Peter Lawrence Montgomery is an American mathematician who has published widely in the more mathematical end of the field of cryptography. He is currently a researcher in the cryptography group at Microsoft Research.
Montgomery is particularly known for his contributions to the elliptic curve method of factorization, which include a method for speeding up the second stage of algebraic-group factorization algorithms using FFT techniques for fast polynomial evaluation at equally-spaced points. This was the subject of his dissertation, for which he received his Ph.D. in 1992 from the University of California, Los Angeles.
He also invented the Block Lanczos algorithm for nullspace of a matrix over a finite field, which is very widely used for the quadratic sieve and number field sieve methods of factorization; he has been involved in the computations which set a number of integer factorization records.
He has an Erdős number of 1 and was a Putnam Fellow in 1967.
An incomplete list of his papers is available at the DBLP bibliography server.