Edit Profile (opens in new tab) Montgomery, Peter Lawrence (b. 1947 d. 2020) Co-Author Distance Author ID: montgomery.peter-l Published as: Montgomery, Peter L.; Montgomery, P.; Montgomery, Peter more...less 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 all top 5 Co-Authors 7 single-authored 5 Bos, Joppe W. 5 Lenstra, Arjen K. 4 Lauter, Kristin Estella 4 te Riele, Herman 3 Cavallar, Stefania Hedwig 3 Kleinjung, Thorsten 3 Silverman, Robert D. 3 Zimmermann, Paul 2 Dodson, Bruce A. 2 Eisenträger, Kirsten 2 Elkenbracht-Huizing, Reina-Marije 2 Erdős, Pál 2 Graham, Ronald Lewis 2 Kruppa, Alexander 2 Leyland, Paul C. 2 Lioen, Walter M. 2 Rothschild, Bruce L. 2 Spencer, Joel H. 2 Straus, Ernst G. 2 Wagstaff, Samuel Standfield jun. 1 Aardal, Karen I. 1 Aoki, Kazumaro 1 Barbulescu, Razvan 1 Bhaskar, Raghav 1 Bouvier, Cyril 1 Brillhart, John 1 Chandrasekaran, Karthekeyan 1 Ciet, Mathieu 1 Cowie, James 1 Dodsons, Bruce 1 Franke, Jens 1 Gaudry, Pierrick 1 Gilchrist, Jeff 1 Guillerm, Gérard 1 Joye, Marc 1 Kaihara, Marcelo E. 1 Lokam, Satyanarayana V. 1 Marchand, Joël 1 Morain, François 1 Muffett, Alec 1 Naehrig, Michael 1 Nahm, Sangil 1 Osvik, Dag Arne 1 Putnam, Chris 1 Putnam, Craig 1 Shumow, Daniel 1 Thomé, Emmanuel 1 Timofeev, Andrey V. 1 Venkatesan, Ramarathnam 1 Wackerbarth, R. K. 1 Yacobi, Yacov 1 Zaverucha, Gregory M. 1 Zayer, Jörg all top 5 Serials 6 Mathematics of Computation 2 CWI Quarterly 1 IEEE Transactions on Computers 1 Journal of Combinatorial Theory. Series A 1 Designs, Codes and Cryptography 1 Serdica Journal of Computing 1 International Journal of Applied Cryptography all top 5 Fields 23 Number theory (11-XX) 11 Information and communication theory, circuits (94-XX) 6 Computer science (68-XX) 5 Algebraic geometry (14-XX) 3 Numerical analysis (65-XX) 2 Combinatorics (05-XX) 1 Mathematical logic and foundations (03-XX) Publications by Year all cited Publications top 5 cited Publications 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 cited Publications top 5 cited Publications 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 all top 5 Cited in 32 Fields 271 Information and communication theory, circuits (94-XX) 220 Number theory (11-XX) 119 Computer science (68-XX) 118 Algebraic geometry (14-XX) 68 Combinatorics (05-XX) 29 Numerical analysis (65-XX) 22 Quantum theory (81-XX) 20 Convex and discrete geometry (52-XX) 13 Field theory and polynomials (12-XX) 9 Commutative algebra (13-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 4 Geometry (51-XX) 3 Mathematical logic and foundations (03-XX) 3 Group theory and generalizations (20-XX) 3 Probability theory and stochastic processes (60-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Approximations and expansions (41-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Operations research, mathematical programming (90-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Topological groups, Lie groups (22-XX) 1 Real functions (26-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Partial differential equations (35-XX) 1 Difference and functional equations (39-XX) 1 Abstract harmonic analysis (43-XX) 1 General topology (54-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Statistics (62-XX) 1 Mechanics of deformable solids (74-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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