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Frey, Gerhard

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Author ID: frey.gerhard Recent zbMATH articles by "Frey, Gerhard"
Published as: Frey, G.; Frey, Gerhard
External Links: MGP · Wikidata · GND
Documents Indexed: 67 Publications since 1972, including 5 Books
Reviewing Activity: 17 Reviews

Publications by Year

Citations contained in zbMATH

51 Publications have been cited 515 times in 434 Documents Cited by Year
Handbook of elliptic and hyperelliptic curve cryptography. Zbl 1082.94001
Cohen, Henri; Frey, Gerhard; Avanzi, Robero M.; Doche, Christophe; Lange, Tanja; Nguyen, Kim; Vercauteren, Frederik
137
2006
A remark concerning \(m\)-divisibility and the discrete logarithm in the divisor class group of curves. Zbl 0813.14045
Frey, Gerhard; Rück, Hans-Georg
72
1994
Approximation theory and the rank of Abelian varieties over large algebraic fields. Zbl 0275.14021
Frey, Gerhard; Jarden, Moshe
32
1974
Curves with infinitely many points of fixed degree. Zbl 0808.14022
Frey, Gerhard
29
1994
The Tate pairing and the discrete logarithm applied to elliptic curve cryptosystems. Zbl 0957.94025
Frey, Gerhard; Müller, Michael; Rück, Hans-Georg
19
1999
Curves of genus 2 covering elliptic curves and an arithmetical application. Zbl 0757.14015
Frey, Gerhard; Kani, Ernst
19
1991
Applications of arithmetical geometry to cryptographic constructions. Zbl 1015.94545
Frey, Gerhard
15
2001
Links between stable elliptic curves and certain diophantine equations. Zbl 0586.10010
Frey, Gerhard
14
1986
Curves with infinite \(K\)-rational geometric fundamental group. Zbl 0978.14021
Frey, Gerhard; Kani, Ernst; Völklein, Helmut
11
1999
Pseudo algebraically closed fields with non-archimedean real valuations. Zbl 0264.12105
Frey, Gerhard
11
1973
On the Selmer group of twists of elliptic curves with \(\mathbb Q\)-rational torsion points. Zbl 0646.14024
Frey, G.
9
1989
Some remarks concerning points of finite order on elliptic curves over global fields. Zbl 0348.14018
Frey, Gerhard
9
1977
On elliptic curves with isomorphic torsion structures and corresponding curves of genus 2. Zbl 0856.11026
Frey, Gerhard
8
1995
On Artin’s conjecture for odd 2-dimensional representations. Zbl 0801.00004
Frey, Gerhard (ed.)
8
1994
On the structure of the class group of a function field. Zbl 0426.14011
Frey, Gerhard
8
1979
On ternary equations of Fermat type and relations with elliptic curves. Zbl 0976.11027
Frey, Gerhard
7
1997
On the different of Abelian extensions of global fields. Zbl 0776.11067
Frey, G.; Perret, M.; Stichtenoth, H.
7
1992
Galois representations of octahedral type and 2-coverings of elliptic curves. Zbl 0712.11035
Bayer, Pilar; Frey, Gerhard
7
1991
Properties of twists of elliptic curves. Zbl 0709.14020
Antoniadis, J. A.; Bungert, M.; Frey, G.
7
1990
Die Klassengruppen quadratischer und kubischer Zahlkörper und die Selmergruppen gewisser elliptischer Kurven. Zbl 0317.14016
Frey, Gerhard
7
1975
Links between solutions of \(A-B=C\) and elliptic curves. Zbl 0688.14018
Frey, Gerhard
6
1989
A remark about isogenies of elliptic curves over quadratic fields. Zbl 0596.14021
Frey, Gerhard
6
1986
The rank of the solutions of \(Y^2=X^3\pm p^3\) over \(\mathbb Q\). Zbl 0564.14011
Frey, Gerhard
6
1984
Computation of the 2-rank of pure cubic fields. Zbl 0385.12001
Eisenbeis, H.; Frey, G.; Ommerborn, B.
5
1978
Curves of genus 2 with elliptic differentials and associated Hurwitz spaces. Zbl 1198.14024
Frey, Gerhard; Kani, Ernst
4
2009
The strong Lefschetz principle in algebraic geometry. Zbl 0609.14019
Frey, Gerhard; Rück, Hans-Georg
4
1986
Fast bilinear maps from the Tate-Lichtenbaum pairing on hyperelliptic curves. Zbl 1143.94345
Frey, Gerhard; Lange, Tanja
3
2006
Mathematical background of public key cryptography. Zbl 1155.11361
Frey, Gerhard; Lange, Tanja
3
2005
Construction and arithmetical applications of modular forms of low weight. Zbl 0814.11027
Frey, Gerhard
3
1994
Links between elliptic curves and solutions of \(A-B=C\). Zbl 0682.14021
