9 citations · 20 across the 10 of their papers we have counts for
10 papers
Comparing the difficulty of factorization and discrete logarithm: a 240-digit experiment
Fabrice Boudot, Pierrick Gaudry, Aurore Guillevic +3
We report on two new records: the factorization of RSA-240, a 795-bit number, and a discrete logarithm computation over a 795-bit prime field. Previous records were the factorizati…
Three Cousins of Recaman's Sequence
Max A. Alekseyev, Joseph Samuel Myers, Richard Schroeppel +3
Although 10^230 terms of Recaman's sequence have been computed, it remains a mystery. Here three distant cousins of that sequence are described, one of which is also mysterious. (i…
Twelve new primitive binary trinomials
Richard P. Brent, Paul Zimmermann
We exhibit twelve new primitive trinomials over GF(2) of record degrees , , and . In addition we report the first Mersenne exponent not ruled out by S…
Maximal determinants and saturated D-optimal designs of orders 19 and 37
Richard P. Brent, William Orrick, Judy-anne Osborn +1
A saturated D-optimal design is a {+1,-1} square matrix of given order with maximal determinant. We search for saturated D-optimal designs of orders 19 and 37, and find that known…
An O(M(n) log n) algorithm for the Jacobi symbol
Richard P. Brent, Paul Zimmermann
The best known algorithm to compute the Jacobi symbol of two n-bit integers runs in time O(M(n) log n), using Schönhage's fast continued fraction algorithm combined with an identit…
The great trinomial hunt
Richard P. Brent, Paul Zimmermann
We describe a search for primitive trinomials of high degree and its interaction with the Great Internet Mersenne prime search (GIMPS). The search is complete for trinomials whose…
Modern Computer Arithmetic (version 0.5.1)
Richard P. Brent, Paul Zimmermann
This is a draft of a book about algorithms for performing arithmetic, and their implementation on modern computers. We are concerned with software more than hardware - we do not co…
Landau's function for one million billions
Marc Deleglise, Jean-Louis Nicolas, Paul Zimmermann
Let denote the symmetric group with letters, and the maximal order of an element of . If the standard factorization of into primes…
A Multi-level Blocking Distinct Degree Factorization Algorithm
Richard Brent, Paul Zimmermann
We give a new algorithm for performing the distinct-degree factorization of a polynomial P(x) over GF(2), using a multi-level blocking strategy. The coarsest level of blocking repl…
Time- and Space-Efficient Evaluation of Some Hypergeometric Constants
Howard Cheng, Guillaume Hanrot, Emmanuel Thomé +2
The currently best known algorithms for the numerical evaluation of hypergeometric constants such as to decimal digits have time complexity and space…