Cryptanalysis of RSA Cryptosystem: Prime Factorization using Genetic Algorithm
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910517837168640 |
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| author | Mobin, Mahadee Al Kamrujjaman, Md |
| author_facet | Mobin, Mahadee Al Kamrujjaman, Md |
| contents | Prime factorization has been a buzzing topic in the field of number theory since time unknown. However, in recent years, alternative avenues to tackle this problem are being explored by researchers because of its direct application in the arena of cryptography. One of such applications is the cryptanalysis of RSA numbers, which requires prime factorization of large semiprimes. Based on numerical experiments, this paper proposes a conjecture on the distribution of digits on prime of infinite length. This paper infuses the theoretical understanding of primes to optimize the search space of prime factors by shrinking it upto 98.15%, which, in terms of application, has shown 26.50% increase in the success rate and 41.91% decrease of the maximum number of generations required by the genetic algorithm used traditionally in the literature. This paper also introduces a variation of the genetic algorithm named Sieve Method that is fine-tuned for factorization of big semi-primes, which was able to factor numbers up to 23 decimal digits with 84% success rate. Our findings shows that sieve methods on average has achieved 321.89% increase in success rate and 64.06% decrement in the maximum number of generations required for the algorithm to converge compared to the existing literatures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05944 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cryptanalysis of RSA Cryptosystem: Prime Factorization using Genetic Algorithm Mobin, Mahadee Al Kamrujjaman, Md General Mathematics Prime factorization has been a buzzing topic in the field of number theory since time unknown. However, in recent years, alternative avenues to tackle this problem are being explored by researchers because of its direct application in the arena of cryptography. One of such applications is the cryptanalysis of RSA numbers, which requires prime factorization of large semiprimes. Based on numerical experiments, this paper proposes a conjecture on the distribution of digits on prime of infinite length. This paper infuses the theoretical understanding of primes to optimize the search space of prime factors by shrinking it upto 98.15%, which, in terms of application, has shown 26.50% increase in the success rate and 41.91% decrease of the maximum number of generations required by the genetic algorithm used traditionally in the literature. This paper also introduces a variation of the genetic algorithm named Sieve Method that is fine-tuned for factorization of big semi-primes, which was able to factor numbers up to 23 decimal digits with 84% success rate. Our findings shows that sieve methods on average has achieved 321.89% increase in success rate and 64.06% decrement in the maximum number of generations required for the algorithm to converge compared to the existing literatures. |
| title | Cryptanalysis of RSA Cryptosystem: Prime Factorization using Genetic Algorithm |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2407.05944 |