56 citations · 86 across the 16 of their papers we have counts for
4 papers · 1 filter
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…
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…
Uses of randomness in computation
Richard P. Brent
Random number generators are widely used in practical algorithms. Examples include simulation, number theory (primality testing and integer factorization), fault tolerance, routing…
Some long-period random number generators using shifts and xors
Richard P. Brent
Marsaglia recently introduced a class of xorshift random number generators (RNGs) with periods 2n-1 for n = 32, 64, etc. Here we give a generalisation of Marsaglia's xorshift gener…