Frey, G.
3
1987
Dualitätssatz für endliche kommutative Gruppenschemata über Kongruenzfunktionenkörpern. Zbl 0375.12015
Frey, Gerhard
3
1978
Elliptische Funktionenkörper mit schlechter Reduktion. Zbl 0241.14023
Frey, G.
3
1972
Über die Fundamentalgruppe von Körpern mit Divisorentheorie. Zbl 0238.12006
Frey, G.; Geyer, W. D.
3
1972
Normal forms of hyperelliptic curves of genus 3. Zbl 1345.14037
Frey, Gerhard; Kani, Ernst
2
2015
Correspondences on hyperelliptic curves and applications to the discrete logarithm. Zbl 1345.14036
Frey, Gerhard; Kani, Ernst
2
2012
On the relation between Brauer groups and discrete logarithms. Zbl 1187.11043
Frey, Gerhard
2
2006
On using expansions to the base of \(-2\). Zbl 1060.94013
Avanzi, Roberto; Frey, Gerhard; Lange, Tanja; Oyono, Roger
2
2004
Horizontal isogeny theorems. Zbl 1040.12005
Frey, Gerhard; Jarden, Moshe
2
2002
Some aspects of the theory of elliptic curves over number fields. Zbl 0596.14022
Frey, Gerhard
2
1986
A relation between the value of the L-series of the curve: \(y^ 2=x^ 3-k^ 3\) in \(s=1\) and its Selmer group. Zbl 0575.14027
Frey, Gerhard
2
1985
Maximal abelsche Erweiterung von Funktionenkörpern über lokalen Körpern. Zbl 0352.14012
Frey, G.
2
1977
Elliptische Funktionenkörper mit schlechter Reduktion und nichttrivialer Hasse-Invariante. Zbl 0238.14013
Frey, G.
2
1972
Isogenies in theory and praxis. Zbl 1364.11109
Frey, Gerhard
1
2014
Relations between arithmetic geometry and public key cryptography. Zbl 1225.11149
Frey, Gerhard
1
2010
On bilinear structures on divisor class groups. Zbl 1187.11044
Frey, Gerhard
1
2009
Non-constant curves of genus 2 with infinite pro-Galois covers. Zbl 1153.14025
Diem, Claus; Frey, Gerhard
1
2008
Projective \(p\)-adic representations of the \(K\)-rational geometric fundamental group. Zbl 1041.14009
Frey, G.; Kani, E.
1
2001
Galois representations attached to elliptic curves and Diophantine problems. Zbl 1006.11027
Frey, Gerhard
1
2001
Arithmetic of modular curves and applications. Zbl 0932.11042
Frey, Gerhard; Müller, Michael
1
1999
Elementare Zahlentheorie. Zbl 0519.10001
Frey, Gerhard
1
1984
Rationale Punkte auf Fermatkurven und getwisteten Modulkurven. Zbl 0474.14011
Frey, G.
1
1982
Normal forms of hyperelliptic curves of genus 3. Zbl 1345.14037
Frey, Gerhard; Kani, Ernst
2
2015
Isogenies in theory and praxis. Zbl 1364.11109
Frey, Gerhard
1
2014
Correspondences on hyperelliptic curves and applications to the discrete logarithm. Zbl 1345.14036
Frey, Gerhard; Kani, Ernst
2
2012
Relations between arithmetic geometry and public key cryptography. Zbl 1225.11149
Frey, Gerhard
1
2010
Curves of genus 2 with elliptic differentials and associated Hurwitz spaces. Zbl 1198.14024
Frey, Gerhard; Kani, Ernst
4
2009
On bilinear structures on divisor class groups. Zbl 1187.11044
Frey, Gerhard
1
2009
Non-constant curves of genus 2 with infinite pro-Galois covers. Zbl 1153.14025
Diem, Claus; Frey, Gerhard
1
2008
Handbook of elliptic and hyperelliptic curve cryptography. Zbl 1082.94001
Cohen, Henri; Frey, Gerhard; Avanzi, Robero M.; Doche, Christophe; Lange, Tanja; Nguyen, Kim; Vercauteren, Frederik
137
2006
Fast bilinear maps from the Tate-Lichtenbaum pairing on hyperelliptic curves. Zbl 1143.94345
Frey, Gerhard; Lange, Tanja
3
2006
On the relation between Brauer groups and discrete logarithms. Zbl 1187.11043
Frey, Gerhard
2
2006
Mathematical background of public key cryptography. Zbl 1155.11361
Frey, Gerhard; Lange, Tanja
3
2005
On using expansions to the base of \(-2\). Zbl 1060.94013
Avanzi, Roberto; Frey, Gerhard; Lange, Tanja; Oyono, Roger
2
2004
Horizontal isogeny theorems. Zbl 1040.12005
Frey, Gerhard; Jarden, Moshe
2
2002
Applications of arithmetical geometry to cryptographic constructions. Zbl 1015.94545
Frey, Gerhard
15
2001
Projective \(p\)-adic representations of the \(K\)-rational geometric fundamental group. Zbl 1041.14009
Frey, G.; Kani, E.
1
2001
Galois representations attached to elliptic curves and Diophantine problems. Zbl 1006.11027
