Related papers: Probability Analysis and Comparison of Well-Known …
We explore an algorithm for approximating roots of integers, discuss its motivation and derivation, and analyze its convergence rates with varying parameters and inputs. We also perform comparisons with established methods for approximating…
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…
In the realm of statistical learning, the increasing volume of accessible data and increasing model complexity necessitate robust methodologies. This paper explores two branches of robust Bayesian methods in response to this trend. The…
Probabilistic computing has been introduced to operate functional networks using a probabilistic bit (p-bit), generating 0 or 1 probabilistically from its electrical input. In contrast to quantum computers, probabilistic computing enables…
For an elliptic curve $E$ over a finite field $\F_q$, where $q$ is a prime power, we propose new algorithms for testing the supersingularity of $E$. Our algorithms are based on the Polynomial Identity Testing (PIT) problem for the $p$-th…
We give an algorithm for computing approximate PSD factorizations of nonnegative matrices. The running time of the algorithm is polynomial in the dimensions of the input matrix, but exponential in the PSD rank and the approximation error.…
Prime factorization has been a buzzing topic in the field of number theory since time unknown. However, in recent years, alternative avenues to tackle this problem are being explored by researchers because of its direct application in the…
We present fast and highly parallelized versions of Shor's algorithm. With a sizable quantum computer it would then be possible to factor numbers with millions of digits. The main algorithm presented here uses FFT-based fast integer…
There are two methods for counting the number of occurrences of a string in another large string. One is to count the number of places where the string is found. The other is to determine how many pieces of string can be extracted without…
Finite population inference is a central goal in survey sampling. Probability sampling is the main statistical approach to finite population inference. Challenges arise due to high cost and increasing non-response rates. Data integration…
A precise estimation of the computational complexity in Shor's factoring algorithm under the condition that the large integer we want to factorize is composed by the product of two prime numbers, is derived by the results related to number…
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…
Often, when solving forward, inverse or data assimilation problems, only a part of the solution is needed. As a model, we consider the stationary diffusion problem. We demonstrate an algorithm that can compute only a part or a functional of…
We report a detailed analysis of the optical realization [1, 3, 2, 4] of the analogue algorithm described in the first paper of this series [5] for the simultaneous factorization of an exponential number of integers. Such an analogue…
We present a new approach to handling the case of Atkin primes in Schoof's algorithm for counting points on elliptic curves over finite fields. Our approach is based on the theory of polynomially cyclic algebras, which we recall as far as…
In this paper, we intend to study the geometric meaning of the discrete logarithm problem defined over an Elliptic Curve. The key idea is to reduce the Elliptic Curve Discrete Logarithm Problem (EC-DLP) into a system of equations. These…
The comparison of benchmark error sets is an essential tool for the evaluation of theories in computational chemistry. The standard ranking of methods by their Mean Unsigned Error is unsatisfactory for several reasons linked to the…
Given an elliptic curve $E$ and a positive integer $N$, we consider the problem of counting the number of primes $p$ for which the reduction of $E$ modulo $p$ possesses exactly $N$ points over $\mathbb F_p$. On average (over a family of…
We design a probabilistic algorithm for computing endomorphism rings of ordinary elliptic curves defined over finite fields that we prove has a subexponential runtime in the size of the base field, assuming solely the generalized Riemann…
We propose an alternative method to factorize an integer by using three harmonic oscillators. These oscillators are coupled together via specific Kerr nonlinear interactions. This method can be applied even if two harmonic oscillators are…