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Peter Lawrence Montgomery (born 25 September 1947) 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.

Peter L. Montgomery
Peter Montgomery.jpg
Peter Montgomery in July 2009 at Microsoft Research.
Born (1947-09-25) September 25, 1947 (age 72)
Alma materUniversity of California, Los Angeles
Scientific career
InstitutionsMicrosoft Research
Doctoral advisorDavid G. Cantor

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.[1]

He also invented the block Lanczos algorithm for finding 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 was a Putnam Fellow in 1967. In that year, he was one of only two contestants, along with child prodigy Don Zagier of MIT, to solve all twelve of the exam problems.

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