Frey, Gerhard
1
2001
The Tate pairing and the discrete logarithm applied to elliptic curve cryptosystems. Zbl 0957.94025
Frey, Gerhard; Müller, Michael; Rück, Hans-Georg
19
1999
Curves with infinite \(K\)-rational geometric fundamental group. Zbl 0978.14021
Frey, Gerhard; Kani, Ernst; Völklein, Helmut
11
1999
Arithmetic of modular curves and applications. Zbl 0932.11042
Frey, Gerhard; Müller, Michael
1
1999
On ternary equations of Fermat type and relations with elliptic curves. Zbl 0976.11027
Frey, Gerhard
7
1997
On elliptic curves with isomorphic torsion structures and corresponding curves of genus 2. Zbl 0856.11026
Frey, Gerhard
8
1995
A remark concerning \(m\)-divisibility and the discrete logarithm in the divisor class group of curves. Zbl 0813.14045
Frey, Gerhard; Rück, Hans-Georg
72
1994
Curves with infinitely many points of fixed degree. Zbl 0808.14022
Frey, Gerhard
29
1994
On Artin’s conjecture for odd 2-dimensional representations. Zbl 0801.00004
Frey, Gerhard (ed.)
8
1994
Construction and arithmetical applications of modular forms of low weight. Zbl 0814.11027
Frey, Gerhard
3
1994
On the different of Abelian extensions of global fields. Zbl 0776.11067
Frey, G.; Perret, M.; Stichtenoth, H.
7
1992
Curves of genus 2 covering elliptic curves and an arithmetical application. Zbl 0757.14015
Frey, Gerhard; Kani, Ernst
19
1991
Galois representations of octahedral type and 2-coverings of elliptic curves. Zbl 0712.11035
Bayer, Pilar; Frey, Gerhard
7
1991
Properties of twists of elliptic curves. Zbl 0709.14020
Antoniadis, J. A.; Bungert, M.; Frey, G.
7
1990
On the Selmer group of twists of elliptic curves with \(\mathbb Q\)-rational torsion points. Zbl 0646.14024
Frey, G.
9
1989
Links between solutions of \(A-B=C\) and elliptic curves. Zbl 0688.14018
Frey, Gerhard
6
1989
Links between elliptic curves and solutions of \(A-B=C\). Zbl 0682.14021
Frey, G.
3
1987
Links between stable elliptic curves and certain diophantine equations. Zbl 0586.10010
Frey, Gerhard
14
1986
A remark about isogenies of elliptic curves over quadratic fields. Zbl 0596.14021
Frey, Gerhard
6
1986
The strong Lefschetz principle in algebraic geometry. Zbl 0609.14019
Frey, Gerhard; Rück, Hans-Georg
4
1986
Some aspects of the theory of elliptic curves over number fields. Zbl 0596.14022
Frey, Gerhard
2
1986
A relation between the value of the L-series of the curve: \(y^ 2=x^ 3-k^ 3\) in \(s=1\) and its Selmer group. Zbl 0575.14027
Frey, Gerhard
2
1985
The rank of the solutions of \(Y^2=X^3\pm p^3\) over \(\mathbb Q\). Zbl 0564.14011
Frey, Gerhard
6
1984
Elementare Zahlentheorie. Zbl 0519.10001
Frey, Gerhard
1
1984
Rationale Punkte auf Fermatkurven und getwisteten Modulkurven. Zbl 0474.14011
Frey, G.
1
1982
On the structure of the class group of a function field. Zbl 0426.14011
Frey, Gerhard
8
1979
Computation of the 2-rank of pure cubic fields. Zbl 0385.12001
Eisenbeis, H.; Frey, G.; Ommerborn, B.
5
1978
Dualitätssatz für endliche kommutative Gruppenschemata über Kongruenzfunktionenkörpern. Zbl 0375.12015
Frey, Gerhard
3
1978
Some remarks concerning points of finite order on elliptic curves over global fields. Zbl 0348.14018
Frey, Gerhard
9
1977
Maximal abelsche Erweiterung von Funktionenkörpern über lokalen Körpern. Zbl 0352.14012
Frey, G.
2
1977
Die Klassengruppen quadratischer und kubischer Zahlkörper und die Selmergruppen gewisser elliptischer Kurven. Zbl 0317.14016
Frey, Gerhard
7
1975
Approximation theory and the rank of Abelian varieties over large algebraic fields. Zbl 0275.14021
Frey, Gerhard; Jarden, Moshe
32
1974
Pseudo algebraically closed fields with non-archimedean real valuations. Zbl 0264.12105
Frey, Gerhard
11
1973
Elliptische Funktionenkörper mit schlechter Reduktion. Zbl 0241.14023
Frey, G.
3
1972
Über die Fundamentalgruppe von Körpern mit Divisorentheorie. Zbl 0238.12006
Frey, G.; Geyer, W. D.
3
1972
Elliptische Funktionenkörper mit schlechter Reduktion und nichttrivialer Hasse-Invariante. Zbl 0238.14013
Frey, G.
2
1972
all top 5

