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Montgomery, Peter Lawrence (b. 1947 d. 2020)

Author ID: montgomery.peter-l Recent zbMATH articles by "Montgomery, Peter Lawrence"
Published as: Montgomery, Peter L.; Montgomery, P.; Montgomery, Peter
External Links: MGP · Wikidata · dblp · GND · IdRef
Documents Indexed: 28 Publications since 1973
Biographic References: 3 Publications
Co-Authors: 53 Co-Authors with 21 Joint Publications
1,589 Co-Co-Authors

Publications by Year

Citations contained in zbMATH Open

25 Publications have been cited 612 times in 501 Documents Cited by Year
Speeding the Pollard and elliptic curve methods of factorization. Zbl 0608.10005
Montgomery, Peter L.
160
1987
Modular multiplication without trial division. Zbl 0559.10006
Montgomery, Peter L.
145
1985
Euclidean Ramsey theorems. I. Zbl 0276.05001
Erdős, Paul; Graham, Ronald L.; Montgomery, P.; Rothschild, B. L.; Spencer, Joel; Straus, E. G.
55
1973
Factorization of a 768-bit RSA modulus. Zbl 1196.11167
Kleinjung, Thorsten; Aoki, Kazumaro; Franke, Jens; Lenstra, Arjen K.; Thomé, Emmanuel; Bos, Joppe W.; Gaudry, Pierrick; Kruppa, Alexander; Montgomery, Peter L.; Osvik, Dag Arne; te Riele, Herman; Timofeev, Andrey; Zimmermann, Paul
36
2010
Euclidean Ramsey theorems. II, III. Zbl 0313.05002
Erdős, Paul; Graham, Ronald L.; Montgomery, P.; Rothschild, B. L.; Spencer, Joel; Straus, E. G.
33
1975
Five, six, and seven-term Karatsuba-like formulae. Zbl 1171.11329
Montgomery, Peter L.
25
2005
A block Lanczos algorithm for finding dependencies over GF(2). Zbl 0973.11520
Montgomery, Peter L.
24
1995
Trading inversions for multiplications in elliptic curve cryptography. Zbl 1116.14026
Ciet, Mathieu; Joye, Marc; Lauter, Kristin; Montgomery, Peter L.
20
2006
New solutions of \(a^{p-1} \equiv 1 (\pmod p^ 2)\). Zbl 0788.11002
Montgomery, Peter L.
19
1993
Fast elliptic curve arithmetic and improved Weil pairing evaluation. Zbl 1038.11079
Eisenträger, Kirsten; Lauter, Kristin; Montgomery, Peter L.
13
2003
The period of the Bell numbers modulo a prime. Zbl 1216.11028
Montgomery, Peter L.; Nahm, Sangil; Wagstaff, Samuel S. jun.
12
2010
Solving a 112-bit prime elliptic curve discrete logarithm problem on game consoles using sloppy reduction. Zbl 1276.94008
Bos, Joppe W.; Kaihara, Marcelo E.; Kleinjung, Thorsten; Lenstra, Arjen K.; Montgomery, Peter L.
12
2012
Tables of Fibonacci and Lucas factorizations. Zbl 0634.10002
Brillhart, John; Montgomery, Peter L.; Silverman, Robert D.
8
1988
Square roots of products of algebraic numbers. Zbl 0819.11069
Montgomery, Peter L.
8
1994
A survey of modern integer factorization algorithms. Zbl 0828.11073
Montgomery, Peter L.
7
1994
An analysis of affine coordinates for pairing computation. Zbl 1287.94079
Lauter, Kristin; Montgomery, Peter L.; Naehrig, Michael
7
2010
Factorization of a 512-bit RSA modulus. Zbl 1082.94511
Cavallar, Stefania; Dodsons, Bruce; Lenstra, Arjen K.; Lioen, Walter; Montgomery, Peter L.; Murphy, Brian; te Riele, Herman; Aardal, Karen; Gilchrist, Jeff; Guillerm, Gérard; Leyland, Paul; Marchand, Joël; Morain, François; Muffett, Alec; Putnam, Chris; Putnam, Craig; Zimmermann, Paul
7
2000
An FFT extension to the \(P-1\) factoring algorithm. Zbl 0712.11075
Montgomery, Peter L.; Silverman, Robert D.
5
1990
Improved Weil and Tate pairings for elliptic and hyperelliptic curves. Zbl 1116.11042
Eisenträger, Kirsten; Lauter, Kristin; Montgomery, Peter L.
3
2004
A world wide number field sieve factoring record: On to 512 bits. Zbl 1028.11500
Cowie, James; Dodson, Bruce; Elkenbracht-Huizing, R. Marije; Lenstra, Arjen K.; Montgomery, Peter L.; Zayer, Jörg
3
1996
Finding ECM-friendly curves through a study of Galois properties. Zbl 1344.11043
Barbulescu, Razvan; Bos, Joppe W.; Bouvier, Cyril; Kleinjung, Thorsten; Montgomery, Peter L.
3
2013
Montgomery multiplication using vector instructions. Zbl 1362.94022
Bos, Joppe W.; Montgomery, Peter L.; Shumow, Daniel; Zaverucha, Gregory M.
3
2014
Factorization of RSA-140 using the number field sieve. Zbl 0971.94008
Cavallar, Stefania; Dodson, Bruce; Lenstra, Arjen; Leyland, Paul; Lioen, Walter; Montgomery, Peter L.; Murphy, Brian; te Riele, Herman; Zimmermann, Paul
