Related papers: Integer Factorisation, Fermat & Machine Learning o…
We give algorithms to factorize large integers in the duality computer. We provide three duality algorithms for factorization based on a naive factorization method, the Shor algorithm in quantum computing, and the Fermat's method in…
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…
This note introduces a new class of integer factoring algorithms. Two versions of this method will be described, deterministic and probabilistic. These algorithms are practical, and can factor large classes of balanced integers N = pq, p <…
To factor an integer N, given that it is equal to the product of two primes, it suffices to find an integer d satisfying a certain simple numerical test. In this approach, the factorization problem equates to the problem of designing an…
In this paper, we introduce a novel quantum algorithm for the factorization of composite odd numbers. This work makes two significant contributions. First, we present a new improvement to the classical Fermat method, fourfold reducing the…
In this paper, we present an approach to integer factorization using distributed representations formed with Vector Symbolic Architectures. The approach formulates integer factorization in a manner such that it can be solved using neural…
Integer factorization is a famous computational problem unknown whether being solvable in the polynomial time. With the rise of deep neural networks, it is interesting whether they can facilitate faster factorization. We present an approach…
Fermat's well-known factorization algorithm is based on finding a representation of natural numbers $N$ as the difference of squares. In 1895, Lawrence generalized this idea and applied it to multiples $kN$ of the original number. A…
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…
We offer multiplication method for factoring big natural numbers which extends the group of the Fermat's and Lehman's factorization algorithms and has run-time complexity $O(n^{1/3})$. This paper is argued the finiteness of proposed…
Judging whether an integer can be divided by prime numbers such as 2 or 3 may appear trivial to human beings, but can be less straightforward for computers. Here, we tested multiple deep learning architectures and feature engineering…
Factoring large integers using a quantum computer is an outstanding research problem that can illustrate true quantum advantage over classical computers. Exponential time order is required in order to find the prime factors of an integer by…
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…
Matrix completion is one of the key problems in signal processing and machine learning. In recent years, deep-learning-based models have achieved state-of-the-art results in matrix completion. Nevertheless, they suffer from two drawbacks:…
Modern cryptography is largely based on complexity assumptions, for example, the ubiquitous RSA is based on the supposed complexity of the prime factorization problem. Thus, it is of fundamental importance to understand how a quantum…
This work focuses on quantum methods for cryptanalysis of schemes based on the integer factorization problem and the discrete logarithm problem. We demonstrate how to practically solve the largest instances of the factorization problem by…
As illustrated by the success of integer linear programming, linear integer arithmetic is a powerful tool for modelling combinatorial problems. Furthermore, the probabilistic extension of linear programming has been used to formulate…
Matrix factorization is a key tool in data analysis; its applications include recommender systems, correlation analysis, signal processing, among others. Binary matrices are a particular case which has received significant attention for…
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…
In this paper, we create a systematic and automatic procedure for transforming the integer factorization problem into the problem of solving a system of Boolean equations. Surprisingly, the resulting system of Boolean equations takes on a…