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