Peter Montgomery | Academic Influence

Peter Montgomery 's AcademicInfluence.com Rankings

Peter Montgomery

Mathematics

#4291

World Rank

#6131

Historical Rank

#1496

USA Rank

Number Theory

#158

World Rank

#207

Historical Rank

#33

USA Rank

Measure Theory

#2916

World Rank

#3464

Historical Rank

#843

USA Rank

mathematics Degrees

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Mathematics

Peter Montgomery 's Degrees

PhD Mathematics Princeton University
Bachelors Mathematics Stanford University

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Why Is Peter Montgomery Influential?

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According to Wikipedia, Peter Lawrence Montgomery was an American mathematician who worked at the System Development Corporation and Microsoft Research. He is best known for his contributions to computational number theory and mathematical aspects of cryptography, including the Montgomery multiplication method for arithmetic in finite fields, the use of Montgomery curves in applications of elliptic curves to integer factorization and other problems, and the Montgomery ladder, which is used to protect against side-channel attacks in elliptic curve cryptography.

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Peter Montgomery 's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Modular multiplication without trial division (1985) (2651)
Speeding the Pollard and elliptic curve methods of factorization (1987) (1249)
Factorization of a 768-Bit RSA Modulus (2010) (487)
A Block Lanczos Algorithm for Finding Dependencies Over GF(2) (1995) (199)
Five, six, and seven-term Karatsuba-like formulae (2005) (191)
Factorization of RSA-140 Using the Number Field Sieve (1999) (179)
Factorization of a 512-Bit RSA Modulus (2000) (176)
Trading Inversions for Multiplications in Elliptic Curve Cryptography (2006) (167)
Division by invariant integers using multiplication (1994) (127)
Fast Elliptic Curve Arithmetic and Improved Weil Pairing Evaluation (2002) (113)
On the Security of 1024-bit RSA and 160-bit Elliptic Curve Cryptography (2009) (99)
A World Wide Number Field Sieve Factoring Record: On to 512 Bits (1996) (94)
An FFT extension of the elliptic curve method of factorization (1992) (94)
Solving a 112-bit prime elliptic curve discrete logarithm problem on game consoles using sloppy reduction (2012) (73)
Square roots of products of algebraic numbers (1994) (56)
A survey of modern integer factorization algorithms (1994) (54)
An Analysis of Affine Coordinates for Pairing Computation (2010) (46)
AN FFT EXTENSION TO THE P - 1 FACTORING ALGORITHM (1990) (42)
Montgomery Multiplication Using Vector Instructions (2013) (35)
Tables of Fibonacci and Lucas factorizations (1988) (30)
Improved Weil and Tate Pairings for Elliptic and Hyperelliptic Curves (2003) (27)
New solutions of ap-1 ≡ 1 (mod p2) (1993) (25)
Efficient SIMD Arithmetic Modulo a Mersenne Number (2011) (22)
New solutions of ^{-1}≡1\pmod{²} (1993) (22)
New Solutions of a p - 1 ≡1 (mod p 2 ) (1993) (21)
A heterogeneous computing environment to solve the 768-bit RSA challenge (2012) (20)
Pollard Rho on the PlayStation 3 (2009) (17)
Finding ECM-Friendly Curves through a Study of Galois Properties (2012) (16)
Speedskate ice friction: review and numerical model - FAST 1.0 (2007) (13)
Montgomery Arithmetic from a Software Perspective (2017) (10)
The period of the Bell numbers modulo a prime (2010) (8)
Improved Stage 2 to P±1 Factoring Algorithms (2008) (7)
An Efficient Procedure to Double and Add Points on an Elliptic Curve (2002) (5)
The number field sieve on many computers (1999) (4)
Side Channel Leakage Profiling in Software (2010) (4)
Supplement to Tables of Fibonacci and Lucas Factorizations (1988) (3)
Evaluation of boolean expressions on one's complement machines (1978) (3)
Update 1 to: factorizations of an±1, 13≤a<100 (1994) (2)
Vulnerabilities in Anonymous Credential Systems (2008) (2)
An Observation about Variations of the Diffie-Hellman Assumption (2009) (2)
Elementary Problems: E2683-E2688 (1977) (2)
A new world record for the special number field sieve factoring method (1997) (2)
Advanced Problems: 6631-6633 (1990) (1)
On The Diffie-Hellman Assumption (2008) (0)
Factorizations of Cunningham numbers with bases 13 to 99 (2010) (0)
New solutions of $a\sp {p-1}\equiv 1\pmod {p\sp 2}$ (1993) (0)
Reportrapport Factorization of a 512--bit Rsa Modulus Factorization of a 5122bit Rsa Modulus (0)
ECC vs. RSA (2015) (0)
Factorizations of $ a ^ n $ + 1, 13 < a < 100 : update 2 (1996) (0)
A heterogeneous computing environment to solve the 768-bit RSA challenge (2010) (0)
Number Theory Elementary Number Theory (2016) (0)

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