Cited by 546 Authors

17 Frey, Gerhard
11 Galbraith, Steven D.
10 Jarden, Moshe
10 Shparlinski, Igor E.
9 Tsyganov, Andreĭ Vladimirovich
8 Sutherland, Andrew V.
7 Kani, Ernst J.
7 Menezes, Alfred J.
6 Lee, Hyangsook
6 Silverberg, Alice
6 Zhang, Fangguo
5 Duquesne, Sylvain
5 Thériault, Nicolas
4 Bröker, Reinier
4 El Mrabet, Nadia
4 Gaudry, Pierrick
4 Geyer, Wulf-Dieter
4 Jacobson, Michael John jun.
4 Jehanne, Arnaud
4 Lauter, Kristin Estella
4 Miret, Josep M.
4 Pujolàs, Jordi
4 Wang, Xueli
3 Avanzi, Roberto Maria
3 Blake, Ian F.
3 Cadoret, Anna
3 Clark, Peter Louis
3 Derickx, Maarten
3 Dominguez Perez, Luis J.
3 Fouotsa, Emmanuel
3 Gorla, Elisa
3 Holden, Joshua Brandon
3 Hubrechts, Hendrik
3 James, Kevin
3 Kamienny, Sheldon
3 Lange, Tanja
3 Lee, Eunjeong
3 Lin, Xibin
3 Lozano-Robledo, Álvaro
3 Lubicz, David
3 Massierer, Maike
3 Najman, Filip
3 Park, Cheol Min
3 Pei, Dingyi
3 Ribet, Kenneth Alan
3 Rodríguez-Henríquez, Francisco
3 Rosen, Michael I.
3 Rück, Hans-Georg
3 Scheidler, Renate
3 Scott, Michael H.
3 Scott, Michael L.
3 Shaska, Tanush
3 Silverman, Joseph Hillel
3 Tamagawa, Akio
3 Teske, Edlyn
3 Xu, Maozhi
3 Zarkhin, Yuriĭ Gennad’evich
3 Zimmer, Horst Günter
2 Abelard, Simon
2 Achter, Jeffrey D.
2 Adachi, Norio
2 Adj, Gora
2 Alimoradi, Reza
2 Benger, Naomi
2 Bhagvati, Chakravarthy
2 Böckle, Gebhard
2 Brion, Michel
2 Bruin, Peter
2 Carter, Gary
2 Castryck, Wouter
2 Charlemagne, Manuel
2 Chen, Yenmei J.
2 Chiesa, Alessandro
2 Choie, YoungJu
2 Constantinescu, Nicolae Mircea
2 Cornelissen, Gunther
2 Cruz-Cortés, Nareli
2 Dawson, Edward
2 Duursma, Iwan Maynard
2 Enge, Andreas
2 Fan, Xinxin
2 Farashahi, Reza Rezaeian
2 Faugère, Jean-Charles
2 Fisher, Tom A.
2 Fontein, Felix
2 Garefalakis, Theo
2 Hadian Dehkordi, Massoud
2 Haloui, Safia
2 Hindry, Marc
2 Hisil, Huseyin
2 Hu, Zhi
2 Huang, Mingdeh
2 Im, Bo-Hae
2 Jeong, Eunkyung
2 Joux, Antoine
2 Kachisa, Ezekiel J.
2 Karati, Sabyasachi
2 Kiming, Ian
2 Koblitz, Neal I.
2 Konstantinou, Elisavet
...and 446 more Authors
all top 5

