# zbMATH — the first resource for mathematics

## Schaefer, Edward F.

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 Author ID: schaefer.edward-f Published as: Schaefer, Edward F. External Links: MGP · dblp
 Documents Indexed: 22 Publications since 1995
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#### Co-Authors

 8 single-authored 4 Stoll, Michael 3 Poonen, Bjorn 2 Flynn, Eugene Victor 1 Djabri, Z. 1 Fisher, Tom A. 1 Kachisa, Ezekiel J. 1 Klassen, Matthew J. 1 Kloosterman, Remke Nanne 1 Leprévost, Franck 1 Miller, Stephen Michael 1 Musa, Mohammad A. 1 Pomerance, Carl Bernard 1 Smart, Nigel P. 1 Stein, William A. 1 Wedig, Stephen 1 Wetherell, Joseph L.
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#### Serials

 5 Journal of Number Theory 3 Transactions of the American Mathematical Society 2 Duke Mathematical Journal 2 Cryptologia 1 American Mathematical Monthly 1 Pi Mu Epsilon Journal 1 Mathematics of Computation 1 Acta Arithmetica 1 Journal für die Reine und Angewandte Mathematik 1 Mathematische Annalen 1 LMS Journal of Computation and Mathematics 1 Research in Number Theory
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#### Fields

 18 Number theory (11-XX) 15 Algebraic geometry (14-XX) 4 Information and communication theory, circuits (94-XX) 1 General and overarching topics; collections (00-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Differential geometry (53-XX) 1 Computer science (68-XX)

#### Citations contained in zbMATH Open

17 Publications have been cited 312 times in 219 Documents Cited by Year
Cycles of quadratic polynomials and rational points on a genus-2 curve. Zbl 0958.11024
Flynn, E. V.; Poonen, Bjorn; Schaefer, Edward F.
1997
Explicit descent for Jacobians of cyclic covers of the projective line. Zbl 0888.11023
Poonen, Bjorn; Schaefer, Edward F.
1997
Computing a Selmer group of a Jacobian using functions on the curve. Zbl 0889.11021
Schaefer, Edward F.
1998
Twists of $$X(7)$$ and primitive solutions to $$x^2+y^3=z^7$$. Zbl 1124.11019
Poonen, Bjorn; Schaefer, Edward F.; Stoll, Michael
2007
2-descent on the Jacobians of hyperelliptic curves. Zbl 0832.14016
Schaefer, Edward F.
1995
Class groups and Selmer groups. Zbl 0859.11034
Schaefer, Edward F.
1996
How to do a $$p$$-descent on an elliptic curve. Zbl 1119.11029
Schaefer, Edward F.; Stoll, Michael
2004
Constructing Brezing-Weng pairing-friendly elliptic curves using elements in the cyclotomic field. Zbl 1186.94451
Kachisa, Ezekiel J.; Schaefer, Edward F.; Scott, Michael
2008
Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves. Zbl 1020.11043
Flynn, E. Victor; Leprévost, Franck; Schaefer, Edward F.; Stein, William A.; Stoll, Michael
2001
Computing the $$p$$-Selmer group of an elliptic curve. Zbl 0954.11022
Djabri, Z.; Schaefer, Edward F.; Smart, N. P.
2000
Selmer groups of elliptic curves that can be arbitrarily large. Zbl 1074.11032
Kloosterman, Remke; Schaefer, Edward F.
2003
A simplified aes algorithm and its linear and differential cryptanalyses. Zbl 1325.94131
Musa, Mohammad A.; Schaefer, Edward F.; Wedig, Stephen
2003
A new proof for the non-degeneracy of the Frey-Rück pairing and a connection to isogenies over the base field. Zbl 1154.14320
Schaefer, Edward F.
2005
Arithmetic and geometry of the curve $$y^ 3+1=x^ 4$$. Zbl 0838.14018
Klassen, Matthew J.; Schaefer, Edward F.
1996
A simplified data encryption standard algorithm. Zbl 0853.94002
Schaefer, Edward F.
1996
Computing the Selmer group of an isogeny between Abelian varieties using a further isogeny to a Jacobian. Zbl 1095.11033
Schaefer, Edward F.; Wetherell, Joseph L.
2005
The yoga of the Cassels-Tate pairing. Zbl 1278.11062
Fisher, Tom; Schaefer, Edward F.; Stoll, Michael
2010
The yoga of the Cassels-Tate pairing. Zbl 1278.11062
Fisher, Tom; Schaefer, Edward F.; Stoll, Michael
2010
Constructing Brezing-Weng pairing-friendly elliptic curves using elements in the cyclotomic field. Zbl 1186.94451
Kachisa, Ezekiel J.; Schaefer, Edward F.; Scott, Michael
2008
Twists of $$X(7)$$ and primitive solutions to $$x^2+y^3=z^7$$. Zbl 1124.11019
Poonen, Bjorn; Schaefer, Edward F.; Stoll, Michael
2007
A new proof for the non-degeneracy of the Frey-Rück pairing and a connection to isogenies over the base field. Zbl 1154.14320
Schaefer, Edward F.
2005
Computing the Selmer group of an isogeny between Abelian varieties using a further isogeny to a Jacobian. Zbl 1095.11033
Schaefer, Edward F.; Wetherell, Joseph L.
2005
How to do a $$p$$-descent on an elliptic curve. Zbl 1119.11029
Schaefer, Edward F.; Stoll, Michael
2004
Selmer groups of elliptic curves that can be arbitrarily large. Zbl 1074.11032
Kloosterman, Remke; Schaefer, Edward F.
2003
A simplified aes algorithm and its linear and differential cryptanalyses. Zbl 1325.94131
Musa, Mohammad A.; Schaefer, Edward F.; Wedig, Stephen
2003
Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves. Zbl 1020.11043
Flynn, E. Victor; Leprévost, Franck; Schaefer, Edward F.; Stein, William A.; Stoll, Michael
2001
Computing the $$p$$-Selmer group of an elliptic curve. Zbl 0954.11022
Djabri, Z.; Schaefer, Edward F.; Smart, N. P.
2000
Computing a Selmer group of a Jacobian using functions on the curve. Zbl 0889.11021
Schaefer, Edward F.
1998
Cycles of quadratic polynomials and rational points on a genus-2 curve. Zbl 0958.11024
Flynn, E. V.; Poonen, Bjorn; Schaefer, Edward F.
1997
Explicit descent for Jacobians of cyclic covers of the projective line. Zbl 0888.11023
Poonen, Bjorn; Schaefer, Edward F.
1997
Class groups and Selmer groups. Zbl 0859.11034
Schaefer, Edward F.
1996
Arithmetic and geometry of the curve $$y^ 3+1=x^ 4$$. Zbl 0838.14018
Klassen, Matthew J.; Schaefer, Edward F.
1996
A simplified data encryption standard algorithm. Zbl 0853.94002
Schaefer, Edward F.
1996
2-descent on the Jacobians of hyperelliptic curves. Zbl 0832.14016
Schaefer, Edward F.
1995
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#### Cited by 261 Authors

