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Montgomery, Peter L.

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Author ID: montgomery.peter-l Recent zbMATH articles by "Montgomery, Peter L."
Published as: Montgomery, Peter L.; Montgomery, P.; Montgomery, Peter
External Links: MGP · Wikidata · dblp · GND
Documents Indexed: 27 Publications since 1973
Biographic References: 1 Publication

Publications by Year

Citations contained in zbMATH Open

22 Publications have been cited 387 times in 337 Documents Cited by Year
Modular multiplication without trial division. Zbl 0559.10006
Montgomery, Peter L.
95
1985
Speeding the Pollard and elliptic curve methods of factorization. Zbl 0608.10005
Montgomery, Peter L.
88
1987
Euclidean Ramsey theorems. I. Zbl 0276.05001
Erdős, Paul; Graham, Ronald L.; Montgomery, P.; Rothschild, B. L.; Spencer, Joel; Straus, E. G.
44
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
26
2010
A block Lanczos algorithm for finding dependencies over GF(2). Zbl 0973.11520
Montgomery, Peter L.
20
1995
New solutions of \(a^{p-1} \equiv 1 (\pmod p^ 2)\). Zbl 0788.11002
Montgomery, Peter L.
16
1993
Five, six, and seven-term Karatsuba-like formulae. Zbl 1171.11329
Montgomery, Peter L.
15
2005
Trading inversions for multiplications in elliptic curve cryptography. Zbl 1116.14026
Ciet, Mathieu; Joye, Marc; Lauter, Kristin; Montgomery, Peter L.
12
2006
Fast elliptic curve arithmetic and improved Weil pairing evaluation. Zbl 1038.11079
Eisenträger, Kirsten; Lauter, Kristin; Montgomery, Peter L.
11
2003
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.
8
2012
Tables of Fibonacci and Lucas factorizations. Zbl 0634.10002
Brillhart, John; Montgomery, Peter L.; Silverman, Robert D.
7
1988
A survey of modern integer factorization algorithms. Zbl 0828.11073
Montgomery, Peter L.
6
1994
An analysis of affine coordinates for pairing computation. Zbl 1287.94079
Lauter, Kristin; Montgomery, Peter L.; Naehrig, Michael
6
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
6
2000
The period of the Bell numbers modulo a prime. Zbl 1216.11028
Montgomery, Peter L.; Nahm, Sangil; Wagstaff, Samuel S. jun.
5
2010
Euclidean Ramsey theorems. II, III. Zbl 0313.05002
Erdős, Paul; Graham, Ronald L.; Montgomery, P.; Rothschild, B. L.; Spencer, Joel; Straus, E. G.
5
1975
An FFT extension to the \(P-1\) factoring algorithm. Zbl 0712.11075
Montgomery, Peter L.; Silverman, Robert D.
4
1990
Square roots of products of algebraic numbers. Zbl 0819.11069
Montgomery, Peter L.
4
1994
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
Improved Weil and Tate pairings for elliptic and hyperelliptic curves. Zbl 1116.11042
Eisenträger, Kirsten; Lauter, Kristin; Montgomery, Peter L.
3
2004
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
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.
8
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
26
2010
An analysis of affine coordinates for pairing computation. Zbl 1287.94079
Lauter, Kristin; Montgomery, Peter L.; Naehrig, Michael
6
2010
The period of the Bell numbers modulo a prime. Zbl 1216.11028
Montgomery, Peter L.; Nahm, Sangil; Wagstaff, Samuel S. jun.
5
2010
Trading inversions for multiplications in elliptic curve cryptography. Zbl 1116.14026
Ciet, Mathieu; Joye, Marc; Lauter, Kristin; Montgomery, Peter L.
12
2006
Five, six, and seven-term Karatsuba-like formulae. Zbl 1171.11329
Montgomery, Peter L.
15
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.
11
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
6
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.
20
1995
A survey of modern integer factorization algorithms. Zbl 0828.11073
Montgomery, Peter L.
6
1994
Square roots of products of algebraic numbers. Zbl 0819.11069
Montgomery, Peter L.
4
1994
New solutions of \(a^{p-1} \equiv 1 (\pmod p^ 2)\). Zbl 0788.11002
Montgomery, Peter L.
16
1993
An FFT extension to the \(P-1\) factoring algorithm. Zbl 0712.11075
Montgomery, Peter L.; Silverman, Robert D.
4
1990
Tables of Fibonacci and Lucas factorizations. Zbl 0634.10002
Brillhart, John; Montgomery, Peter L.; Silverman, Robert D.
7
1988
Speeding the Pollard and elliptic curve methods of factorization. Zbl 0608.10005
Montgomery, Peter L.
88
1987
Modular multiplication without trial division. Zbl 0559.10006
Montgomery, Peter L.
95
1985
Euclidean Ramsey theorems. II, III. Zbl 0313.05002
Erdős, Paul; Graham, Ronald L.; Montgomery, P.; Rothschild, B. L.; Spencer, Joel; Straus, E. G.
5
1975
Euclidean Ramsey theorems. I. Zbl 0276.05001
Erdős, Paul; Graham, Ronald L.; Montgomery, P.; Rothschild, B. L.; Spencer, Joel; Straus, E. G.
44
1973
all top 5

