Related papers: Cryptanalysis of RSA Cryptosystem: Prime Factoriza…
Many modern asymmetric encryption methods rely on prime numbers, as they have distinctive properties. For instance, the security of RSA cryptosystem relies on the computational difficulty of factoring a large composite number in its prime…
Classical public-key cryptography standards rely on the Rivest-Shamir-Adleman (RSA) encryption protocol. The security of this protocol is based on the exponential computational complexity of the most efficient classical algorithms for…
The security of RSA algorithm depends upon the positive integer N, which is the multiple of two precise large prime numbers. Factorization of such great numbers is a problematic process. There are many algorithms has been implemented in the…
The assumed computationally difficulty of factoring large integers forms the basis of security for RSA public-key cryptography, which specifically relies on products of two large primes or semi-primes. The best-known factoring algorithms…
Primality generation is the cornerstone of several essential cryptographic systems. The problem has been a subject of deep investigations, but there is still a substantial room for improvements. Typically, the algorithms used have two parts…
The difficulty of factoring large integers into primes is the basis for cryptosystems such as RSA. Due to the widespread popularity of RSA, there have been many proposed attacks on the factorization problem such as side-channel attacks…
This article proposes a new method to inject backdoors in RSA and other cryptographic primitives based on the Integer Factorization problem for balanced semi-primes. The method relies on mathematical congruences among the factors of the…
This paper explores vulnerabilities in RSA cryptosystems that arise from improper prime number selection during key generation. We examine two primary attack vectors: Fermat's factorization method, which exploits RSA keys generated with…
The RSA cryptosystem, which relies on the computational difficulty of prime factorization, faces growing challenges with the advancement of quantum computing. In this study, we propose a quantum annealing based approach to integer…
Cryptanalysis of knapsack cipher is a fascinating problem which has eluded the computing fraternity for decades. However, in most of the cases either the time complexity of the proposed algorithm is colossal or an insufficient number of…
Shor's factoring algorithm (SFA), by its ability to efficiently factor large numbers, has the potential to undermine contemporary encryption. At its heart is a process called order finding, which quantum mechanics lets us perform…
New algorithms for prime factorization that outperform the existing ones or take advantage of particular properties of the prime factors can have a practical impact on present implementations of cryptographic algorithms that rely on the…
Integer factorization is a fundamental problem in algorithmic number theory and computer science. It is considered as a one way or trapdoor function in the (RSA) cryptosystem. To date, from elementary trial division to sophisticated methods…
Genetic algorithms are a population-based Meta heuristics. They have been successfully applied to many optimization problems. However, premature convergence is an inherent characteristic of such classical genetic algorithms that makes them…
This paper elaborates on a sieving technique that has first been applied in 2018 for improving bounds on deterministic integer factorization. We will generalize the sieve in order to obtain a polynomial-time reduction from integer…
Numerous methods have been considered to create a fast integer factorization algorithm. Despite its apparent simplicity, the difficulty to find such an algorithm plays a crucial role in modern cryptography, notably, in the security of RSA…
We report preliminary results on using the MEMCPU\texttrademark{} Platform to compute the prime factorization of large biprimes. The first approach, the direct model, directly returns the factors of a given biprime. The second approach, the…
We present a new approach to RSA factorization inspired by geometric interpretations and square differences. This method reformulates the problem in terms of the distance between perfect squares and provides a recurrence relation that…
The security of the RSA cryptosystem is based on the difficulty of factoring a large number N into prime numbers p and q satisfying N=p*q . This paper presents a prime factoriaation method using D-Wave quantum computer that can threaten the…
Current asymmetric cryptography is based on the principle that while classical computers can efficiently multiply large integers, the inverse operation, factorization, is significantly more complex. For sufficiently large integers, this…