Peter Montgomery (mathematician)

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Peter Montgomery 2009

Peter Lawrence Montgomery (born September 25, 1947 in San Francisco , † February 18, 2020 in Pong ) was an American mathematician who dealt with cryptography and algorithmic number theory.

In 1967 he was a Putnam winner at the University of California, Berkeley , where he received his bachelor's degree in 1969 and his master's degree in 1971. He received his PhD in 1992 from the University of California, Los Angeles with David Cantor (An FFT Extension of the Elliptic Curve Method of Factorization) and was then Assistant Visiting Professor at Oregon State University . Montgomery was with Unisys for 17 years and from 1998 a scientist with Microsoft Research . In the 1990s and 2000s he also worked at the Centrum Wiskunde & Informatica in Amsterdam .

In his dissertation in 1992 he improved the factorization method with elliptic curves (introduced by Hendrik Lenstra ) with the help of the fast Fourier transform . He also improved factorization algorithms for large composite numbers , such as the square sieve and the number field sieve , the efficiency of which is influenced by linear algebra algorithms - in 1995 he developed the Block- Lanczos algorithm to determine the kernel of large matrices over finite fields. This set new records for factoring large numbers (he was involved in solving the RSA challenges RSA-130 from 1996, RSA-140 and RSA-155 from 1999, each of which won first prizes, as well as RSA-576 with 174 positions in 2003, among others with Herman te Riele and Jens Franke ).

In 1985 he introduced an efficient version of modular arithmetic for large numbers (Montgomery multiplication or Montgomery reduction).

At Microsoft Research, he wrote most of the msbignum library for Windows Vista .

Fonts

  • An FFT extension of the elliptic curve method of factorization , University of California, Los Angeles 1992 (English; dissertation; with curriculum vitae; online ( Memento from May 2, 2014 in the Internet Archive ))

Web links

Commons : Peter Montgomery (mathematician)  - Collection of images, videos and audio files

References

  1. ↑ Obituary
  2. ↑ Montgomery 1994 report on factoring a 162-digit number
  3. ↑ Named after the similarity to the Lanczos method for eigenvalue calculations of large sparse matrices. Montgomery: A block Lanczos algorithm for finding dependencies over GF (2) , Eurocrypt 95, Lecture Notes in Computer Science Vol. 921, Springer, pp. 106-120.
  4. ↑ RSA challenge list , program in algorithmic number theory at the CWI ( Memento from January 26, 2011 in the Internet Archive )
  5. ^ Montgomery, Modular Multiplication Without Trial Division, Math. Computation, Vol. 44, 1985, pp. 519-521
personal data
SURNAME Montgomery, Peter
ALTERNATIVE NAMES Montgomery, Peter Lawrence (full name)
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH September 25, 1947
PLACE OF BIRTH San Francisco
DATE OF DEATH February 18, 2020
Place of death Pong