P. L. Montgomery

发表

AN FFT EXTENSION TO THE P - 1 FACTORING ALGORITHM

Robert D. Silverman, P. L. Montgomery, 1990 .

Modular multiplication without trial division

P. L. Montgomery, 1985 .

A Block Lanczos Algorithm for Finding Dependencies Over GF(2)

Peter L. Montgomery, P. L. Montgomery, 1995, EUROCRYPT.

The number field sieve on many computers

Robert D. Silverman, S. Wagstaff, P. L. Montgomery, 1999 .

Speeding the Pollard and elliptic curve methods of factorization

P. L. Montgomery, 1987 .

Factorization of RSA-140 Using the Number Field Sieve

Walter M. Lioen, A. K. Lenstra, P. Zimmermann, 1999, CRYPTO 1999.

A survey of modern integer factorization algorithms

P. L. Montgomery, AlgorithmsPeter, L. Montgomery, 1994 .

Number Theory Elementary Number Theory

Jonathan M. Borwein, Igor E. Shparlinski, David H. Bailey, 2016 .

An Analysis of Affine Coordinates for Pairing Computation

Michael Naehrig, Kristin E. Lauter, Peter L. Montgomery, 2010, Pairing.

Reportrapport Factorization of a 512--bit Rsa Modulus Factorization of a 5122bit Rsa Modulus

Walter M. Lioen, A. K. Lenstra, P. L. Montgomery, 2022 .

Pollard Rho on the PlayStation 3

Marcelo E. Kaihara, Peter L. Montgomery, Joppe W. Bos, 2009 .

New solutions of ap-1 ≡ 1 (mod p2)

P. L. Montgomery, 1993 .

Trading Inversions for Multiplications in Elliptic Curve Cryptography

Marc Joye, Kristin E. Lauter, Peter L. Montgomery, 2006, Des. Codes Cryptogr..

On The Diffie-Hellman Assumption

K. Chandrasekaran, Raghav Bhaskar, Satyanarayana V. Lokam, 2008, IACR Cryptol. ePrint Arch..

Update 1 to: factorizations of an±1, 13≤a<100

R. Brent, P. L. Montgomery, H. Riele, 1994 .

New Solutions of a p - 1 ≡1 (mod p 2 )

Peter L. Montgomery, P. L. Montgomery, 1993 .

Fast Elliptic Curve Arithmetic and Improved Weil Pairing Evaluation

P. L. Montgomery, K. Lauter, Kirsten Eisenträger, 2002, CT-RSA.

Square roots of products of algebraic numbers

Peter L. Montgomery, P. L. Montgomery, 1994 .

An FFT extension of the elliptic curve method of factorization

P. L. Montgomery, Peter Lawrence Montgomery, 1992 .

Factorization of a 768-Bit RSA Modulus

Arjen K. Lenstra, Kazumaro Aoki, Pierrick Gaudry, 2010, CRYPTO.

Finding ECM-Friendly Curves through a Study of Galois Properties pdf

Razvan Barbulescu, Thorsten Kleinjung, Peter L. Montgomery, 2012, IACR Cryptol. ePrint Arch..

Efficient SIMD Arithmetic Modulo a Mersenne Number

Arjen K. Lenstra, Thorsten Kleinjung, Peter L. Montgomery, 2011, 2011 IEEE 20th Symposium on Computer Arithmetic.

Montgomery Arithmetic from a Software Perspective

Peter L. Montgomery, Joppe W. Bos, P. L. Montgomery, 2017, IACR Cryptol. ePrint Arch..

Speedskate ice friction: review and numerical model - FAST 1.0

Edward P. Lozowski, Alan J. Penny, Susan Jane Maw, 2007 .

Solving a 112-bit prime elliptic curve discrete logarithm problem on game consoles using sloppy reduction

Arjen K. Lenstra, Thorsten Kleinjung, Marcelo E. Kaihara, 2012, Int. J. Appl. Cryptogr..

A World Wide Number Field Sieve Factoring Record: On to 512 Bits

Arjen K. Lenstra, Peter L. Montgomery, Bruce Dodson, 1996, ASIACRYPT.

On the Security of 1024-bit RSA and 160-bit Elliptic Curve Cryptography

Arjen K. Lenstra, Thorsten Kleinjung, Marcelo E. Kaihara, 2009, IACR Cryptol. ePrint Arch..

Montgomery Multiplication Using Vector Instructions

Daniel Shumow, Peter L. Montgomery, Joppe W. Bos, 2013, Selected Areas in Cryptography.

Factorization of a 512-Bit RSA Modulus

Jeff Gilchrist, Arjen K. Lenstra, Karen Aardal, 2000, EUROCRYPT.

An Efficient Procedure to Double and Add Points on an Elliptic Curve

Kristin E. Lauter, Kirsten Eisenträger, Peter L. Montgomery, 2002, IACR Cryptol. ePrint Arch..

Finding ECM-Friendly Curves through a Study of Galois Properties

Joppe W. Bos, P. L. Montgomery, T. Kleinjung, 2012, IACR Cryptol. ePrint Arch..

Trading Inversions for Multiplications in Elliptic Curve Cryptography

Mun-Kyu Lee, Kunsoo Park, Tae-Jun Park, 2006, Des. Codes Cryptogr..

A new world record for the special number field sieve factoring method

P. L. Montgomery, S. Cavallar, H.J.J. teRiele, 1997 .

Evaluation of boolean expressions on one's complement machines

Peter L. Montgomery, P. L. Montgomery, 1978, SIGP.

Division by invariant integers using multiplication

Peter L. Montgomery, Torbjörn Granlund, P. L. Montgomery, 1994, PLDI '94.

Improved Stage 2 to P±1 Factoring Algorithms

Peter L. Montgomery, Alexander Kruppa, P. L. Montgomery, 2008, ANTS.

Five, six, and seven-term Karatsuba-like formulae

Peter L. Montgomery, P. L. Montgomery, 2005, IEEE Transactions on Computers.

Side Channel Leakage Profiling in Software

Daniel Shumow, Peter L. Montgomery, P. L. Montgomery, 2010 .