Cryptanalysis of RSA: Integer Prime Factorization Using Genetic Algorithms

Rutkowski, Emilia; Houghten, Sheridan

doi:10.1109/cec48606.2020.9185728

Cited by 8 publications

(4 citation statements)

References 13 publications

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“…Algoritme RSA didasarkan pada masalah faktorisasi bilangan bulat (IFP), sedangkan Algoritme El-Gamal didasarkan pada masalah logaritma diskrit (DLP), keduanya memberikan kecepatan komputasi untuk kriptosistem asimetris dan bergantung pada kesulitan penyelesaian kedua masalah ini (Rutkowski & Houghten, 2020) (Rezal et al, 2018) (Meneses et al, 2016). IFP dari Algoritme RSA adalah kesulitan faktorisasi yang digunakan pada generate key Algoritme RSA (N=p x q) dan (e x d ≡1 mod Ф(N)).…”

Section: Pendahuluanunclassified

Kriptosistem Hybrid Algoritme RSA dan El-Gamal Menggunakan Socket TCP pada Instant Messaging

Aminudin,

Hakim,

Nuryasin

et al. 2024

JRST

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Kriptografi adalah ilmu yang digunakan untuk mengamankan pesan agar hanya dapat dibaca oleh pihak yang berwenang. Salah satu teknik kriptografi yang umum digunakan adalah RSA dan El-Gamal. RSA adalah teknik kriptografi asimetris yang menggunakan kunci publik dan kunci pribadi untuk enkripsi dan dekripsi pesan. Sementara El-Gamal adalah teknik kriptografi yang juga asimetris, tetapi menggunakan operasi eksponensial modular pada bilangan prima sebagai dasar dari Algoritmenya. Pada paper ini akan dibahas kombinasi Teknik Algoritme RSA dan El-Gamal untuk mempersulit memecahkan pesan bagi pihak yang tidak punya kepentingan. Dalam metode ini, pesan dienkripsi dengan El-Gamal menggunakan kunci sesi yang hanya diketahui oleh pengirim dan penerima. Kunci sesi ini kemudian dienkripsi dengan RSA untuk memastikan bahwa hanya penerima yang dapat membaca pesan tersebut. Berdasarkan hasil pengujian menunjukkan bahwa metode yang diusulkan mampu menyulitkan pembacaan pesan bagi pihak yang tidak berkepentingan dibandingkan dengan menggunakan RSA atau El-Gamal secara terpisah dengan menggunakan menggunakan metode penyerangan baby step-giant step.

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Section: Pendahuluanunclassified

Kriptosistem Hybrid Algoritme RSA dan El-Gamal Menggunakan Socket TCP pada Instant Messaging

Aminudin,

Hakim,

Nuryasin

et al. 2024

JRST

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“…Another work shows the decomposition of the two prime numbers with the Pisano period factorization method, which has been proven to be a subexponential complexity method [74]. Several integer factorization methods have also suggested direct application to cryptanalysis of RSA by applying different genetic algorithms [75]. While genetic algorithms could be a promising avenue of research for integer factorization, they are computationally complex.…”

Section: Application Example 1 Let Us Consider Case Example 2 With N = 377mentioning

confidence: 99%

New Semi-Prime Factorization and Application in Large RSA Key Attacks

Overmars¹,

Venkatraman²

2021

JCP

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Semi-prime factorization is an increasingly important number theoretic problem, since it is computationally intractable. Further, this property has been applied in public-key cryptography, such as the Rivest–Shamir–Adleman (RSA) encryption systems for secure digital communications. Hence, alternate approaches to solve the semi-prime factorization problem are proposed. Recently, Pythagorean tuples to factor semi-primes have been explored to consider Fermat’s Christmas theorem, with the two squares having opposite parity. This paper is motivated by the property that the integer separating these two squares being odd reduces the search for semi-prime factorization by half. In this paper, we prove that if a Pythagorean quadruple is known and one of its squares represents a Pythagorean triple, then the semi-prime is factorized. The problem of semi-prime factorization is reduced to the problem of finding only one such sum of three squares to factorize a semi-prime. We modify the Lebesgue identity as the sum of four squares to obtain four sums of three squares. These are then expressed as four Pythagorean quadruples. The Brahmagupta–Fibonacci identity reduces these four Pythagorean quadruples to two Pythagorean triples. The greatest common divisors of the sides contained therein are the factors of the semi-prime. We then prove that to factor a semi-prime, it is sufficient that only one of these Pythagorean quadruples be known. We provide the algorithm of our proposed semi-prime factorization method, highlighting its complexity and comparative advantage of the solution space with Fermat’s method. Our algorithm has the advantage when the factors of a semi-prime are congruent to 1 modulus 4. Illustrations of our method for real-world applications, such as factorization of the 768-bit number RSA-768, are established. Further, the computational viabilities, despite the mathematical constraints and the unexplored properties, are suggested as opportunities for future research.

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“…In the past two decades, integer factorization algorithms have evolved by improving existing ones to a great extent such that very large semi-primes of more than 250 decimal digits can be factorized with sufficient computing power [14][15][16][17]. Some of the famous integer factorization algorithms are Lenstra's elliptic curve algorithm [18], Pomerance's quadratic sieve, and the General Number Field Sieve [19,20].…”

Section: Introductionmentioning

confidence: 99%

Continued Fractions Applied to the One Line Factoring Algorithm for Breaking RSA

Overmars,

Venkatraman

2024

JCP

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The RSA (Rivest–Shamir–Adleman) cryptosystem is an asymmetric public key cryptosystem popular for its use in encryptions and digital signatures. However, the Wiener’s attack on the RSA cryptosystem utilizes continued fractions, which has generated much interest in developing competitive factoring algorithms. A general-purpose integer factorization method first proposed by Lehmer and Powers formed the basis of the well-known Continued Fraction Factorization (CFRAC) method. Recent work on the one line factoring algorithm by Hart and its connection with Lehman’s factoring method have motivated this paper. The emphasis of this paper is to explore the representations of PQ as continued fractions and the suitability of lower ordered convergences as representations of ab. These simpler convergences are then prescribed to Hart’s one line factoring algorithm. As an illustration, we demonstrate the working of our approach with two numbers: one smaller number and another larger number occupying 95 bits. Using our method, the fourth convergence finds the factors as the solution for the smaller number, while the eleventh convergence finds the factors for the larger number. The security of the RSA public key cryptosystem relies on the computational difficulty of factoring large integers. Among the challenges in breaking RSA semi-primes, RSA250, which is an 829-bit semi-prime, continues to hold a research record. In this paper, we apply our method to factorize RSA250 and present the practical implementation of our algorithm. Our approach’s theoretical and experimental findings demonstrate the reduction of the search space and a faster solution to the semi-prime factorization problem, resulting in key contributions and practical implications. We identify further research to extend our approach by exploring limitations and additional considerations such as the difference of squares method, paving the way for further research in this direction.

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Cryptanalysis of RSA: Integer Prime Factorization Using Genetic Algorithms

Cited by 8 publications

References 13 publications

Kriptosistem Hybrid Algoritme RSA dan El-Gamal Menggunakan Socket TCP pada Instant Messaging

Kriptosistem Hybrid Algoritme RSA dan El-Gamal Menggunakan Socket TCP pada Instant Messaging

New Semi-Prime Factorization and Application in Large RSA Key Attacks

Continued Fractions Applied to the One Line Factoring Algorithm for Breaking RSA

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