2
1999
The number field sieve on many computers. Zbl 0936.11070
Elkenbracht-Huizing, R.-M.; Montgomery, Peter L.; Silverman, R. D.; Wackerbarth, R. K.; Wagstaff, S. S. jun.
1
1999
Montgomery arithmetic from a software perspective. Zbl 1527.11098
Bos, Joppe W.; Montgomery, Peter L.
1
2017
Montgomery arithmetic from a software perspective. Zbl 1527.11098
Bos, Joppe W.; Montgomery, Peter L.
1
2017
Montgomery multiplication using vector instructions. Zbl 1362.94022
Bos, Joppe W.; Montgomery, Peter L.; Shumow, Daniel; Zaverucha, Gregory M.
3
2014
Finding ECM-friendly curves through a study of Galois properties. Zbl 1344.11043
Barbulescu, Razvan; Bos, Joppe W.; Bouvier, Cyril; Kleinjung, Thorsten; Montgomery, Peter L.
3
2013
Solving a 112-bit prime elliptic curve discrete logarithm problem on game consoles using sloppy reduction. Zbl 1276.94008
Bos, Joppe W.; Kaihara, Marcelo E.; Kleinjung, Thorsten; Lenstra, Arjen K.; Montgomery, Peter L.
12
2012
Factorization of a 768-bit RSA modulus. Zbl 1196.11167
Kleinjung, Thorsten; Aoki, Kazumaro; Franke, Jens; Lenstra, Arjen K.; Thomé, Emmanuel; Bos, Joppe W.; Gaudry, Pierrick; Kruppa, Alexander; Montgomery, Peter L.; Osvik, Dag Arne; te Riele, Herman; Timofeev, Andrey; Zimmermann, Paul
36
2010
The period of the Bell numbers modulo a prime. Zbl 1216.11028
Montgomery, Peter L.; Nahm, Sangil; Wagstaff, Samuel S. jun.
12
2010
An analysis of affine coordinates for pairing computation. Zbl 1287.94079
Lauter, Kristin; Montgomery, Peter L.; Naehrig, Michael
7
2010
Trading inversions for multiplications in elliptic curve cryptography. Zbl 1116.14026
Ciet, Mathieu; Joye, Marc; Lauter, Kristin; Montgomery, Peter L.
20
2006
Five, six, and seven-term Karatsuba-like formulae. Zbl 1171.11329
Montgomery, Peter L.
25
2005
Improved Weil and Tate pairings for elliptic and hyperelliptic curves. Zbl 1116.11042
Eisenträger, Kirsten; Lauter, Kristin; Montgomery, Peter L.
3
2004
Fast elliptic curve arithmetic and improved Weil pairing evaluation. Zbl 1038.11079
Eisenträger, Kirsten; Lauter, Kristin; Montgomery, Peter L.
13
2003
Factorization of a 512-bit RSA modulus. Zbl 1082.94511
Cavallar, Stefania; Dodsons, Bruce; Lenstra, Arjen K.; Lioen, Walter; Montgomery, Peter L.; Murphy, Brian; te Riele, Herman; Aardal, Karen; Gilchrist, Jeff; Guillerm, Gérard; Leyland, Paul; Marchand, Joël; Morain, François; Muffett, Alec; Putnam, Chris; Putnam, Craig; Zimmermann, Paul
7
2000
Factorization of RSA-140 using the number field sieve. Zbl 0971.94008
Cavallar, Stefania; Dodson, Bruce; Lenstra, Arjen; Leyland, Paul; Lioen, Walter; Montgomery, Peter L.; Murphy, Brian; te Riele, Herman; Zimmermann, Paul
2
1999
The number field sieve on many computers. Zbl 0936.11070
Elkenbracht-Huizing, R.-M.; Montgomery, Peter L.; Silverman, R. D.; Wackerbarth, R. K.; Wagstaff, S. S. jun.
1
1999
A world wide number field sieve factoring record: On to 512 bits. Zbl 1028.11500
Cowie, James; Dodson, Bruce; Elkenbracht-Huizing, R. Marije; Lenstra, Arjen K.; Montgomery, Peter L.; Zayer, Jörg
3
1996
A block Lanczos algorithm for finding dependencies over GF(2). Zbl 0973.11520
Montgomery, Peter L.
24
1995
Square roots of products of algebraic numbers. Zbl 0819.11069
Montgomery, Peter L.
8
1994
A survey of modern integer factorization algorithms. Zbl 0828.11073
Montgomery, Peter L.
7
1994
New solutions of \(a^{p-1} \equiv 1 (\pmod p^ 2)\). Zbl 0788.11002
Montgomery, Peter L.
19
1993
An FFT extension to the \(P-1\) factoring algorithm. Zbl 0712.11075
Montgomery, Peter L.; Silverman, Robert D.
5
1990
Tables of Fibonacci and Lucas factorizations. Zbl 0634.10002
Brillhart, John; Montgomery, Peter L.; Silverman, Robert D.
8
1988
Speeding the Pollard and elliptic curve methods of factorization. Zbl 0608.10005
Montgomery, Peter L.
160
1987
Modular multiplication without trial division. Zbl 0559.10006
Montgomery, Peter L.
145
1985
Euclidean Ramsey theorems. II, III. Zbl 0313.05002
Erdős, Paul; Graham, Ronald L.; Montgomery, P.; Rothschild, B. L.; Spencer, Joel; Straus, E. G.
33
1975
Euclidean Ramsey theorems. I. Zbl 0276.05001
Erdős, Paul; Graham, Ronald L.; Montgomery, P.; Rothschild, B. L.; Spencer, Joel; Straus, E. G.
55
1973
all top 5

