Related papers: Analogue algorithm for parallel factorization of a…
A new integer deterministic factorization algorithm, rated at arithmetic operations to $O(N^{1/6+\varepsilon})$ arithmetic operations, is presented in this note. Equivalently, given the least $(\log N)/6$ bits of a factor of the balanced…
Quantum integer factorization is a potential quantum computing solution that may revolutionize cryptography. Nevertheless, a scalable and efficient quantum algorithm for noisy intermediate-scale quantum computers looks far-fetched. We…
The number of steps any classical computer requires in order to find the prime factors of an $l$-digit integer $N$ increases exponentially with $l$, at least using algorithms known at present. Factoring large integers is therefore…
We propose two algorithms to factor numbers using Gauss sums and entanglement: (i) in a Shor-like algorithm we encode the standard Gauss sum in one of two entangled states and (ii) in an interference algorithm we create a superposition of…
Shor's powerful quantum algorithm for factoring represents a major challenge in quantum computation and its full realization will have a large impact on modern cryptography. Here we implement a compiled version of Shor's algorithm in a…
In this article we develop an algorithm which computes a divisor of an integer $N$, which is assumed to be neither prime nor the power of a prime. The algorithm uses discrete time heat diffusion on a finite graph. If $N$ has $m$ distinct…
Exponential parallelism, a defining principle of advanced computational systems, holds promise for transformative impacts across several scientific and industrial domains. This feature paper provides a comparative overview of Quantum…
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…
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…
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…
Programmable linear optical interferometers are important for classical and quantum information technologies, as well as for building hardware-accelerated artificial neural networks. Recent results showed the possibility of constructing…
Sorting is one of the fundamental problems in computer science. Playing a role in many processes, it has a lower complexity bound imposed by $\mathcal{O}(n\log{n})$ when executing on a sequential machine. This limit can be brought down to…
Lenstra's integer factorization algorithm is asymptotically one of the fastest known algorithms, and is ideally suited for parallel computation. We suggest a way in which the algorithm can be speeded up by the addition of a second phase.…
As multicore systems continue to gain ground in the High Performance Computing world, linear algebra algorithms have to be reformulated or new algorithms have to be developed in order to take advantage of the architectural features on these…
Considering its relevance in the field of cryptography, integer factorization is a prominent application where Quantum computers are expected to have a substantial impact. Thanks to Shor's algorithm this peculiar problem can be solved in…
The task of factoring integers poses a significant challenge in modern cryptography, and quantum computing holds the potential to efficiently address this problem compared to classical algorithms. Thus, it is crucial to develop quantum…
Shor's algorithm for integer factorization offers an exponential speedup over classical methods but remains impractical on Noisy Intermediate Scale Quantum (NISQ) hardware due to the need for many coherent qubits and very deep circuits.…
A deterministic algorithm for factoring $n$ using $n^{1/3+o(1)}$ bit operations is presented. The algorithm tests the divisibility of $n$ by all the integers in a short interval at once, rather than integer by integer as in trial division.…
We report on an experimental investigation into opportunities for parallelism in beliefnet inference. Specifically, we report on a study performed of the available parallelism, on hypercube style machines, of a set of randomly generated…
We discuss the parallelization of algorithms for solving polynomial systems symbolically by way of triangular decomposition. Algorithms for solving polynomial systems combine low-level routines for performing arithmetic operations on…