Cited by 588 Authors

6 Costello, Craig
6 Galbraith, Steven D.
6 Naccache, David
5 Rodl, Vojtech
5 Schost, Éric
5 Yoo, Keeyoung
4 Anisimov, Anatoly V.
4 Azarderakhsh, Reza
4 Duquesne, Sylvain
4 El Mrabet, Nadia
4 Frankl, Péter
4 Hisil, Huseyin
4 Morain, François
4 Sagdeev, A. A.
4 Thomé, Emmanuel
4 Wu, Chialong
3 Bernstein, Daniel Julius
3 Brent, Richard Peirce
3 Cenk, Murat
3 Chang, Te-Jen
3 Crandall, Richard E.
3 De Feo, Luca
3 Dujella, Andrej
3 Faugère, Jean-Charles
3 Fouotsa, Emmanuel
3 Gaudry, Pierrick
3 Géraud, Rémi
3 Joye, Marc
3 Keller, Wilfrid
3 Kong, Yinan
3 Lauter, Kristin Estella
3 Lee, Keon-Jik
3 Lin, Xibin
3 Lou, Der-Chyuan
3 Menezes, Alfred J.
3 Mozaffari-Kermani, Mehran
3 Naehrig, Michael
3 Özbudak, Ferruh
3 Paar, Christof
3 Page, Dan
3 Tibouchi, Mehdi
3 Tunstall, Michael J.
3 Vercauteren, Frederik
3 Yao, David D. W.
3 Zhang, Fangguo
3 Zimmermann, Paul
2 Atkin, Arthur Oliver Lonsdale
2 Bach, Eric
2 Bai, Shi
2 Barbulescu, Razvan
2 Buell, Duncan A.
2 Carter, Gary
2 Cherepniov, M. A.
2 Dawson, Edward
2 Dilcher, Karl
2 Dimitrov, Vassil S.
2 Dumas, Jean-Guillaume
2 Dumitrescu, Adrian
2 Fan, Haining
2 Farashahi, Reza Rezaeian
2 Feix, Benoit
2 Ferradi, Houda
2 Fousse, Laurent
2 Fox, Jacob
2 Gollmann, Dieter
2 Gorla, Elisa
2 Graham, Ronald Lewis
2 Großschädl, Johann
2 Guajardo, Jorge
2 Guillevic, Aurore
2 Guilley, Sylvain
2 Harvey, David I.
2 Hasan, M. Anwar
2 Hutter, Michael
2 Ibrahimi, Morteza
2 Jeon, Jun-Cheol
2 Karati, Sabyasachi
2 Khleborodov, Denis
2 Kim, Taehyun
2 Kleinjung, Thorsten
2 Kogure, Jun
2 Kohel, David R.
2 Koziel, Brian
2 Kraning, Matt
2 Kumar, Sandeep S.
2 Lai, Jui-Chang
2 Lange, Tanja
2 Lenstra, Arjen K.
2 Lercier, Reynald
2 Longa, Patrick
2 Maimuţ, Diana-Ştefania
2 Massierer, Maike
2 Montanari, Andrea
2 Moody, Dustin
2 Muñoz Masqué, Jaime
2 Negre, Christophe
2 Okeya, Katsuyuki
2 Paterson, Kenneth G.
2 Pelzl, Jan
2 Phillips, Braden J.
...and 488 more Authors
all top 5

Cited in 93 Serials

48 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
7 Computers & Mathematics with Applications
7 Journal of Number Theory
6 Journal of Symbolic Computation
6 Applicable Algebra in Engineering, Communication and Computing
5 Cybernetics and Systems Analysis
5 Journal of Mathematical Sciences (New York)
5 Finite Fields and their Applications
5 Advances in Mathematics of Communications
4 Theoretical Computer Science
4 Acta Applicandae Mathematicae
4 Linear Algebra and its Applications
4 Wuhan University Journal of Natural Sciences (WUJNS)
4 Journal of Mathematical Cryptology
4 Cryptography and Communications
3 Information Sciences
3 European Journal of Combinatorics
3 Information and Computation
3 The Journal of Supercomputing
2 Discrete Applied Mathematics
2 Periodica Mathematica Hungarica
2 Journal of Computational and Applied Mathematics
2 Mathematics and Computers in Simulation
2 Transactions of the American Mathematical Society
2 Discrete & Computational Geometry
2 Afrika Matematika
2 Prikladnaya Diskretnaya Matematika
1 Analysis Mathematica
1 International Journal of Mathematical Education in Science and Technology
1 Israel Journal of Mathematics
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 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 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 SIAM Journal on Discrete Mathematics
1 Random Structures & Algorithms
1 Japan Journal of Industrial and Applied Mathematics
1 The Annals of Applied Probability
1 RAIRO. Informatique Théorique et Applications
1 Archive for Mathematical Logic
1 Journal de Théorie des Nombres de Bordeaux
1 The Electronic Journal of Combinatorics
1 Advances in Computational Mathematics
1 Mathematical Problems in Engineering
1 Doklady Mathematics
1 The Ramanujan Journal
1 Annals of Mathematics. Second Series
1 LMS Journal of Computation and Mathematics
1 Lobachevskii Journal of Mathematics
1 Journal of the Australian Mathematical Society
1 Journal of Applied Mathematics
1 Entropy
1 Quantum Information Processing
1 Journal of Algebra and its Applications
1 Science in China. Series F
1 International Journal of Number Theory
1 Proyecciones
1 Mathematics in Computer Science
1 Groups, Complexity, Cryptology
1 Journal of Electrical and Computer Engineering
1 Computer Science Review
1 Research in the Mathematical Sciences
1 Research in Number Theory

Citations by Year

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