Cited by 851 Authors

11 Costello, Craig
10 Azarderakhsh, Reza
8 Sagdeev, Arsenii
7 Bernstein, Daniel Julius
7 Lange, Tanja
7 Naccache, David
7 Naehrig, Michael
7 Thomé, Emmanuel
6 Duquesne, Sylvain
6 Galbraith, Steven D.
6 Großschädl, Johann
6 Joye, Marc
6 Mozaffari-Kermani, Mehran
6 Schwabe, Peter
5 Cenk, Murat
5 De Feo, Luca
5 El Mrabet, Nadia
5 Gaudry, Pierrick
5 Guillevic, Aurore
5 Hisil, Huseyin
5 Liu, Zhe
5 López, Julio E.
5 Morain, François
5 Özbudak, Ferruh
5 Rodl, Vojtech
5 Schost, Éric
5 Yoo, Keeyoung
5 Zimmermann, Paul
4 Anisimov, Anatoly V.
4 Brent, Richard Peirce
4 Dujella, Andrej
4 Faz-Hernández, Armando
4 Frankl, Péter
4 Gallardo, Luis Henri
4 Kleinjung, Thorsten
4 Lauter, Kristin Estella
4 Lenstra, Arjen K.
4 Longa, Patrick
4 Onuki, Hiroshi
4 Paar, Christof
4 Sarkar, Palash
4 Takagi, Tsuyoshi
4 Tibouchi, Mehdi
4 Wu, Chialong
4 Yao, David D. W.
4 Zhang, Fangguo
3 Aranha, Diego F.
3 Barbulescu, Razvan
3 Bouvier, Cyril
3 Brumley, Billy Bob
3 Chang, Te-Jen
3 Crandall, Richard E.
3 Dilcher, Karl
3 Dimitrov, Vassil S.
3 Farashahi, Reza Rezaeian
3 Faugère, Jean-Charles
3 Feix, Benoit
3 Fouotsa, Emmanuel
3 Frankl, Nóra
3 Géraud, Rémi
3 Gorla, Elisa
3 Guilley, Sylvain
3 Harvey, David
3 Hasan, M. Anwar
3 Hutter, Michael
3 Imbert, Laurent
3 Joux, Antoine
3 Karabina, Koray
3 Keller, Wilfrid
3 Kohel, David R.
3 Kong, Yinan
3 Koziel, Brian
3 Kupavskii, Andrey
3 Lee, Keon-Jik
3 Lin, Xibin
3 Lou, Der-Chyuan
3 May, Alexander
3 Menezes, Alfred J.
3 Montgomery, Peter Lawrence
3 Negre, Christophe
3 Page, Dan
3 Paterson, Kenneth G.
3 Plantard, Thomas
3 Renes, Joost
3 Rodríguez-Henríquez, Francisco
3 Seo, Hwajeong
3 Smart, Nigel Paul
3 Takahashi, Daisuke A.
3 Tunstall, Michael J.
3 Vercauteren, Frederik
3 Vergnaud, Damien
3 Yasuda, Masaya
2 Amiel, Frederic
2 Atkin, Arthur Oliver Lonsdale
2 Bach, Eric
2 Bai, Guoqiang
2 Bai, Shi
2 Bajard, Jean-Claude
2 Batina, Lejla
2 Birkner, Peter
...and 751 more Authors
all top 5