 15 Flynn, Eugene Victor 14 Stoll, Michael 10 Fisher, Tom A. 9 Creutz, Brendan 9 Schaefer, Edward F. 7 Bruin, Nils 7 Siksek, Samir 7 Zarkhin, Yuriĭ Gennad’evich 6 Doyle, John R. 4 Balakrishnan, Jennifer S. 4 Cremona, John E. 4 Dokchitser, Tim 4 Poonen, Bjorn 3 Bandini, Andrea 3 Benedetto, Robert L. 3 Bhargava, Manjul 3 Česnavičius, Kęstutis 3 Dominguez Perez, Luis J. 3 Duquesne, Sylvain 3 Freitas, Nuno 3 Girard, Martine 3 Hutz, Benjamin 3 Lee, Hyangsook 3 Lorenzo García, Elisa 3 Manes, Michelle 3 Müller, Jan Steffen 3 Stein, William A. 3 Top, Jaap 3 Wang, Xiaoheng 3 Xue, Jiangwei 2 Bekker, Boris Mikhaĭlovich 2 Benger, Naomi 2 Bruin, Peter 2 Byeon, Dongho 2 Canci, Jung Kyu 2 Charlemagne, Manuel 2 Chen, Imin 2 Costello, Craig 2 Dahmen, Sander R. 2 Dokchitser, Vladimir 2 Faber, Xander 2 Fall, Moussa 2 Fotiadis, Georgios 2 Fouotsa, Emmanuel 2 Ghammam, Loubna 2 Gross, Benedict Hyman 2 Hirakawa, Yoshinosuke 2 Ingram, Patrick 2 Jedrzejak, Tomasz 2 Kachisa, Ezekiel J. 2 Kirst, Peter 2 Kloosterman, Remke Nanne 2 Konstantinou, Elisavet 2 Kosunen, Pekka 2 Krumm, David 2 Kulesz, Leopoldo 2 Lee, Eunjeong 2 Logan, Adam 2 Luca, Florian 2 Matsumura, Hideki 2 Miller, Robert L. 2 Narkiewicz, Władysław 2 Paladino, Laura 2 Park, Cheol Min 2 Pries, Rachel J. 2 Rodríguez-Henríquez, Francisco 2 Rouse, Jeremy A. 2 Sall, Oumar 2 Shparlinski, Igor E. 2 Silverberg, Alice 2 Silverman, Joseph Hillel 2 Smart, Nigel P. 2 Stein, Oliver 2 Sutherland, Andrew V. 2 van Bommel, Raymond 2 Viray, Bianca 2 Vishkautsan, Solomon 2 Zureick-Brown, David 1 Abdullah, Rosni 1 Agashe, Amod 1 Almazrooie, Mishal 1 Anderson, Greg W. 1 Arnth-Jensen, Anna 1 Baker, Matthew H. 1 Barbulescu, Razvan 1 Bartel, Alex 1 Bennett, Michael A. 1 Berger, Lisa 1 Besser, Amnon 1 Binegar, Skye 1 Boyd, Colin A. 1 Bremner, Andrew 1 Bright, M. J. 1 Brumer, Armand 1 Chen, Ruqian 1 Chen, Zexiang 1 Corn, Patrick 1 Cruz-Cortés, Nareli 1 Daniels, Harris B. 1 de Graaf, Willem Adriaan ...and 161 more Authors
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#### Cited in 68 Serials

