most citedSome integer factorization algorithms using elliptic curves

56 citations · 78 across the 13 of their papers we have counts for

collaborators

13 papers

cs.DS20104 cited

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…

math.NT20102 cited

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…

cs.MS20104 cited

The myth of equidistribution for high-dimensional simulation

Richard P. Brent

A pseudo-random number generator (RNG) might be used to generate w-bit random samples in d dimensions if the number of state bits is at least dw. Some RNGs perform better than othe…

cs.DS20101 cited

A Simple Approach to Error Reconciliation in Quantum Key Distribution

Richard P. Brent

We discuss the error reconciliation phase in quantum key distribution (QKD) and analyse a simple scheme in which blocks with bad parity (that is, blocks containing an odd number of…

math.NA2010

Note on Computing Ratings from Eigenvectors

Richard P. Brent

We consider the problem of computing ratings using the results of games played between a set of n players, and show how this problem can be reduced to computing the positive eigenv…

math.NT2010

On computing factors of cyclotomic polynomials

Richard P. Brent

For odd square-free n > 1 the n-th cyclotomic polynomial satisfies an identity of Gauss. There are similar identity of Aurifeuille, Le Lasseur and Lucas. These identities all invol…