Cited in 115 Serials

51 Mathematics of Computation
16 Journal of Cryptology
14 Designs, Codes and Cryptography
13 Journal of Combinatorial Theory. Series A
12 Information Processing Letters
10 Applied Mathematics and Computation
8 Discrete Mathematics
8 Journal of Number Theory
8 Finite Fields and their Applications
7 Computers & Mathematics with Applications
6 Journal of Symbolic Computation
6 Applicable Algebra in Engineering, Communication and Computing
6 Cybernetics and Systems Analysis
5 Journal of Mathematical Sciences (New York)
5 Journal of Mathematical Cryptology
5 Advances in Mathematics of Communications
4 Theoretical Computer Science
4 European Journal of Combinatorics
4 Acta Applicandae Mathematicae
4 Linear Algebra and its Applications
4 The Electronic Journal of Combinatorics
4 Wuhan University Journal of Natural Sciences (WUJNS)
4 Cryptography and Communications
4 Matematicheskie Voprosy Kriptografii
3 Discrete Applied Mathematics
3 Information Sciences
3 Discrete & Computational Geometry
3 Information and Computation
3 The Journal of Supercomputing
3 Journal of Discrete Mathematical Sciences & Cryptography
2 Periodica Mathematica Hungarica
2 ACM Transactions on Mathematical Software
2 Journal of Computational and Applied Mathematics
2 Mathematics and Computers in Simulation
2 Transactions of the American Mathematical Society
2 SIAM Journal on Discrete Mathematics
2 Rad Hrvatske Akademije Znanosti i Umjetnosti. Matematičke Znanosti
2 Doklady Mathematics
2 The Ramanujan Journal
2 Fundamenta Informaticae
2 Quantum Information Processing
2 Science China. Information Sciences
2 Afrika Matematika
2 Research in Number Theory
2 Prikladnaya Diskretnaya Matematika
1 American Mathematical Monthly
1 Analysis Mathematica
1 International Journal of Mathematical Education in Science and Technology
1 Israel Journal of Mathematics
1 Journal of Computational Physics
1 Mathematical Notes
1 Mathematical Proceedings of the Cambridge Philosophical Society
1 Mathematische Semesterberichte
1 Problems of Information Transmission
1 Rocky Mountain Journal of Mathematics
1 Russian Mathematical Surveys
1 Acta Arithmetica
1 Annales de l’Institut Fourier
1 Annali di Matematica Pura ed Applicata. Serie Quarta
1 Annales Universitatis Mariae Curie-Skłodowska. Sectio A. Mathematica
1 Geometriae Dedicata
1 International Journal of Mathematics and Mathematical Sciences
1 Journal of Computer and System Sciences
1 Journal of Pure and Applied Algebra
1 Journal für die Reine und Angewandte Mathematik
1 Mathematika
1 Memoirs of the American Mathematical Society
1 Monatshefte für Mathematik
1 Proceedings of the Japan Academy. Series A
1 Programming and Computer Software
1 Ricerche di Matematica
1 Advances in Applied Mathematics
1 Science of Computer Programming
1 Combinatorica
1 Circuits, Systems, and Signal Processing
1 Journal of Complexity
1 Algorithmica
1 International Journal of Parallel Programming
1 Journal of the American Mathematical Society
1 Mathematical and Computer Modelling
1 Random Structures & Algorithms
1 Japan Journal of Industrial and Applied Mathematics
1 The Annals of Applied Probability
1 Computational Geometry
1 RAIRO. Informatique Théorique et Applications
1 Archive for Mathematical Logic
1 SIAM Journal on Scientific Computing
1 Journal de Théorie des Nombres de Bordeaux
1 Bulletin of the Belgian Mathematical Society - Simon Stevin
1 Advances in Computational Mathematics
1 Mathematical Problems in Engineering
1 Annals of Combinatorics
1 Journal of Integer Sequences
1 Annals of Mathematics. Second Series
1 LMS Journal of Computation and Mathematics
1 Lobachevskii Journal of Mathematics
1 Integers
1 Journal of the Australian Mathematical Society
1 Applied Mathematics E-Notes
1 Journal of Applied Mathematics
...and 15 more Serials

Citations by Year

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