Related papers: Cryptoanalysis of RSA variants with special struct…

We revisit Fermat's factorization method for a positive integer $n$ that is a product of two primes $p$ and $q$. Such an integer is used as the modulus for both encryption and decryption operations of an RSA cryptosystem. The security of…

In RSA cryptography numbers of the form $pq$, with $p$ and $q$ two distinct proportional primes play an important role. For a fixed real number $r>1$ we formalize this by saying that an integer $pq$ is an RSA-integer if $p$ and $q$ are…

An efficient integer factorization algorithm would reduce the security of all variants of the RSA cryptographic scheme to zero. Despite the passage of years, no method for efficiently factoring large semiprime numbers in a classical…

In this paper we present new arithmetical and algebraic results following the work of Babindamana and al. on hyperbolas and describe in the new results an approach to attacking a RSA-type modulus based on continued fractions, independent…

Wiener's attack is a well-known polynomial-time attack on a RSA cryptosystem with small secret decryption exponent d, which works if d<n^{0.25}, where n=pq is the modulus of the cryptosystem. Namely, in that case, d is the denominator of…

The basic properties of RSA cryptosystems and some classical attacks on them are described. Derived from geometric properties of the Euler functions, the Euler function rays, a new ansatz to attack RSA cryptosystems is presented. A…

We point out critical deficiencies in lattice-based cryptanalysis of common prime RSA presented in ``Remarks on the cryptanalysis of common prime RSA for IoT constrained low power devices'' [Information Sciences, 538 (2020) 54--68]. To…

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 RSA cryptosystem could be easily broken with large scale general purpose quantum computers running Shor's factorization algorithm. Being such devices still in their infancy, a quantum annealing approach to integer factorization has…

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…

After attacking the RSA by injecting fault and corresponding countermeasures, works appear now about the need for protecting RSA public elements against fault attacks. We provide here an extension of a recent attack based on the public…

In the RSA cryptosystem integers of the form n=p.q with p and q primes of comparable size (`RSA-integers') play an important role. It is a folklore result of cryptographers that C_r(x), the number of integers n<=x that are of the form n=pq…

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…

In this paper we present a new efficient algorithm for factoring the RSA and the Rabin moduli in the particular case when the difference between their two prime factors is bounded. As an extension, we also give some theoretical results on…

In this paper we give a polynomial time algorithm to compute $\varphi(N)$ for an RSA module $N$ using as input the order modulo $N$ of a randomly chosen integer. This provides a new insight in the very important problem of factoring an RSA…

We present a special-purpose algorithm for factoring semiprimes $N = pq$ in which one prime factor satisfies $p \approx c\,(a/b)^n$ for positive integers $a, b, c, n$ with $a > b$ and $\gcd(a,b) = 1$. Given the correct parameters $(a, b)$,…

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…

Many variants of RSA cryptosystem exist in the literature. One of them is RSA over polynomials based on Galois approach. In standard RSA modulus is product of two large primes whereas in the Galois approach author considered the modulus as…

In this paper we address two different problems related with the factorization of an RSA module N. First we can show that factoring is equivalent in deterministic polynomial time to counting points on a pair of twisted Elliptic curves…

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…