Peter Montgomery
Encyclopedia
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.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who has published widely in the more mathematical end of the field of cryptography
Cryptography
Cryptography is the practice and study of techniques for secure communication in the presence of third parties...
. He is currently a researcher in the cryptography group at Microsoft Research
Microsoft Research
Microsoft Research is the research division of Microsoft created in 1991 for developing various computer science ideas and integrating them into Microsoft products. It currently employs Turing Award winners C.A.R. Hoare, Butler Lampson, and Charles P...
.
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.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
in 1992 from the University of California, Los Angeles
University of California, Los Angeles
The University of California, Los Angeles is a public research university located in the Westwood neighborhood of Los Angeles, California, USA. It was founded in 1919 as the "Southern Branch" of the University of California and is the second oldest of the ten campuses...
.
He also invented the Block Lanczos algorithm for nullspace of a matrix over a finite field
Block Lanczos algorithm for nullspace of a matrix over a finite field
The block Lanczos algorithm for nullspace of a matrix over a finite field is a procedure for finding the nullspace of a matrix using only multiplication of the matrix by long, thin matrices...
, which is very widely used for the quadratic sieve
Quadratic sieve
The quadratic sieve algorithm is a modern integer factorization algorithm and, in practice, the second fastest method known . It is still the fastest for integers under 100 decimal digits or so, and is considerably simpler than the number field sieve...
and number field sieve methods of factorization; he has been involved in the computations which set a number of integer factorization records
Integer factorization records
Integer factorization is the process of determining which prime numbers divide a given positive integer. Doing this quickly has applications in cryptography...
.
He has an Erdős number
Erdos number
The Erdős number describes the "collaborative distance" between a person and mathematician Paul Erdős, as measured by authorship of mathematical papers.The same principle has been proposed for other eminent persons in other fields.- Overview :...
of 1 and was a Putnam Fellow in 1967.
An incomplete list of his papers is available at the DBLP bibliography server.