Concept
Factorisation aurifeuillienne
Publications associées (18)
Analysis of Bernstein's factorization circuit
D.J. Bernstein has proposed a circuit-based implementation of the matrix step of the number field sieve factorization algorithm (see "Circuits for integer factorization: a proposal", http://cr.yp.to/papers.html#nfscircuit, 2001). These circuits offer an as ...
2002The Factorization of the ninth Fermat Number
In this paper we exhibit the full prime factorization of the ninth Fermat number F9 = 2(512) + 1. It is the product of three prime factors that have 7, 49, and 99 decimal digits. We found the two largest prime factors by means of the number field sieve, wh ...
American Mathematical Society1993The number field sieve
The number field sieve is an algorithm to factor integers of the form for small positive and . The authors present a report on work in progress on this algorithm. They informally describe the algorithm, discuss several implementation related ...
Springer Berlin Heidelberg1993Polynomial factorization and nonrandomness of bits of algebraic and some transcendental numbers
It is shown that the binary expansions of algebraic numbers do not form secure pseudorandom sequences, given sufficiently many initial bits of an algebraic number, its minimal polynomial can be reconstructed, and therefore the further bits of the algebraic ...
1988Factorization of polynomials by transcendental evaluation
A new polynomial-time algorithm for the factorization of polynomials in two variables with rational coefficients is presented. The algorithm works by replacing one of the variables by an approximation of a transcendental number. It generalizes recent resul ...
1985Polynomial-time algorithms for the factorization of polynomials
In 1982 a polynomial-time algorithm for factoring polynomials in one variable with rational coefficients was published (see A.K. Lenstra, H.W. Lenstra, Jr. and L. Lovasz, Math. Ann., vol.261, p.515-34, 1982). This L3-algorithm came as a r ...
1984Factoring multivariate polynomials over finite fields
This paper describes an algorithm for the factorization of multivariate polynomials with coefficients in a finite field that is polynomial-time in the degrees of the polynomial to be factored. The algorithm makes use of a new basis reduction algorithm for ...
1983Lattices and factorization of polynomials
Discusses an algorithm to factorize univariate polynomials over an algebraic number field which has been implemented in Algol-68 on a CDC-Cyber 170-750 computer ...
Association for Computing Machinery1981