Cited in 120 Serials

35 Journal of Number Theory
21 Mathematics of Computation
18 Designs, Codes and Cryptography
15 Manuscripta Mathematica
13 Finite Fields and their Applications
12 Mathematische Annalen
12 LMS Journal of Computation and Mathematics
11 Archiv der Mathematik
11 Journal de Théorie des Nombres de Bordeaux
10 Israel Journal of Mathematics
10 Journal of Algebra
10 Journal of Cryptology
9 Information Processing Letters
9 Applicable Algebra in Engineering, Communication and Computing
8 Duke Mathematical Journal
7 Transactions of the American Mathematical Society
7 Journal of Symbolic Computation
6 Mathematische Zeitschrift
6 Proceedings of the American Mathematical Society
5 Applied Mathematics and Computation
5 Inventiones Mathematicae
5 Proceedings of the Japan Academy. Series A
5 Journal of Mathematical Cryptology
5 Advances in Mathematics of Communications
4 Journal of Mathematical Physics
4 Annales de l’Institut Fourier
4 Theoretical Computer Science
4 International Journal of Number Theory
3 Communications in Algebra
3 Discrete Applied Mathematics
3 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
3 Compositio Mathematica
3 Information Sciences
3 Journal of Complexity
3 Journal of the American Mathematical Society
3 Bulletin of the American Mathematical Society. New Series
3 Experimental Mathematics
3 Foundations of Computational Mathematics
3 Mathematics in Computer Science
2 Bulletin of the Australian Mathematical Society
2 Theoretical and Mathematical Physics
2 Journal of Geometry and Physics
2 Acta Mathematica
2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
2 Journal of Combinatorial Theory. Series A
2 Journal of Computational and Applied Mathematics
2 Journal of Pure and Applied Algebra
2 Journal für die Reine und Angewandte Mathematik
2 Journal of Soviet Mathematics
2 Results in Mathematics
2 International Journal of Computer Mathematics
2 Journal of Mathematical Sciences (New York)
2 Journal of the European Mathematical Society (JEMS)
2 Groups, Complexity, Cryptology
2 Cryptography and Communications
2 Annales Mathématiques du Québec
1 Computers & Mathematics with Applications
1 Letters in Mathematical Physics
1 Mathematical Notes
1 Mathematische Semesterberichte
1 Arkiv för Matematik
1 Acta Arithmetica
1 Advances in Mathematics
1 Algebra and Logic
1 Collectanea Mathematica
1 Commentarii Mathematici Helvetici
1 Journal of Computer and System Sciences
1 Kodai Mathematical Journal
1 Michigan Mathematical Journal
1 Nagoya Mathematical Journal
1 Ricerche di Matematica
1 Tokyo Journal of Mathematics
1 Annales de la Faculté des Sciences de Toulouse. Série V. Mathématiques
1 Acta Mathematica Hungarica
1 Acta Applicandae Mathematicae
1 Journal of Computer Science and Technology
1 Algorithmica
1 Discrete & Computational Geometry
1 Revista Matemática Iberoamericana
1 Mathematical and Computer Modelling
1 Forum Mathematicum
1 Science in China. Series A
1 International Journal of Mathematics
1 Japan Journal of Industrial and Applied Mathematics
1 Expositiones Mathematicae
1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
1 Tatra Mountains Mathematical Publications
1 Journal of Algebraic Geometry
1 Annales Mathématiques Blaise Pascal
1 Selecta Mathematica. New Series
1 Advances in Computational Mathematics
1 Arab Journal of Mathematical Sciences
1 Documenta Mathematica
1 Mathematical Problems in Engineering
1 The Ramanujan Journal
1 Journal of Discrete Mathematical Sciences & Cryptography
1 Journal of Integer Sequences
1 Annals of Mathematics. Second Series
1 Acta Mathematica Sinica. English Series
1 Lobachevskii Journal of Mathematics
...and 20 more Serials

Citations by Year

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