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MPFR: A multiple-precision binary floating-point library with correct rounding
This article presents a multiple-precision binary floating-point library, written in the ISO C language, and based on the GNU MP library. Its particularity is to extend to arbitrary-precision, ideasExpand
Imperfect Forward Secrecy: How Diffie-Hellman Fails in Practice
Logjam, a novel flaw in TLS that lets a man-in-the-middle downgrade connections to "export-grade" Diffie-Hellman, is presented and a close reading of published NSA leaks shows that the agency's attacks on VPNs are consistent with having achieved a break. Expand
GFUN: a Maple package for the manipulation of generating and holonomic functions in one variable
We describe the GFUN package which contains functions for manipulating sequences, linear recurrences, or differential equations and generating functions of various types. This article is intendedExpand
A Calculus for the Random Generation of Labelled Combinatorial Structures
A general strategy is developed for solving the random generation problem with two closely related types of methods: for structures of size n, the boustrophedonic algorithms exhibit a worst-case behaviour of the form O(n log n); the sequential algorithms have worst case O( n2), while offering good potential for optimizations in the average case. Expand
Efficient isolation of polynomial's real roots
This paper revisits an algorithm isolating the real roots of a univariate polynomial using Descartes' rule of signs. It follows work of Vincent, Uspensky, Collins and Akritas, Johnson, Krandick.OurExpand
Factorization of a 768-Bit RSA Modulus
This paper reports on the factorization of the 768-bit number RSA-768 by the number field sieve factoring method and discusses some implications for RSA.
Modern Computer Arithmetic
Modern Computer Arithmetic focuses on arbitrary-precision algorithms for efficiently performing arithmetic operations such as addition, multiplication and division, and their connections to topicsExpand
Factorization of a 512-Bit RSA Modulus
This paper reports on the factorization of the 512-bit number RSA-155 by the Number Field Sieve factoring method (NFS) and discusses the implications for RSA.
Automatic Average-Case Analysis of Algorithm
This paper presents a general framework in which decision procedures can be developed based on a combination of generating function techniques for counting, and complex analysis techniques for asymptotic estimations, and exposes here the theory of exact analysis in terms of generating functions for four different domains. Expand