Related papers: Revisiting Fermat's Factorization for the RSA Modu…

This paper proposes a new signature scheme based on two hard problems : the cube root extraction modulo a composite moduli (which is equivalent to the factorisation of the moduli, IFP) and the discrete logarithm problem(DLP). By combining…

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…

RSA is one of the most popular Public Key Cryptography based algorithm mainly used for digital signatures, encryption/decryption etc. It is based on the mathematical scheme of factorization of very large integers which is a…

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…

Mersenne numbers and Fermat numbers are two hot and difficult issues in number theory. This paper constructs a special group for every positive odd number other than 1, and discovers an algorithm for determining the multiplicative order of…

We introduce DM-RSA (Dual Modulus RSA), a variant of the RSA cryptosystem that employs two distinct moduli symmetrically to enhance security. By leveraging the Chinese Remainder Theorem (CRT) for decryption, DM-RSA provides increased…

Let N and p be two prime numbers > 3 such that p divides N-1. We estimate the p-rank of the class group of Q(N^(1/p)) in terms of the discrete logarithm, with values un F_p, of certain units. Using the Gross--Koblitz formula and identities…

Let $f(x)\in \mathbb{F}_q[x]$ be an irreducible polynomial of degree $m$ and exponent $e$, and $n$ be a positive integer such that $\nu_p(q-1)\ge \nu_{p}(e)+\nu_p(n)$ for all $p$ prime divisor of $n$. We show a fast algorithm to determine…

We define an isomorphism between the group of points of a conic and the set of integers modulo a prime equipped with a non-standard product. This product can be efficiently evaluated through the use of R\'edei rational functions. We then…

A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not…

The problem of factorising positive integer $N$ into two integer factors $x$ and $y$ is first reformulated as an optimisation problem over the positive integer domain of either of the Diophantine polynomials $Q_N(x,y)=N^2(N-xy)^2 +…

We construct algorithms that efficiently generate random factorisations of values $P(n)$ as products of two integers, where $P\in\mathbb{Z}[x]$ is a given quadratic or cubic monic polynomial. In other words, the algorithms produce random…

In \cite{Tm}, the authors give two public key encryptions based on third order linear sequences modulo $n^2$, where $n=pq$ is an RSA integer. In their scheme (3), there are two mistakes in the decryption procedure

We propose a generalization of an RSA-like scheme based on R\'edei rational functions over the Pell hyperbola. Instead of a modulus which is a product of two primes, we define the scheme on a multi-factor modulus, i.e. on a product of more…

With the advancement of quantum technologies, there is a potential threat to traditional encryption systems based on integer factorization. Therefore, developing techniques for accurately measuring the performance of associated quantum…

We show that the effective factorization of Ore polynomials over $\mathbb{F}_q(t)$ is still an open problem. This is so because the known algorithm in [1] presents two gaps, and therefore it does not cover all the examples. We amend one of…

Shor's algorithm has seriously challenged information security based on public key cryptosystems. However, to break the widely used RSA-2048 scheme, one needs millions of physical qubits, which is far beyond current technical capabilities.…

Shor's algorithm is one of the most promising applications of quantum computers. However, since $\sim 10^6$ physical qubits are believed to be required for established approaches, the algorithm will need to be distributed across many…

Several physics-based algorithms for factorizing large number were recently published. A notable recent one by Schleich et al. uses Gauss sums for distinguishing between factors and non-factors. We demonstrate two NMR techniques that…

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…