 25 Mathematics of Computation 21 Journal of Number Theory 11 Journal de Théorie des Nombres de Bordeaux 11 International Journal of Number Theory 9 Transactions of the American Mathematical Society 7 Compositio Mathematica 7 LMS Journal of Computation and Mathematics 6 Acta Arithmetica 6 Manuscripta Mathematica 5 Duke Mathematical Journal 5 Journal of Algebra 5 Mathematische Zeitschrift 5 Research in Number Theory 4 Journal für die Reine und Angewandte Mathematik 4 Proceedings of the American Mathematical Society 4 Journal of Symbolic Computation 4 Journal of Cryptology 3 Rocky Mountain Journal of Mathematics 3 Cryptologia 3 Finite Fields and their Applications 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Archiv der Mathematik 2 Indagationes Mathematicae. New Series 2 Experimental Mathematics 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 JSIAM Letters 2 Research in the Mathematical Sciences 1 Bulletin of the Australian Mathematical Society 1 Communications in Algebra 1 Discrete Applied Mathematics 1 Advances in Mathematics 1 Commentarii Mathematici Helvetici 1 Czechoslovak Mathematical Journal 1 Functiones et Approximatio. Commentarii Mathematici 1 Glasgow Mathematical Journal 1 Illinois Journal of Mathematics 1 Information Sciences 1 Inventiones Mathematicae 1 Journal of Combinatorial Theory. Series B 1 Journal of Optimization Theory and Applications 1 Mathematische Annalen 1 Memoirs of the American Mathematical Society 1 Michigan Mathematical Journal 1 Theoretical Computer Science 1 Ergodic Theory and Dynamical Systems 1 Journal of the American Mathematical Society 1 Journal of Global Optimization 1 Bulletin of the American Mathematical Society. New Series 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Applicable Algebra in Engineering, Communication and Computing 1 St. Petersburg Mathematical Journal 1 Izvestiya: Mathematics 1 Annales Academiae Scientiarum Fennicae. Mathematica 1 Transformation Groups 1 The Ramanujan Journal 1 Journal of the European Mathematical Society (JEMS) 1 Journal of Applied Mathematics and Computing 1 Quantum Information Processing 1 Proceedings of the Steklov Institute of Mathematics 1 Journal of Mathematical Cryptology 1 Algebra & Number Theory 1 Involve 1 Afrika Matematika 1 Forum of Mathematics, Sigma 1 Carpathian Mathematical Publications 1 Journal of Complex Analysis 1 Proceedings of the American Mathematical Society. Series B 1 Prikladnaya Diskretnaya Matematika
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#### Cited in 19 Fields

 171 Number theory (11-XX) 130 Algebraic geometry (14-XX) 30 Dynamical systems and ergodic theory (37-XX) 29 Information and communication theory, circuits (94-XX) 5 Computer science (68-XX) 4 Field theory and polynomials (12-XX) 3 Combinatorics (05-XX) 2 Commutative algebra (13-XX) 2 Associative rings and algebras (16-XX) 2 Nonassociative rings and algebras (17-XX) 2 Functions of a complex variable (30-XX) 2 Quantum theory (81-XX) 2 Operations research, mathematical programming (90-XX) 1 History and biography (01-XX) 1 Group theory and generalizations (20-XX) 1 Real functions (26-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Probability theory and stochastic processes (60-XX) 1 Numerical analysis (65-XX)