Related papers: Algorithm for factoring some RSA and Rabin moduli
Let n be any odd natural number other than a perfect square, in this article it is demonstrated that this new factorization algorithm is much more efficient than the implementation technique [2,3 p.1470], described in this article, of the…
This project involves an implementation of the Rivest Shamir Adleman (RSA) encryption algorithm in C. It consists of generation of two random prime numbers and a number co- prime to phi(n) also called euler toitent function. These three are…
Mehring et al. have recently described an elegant nuclear magnetic resonance (NMR) experiment implementing an algorithm to factor numbers based on the properties of Gauss sums. Similar experiments have also been described by Mahesh et al.…
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…
In this paper we describe a deep learning--based probabilistic algorithm for integer factorisation. We use Lawrence's extension of Fermat's factorisation algorithm to reduce the integer factorisation problem to a binary classification…
Two known computation methods and one new computation method for matrix determinant over an integral domain are discussed. For each of the methods we evaluate the computation times for different rings and show that the new method is the…
Integer factorization is one of the vital algorithms discussed as a part of analysis of any black-box cipher suites where the cipher algorithm is based on number theory. The origin of the problem is from Discrete Logarithmic Problem which…
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…
In this paper, a randomized algorithm for deciding the irreducibility of an irreducible polynomial and factoring a reducible polynomial over the field of rational numbers is presented. The main idea underlying the algorithm is based on…
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…
We give some theoretical and computational results on "random" harmonic sums with prime numbers, and more generally, for integers with a fixed number of prime factors.
String matching algorithms are among one of the most widely used algorithms in computer science. Traditional string matching algorithms efficiency of underlaying string matching algorithm will greatly increase the efficiency of any…
The square root modulo problem is a known primitive in designing an asymmetric cryptosystem. It was first attempted by Rabin. Decryption failure of the Rabin cryptosystem caused by the 4-to-1 decryption output is overcome efficiently in…
Modern robotics often involves multiple embodied agents operating within a shared environment. Path planning in these cases is considerably more challenging than in single-agent scenarios. Although standard Sampling-based Algorithms (SBAs)…
Regev recently introduced a quantum factoring algorithm that may be perceived as a $d$-dimensional variation of Shor's factoring algorithm. In this work, we extend Regev's factoring algorithm to an algorithm for computing discrete…
In both observational data and randomized control trials, researchers select statistical models to articulate how the outcome of interest varies with combinations of observable covariates. Choosing a model that is too simple can obfuscate…
We describe explicit algorithms for factoring q-difference operators and solving q-difference equations. These are well known results, presented in a "concrete" form. ----- Nous decrivons des algorithmes explicites pour la factorisation…
Boolean matrix factorization (BMF) approximates a given binary input matrix as the product of two smaller binary factors. As opposed to binary matrix factorization which uses standard arithmetic, BMF uses the Boolean OR and Boolean AND…
A standard method for finding a rational number from its values modulo a collection of primes is to determine its value modulo the product of the primes via Chinese remaindering, and then use Farey sequences for rational reconstruction.…
The best known unconditional deterministic complexity bound for computing the prime factorization of an integer N is O(M_int(N^(1/4) log N)), where M_int(k) denotes the cost of multiplying k-bit integers. This result is due to…