3. 3 An Efficient RSA Public Key Encryption Scheme [DOI]
  4. 4 Quantum Computing and Shor's Algorithm
  5. 5 Large Semi Primes Factorization with Its Implications to RSA Cryptosystems [DOI]
  6. 6 Implementation of Shor’s Quantum Factoring Algorithm Using ProjectQ Framework [DOI]
  7. 7 Full Euclidean Algorithm by Means of a Steady Walk [DOI]
  8. 8 Large semi primes factorization with its implications to RSAcryptosystems [DOI]

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