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## Eisenträger, Kirsten

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 Author ID: eisentrager.kirsten Published as: Eisenträger, Kirsten
 Documents Indexed: 25 Publications since 2003
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#### Co-Authors

 8 single-authored 6 Lauter, Kristin Estella 5 Hallgren, Sean 4 Shlapentokh, Alexandra 3 Morrison, Travis 2 Everest, Graham Robert 2 Montgomery, Peter L. 2 Park, Jennifer 1 Balakrishnan, Jennifer S. 1 Bank, Efrat 1 Belding, Juliana V. 1 Camacho-Navarro, Catalina 1 Chisholm, Sarah 1 Jetchev, Dimitar P. 1 Kitaev, Alexei Yu. 1 Miller, Russell G. 1 Petit, Christophe 1 Song, Fang 1 Stange, Katherine E. 1 Teske, Edlyn
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#### Serials

 2 IMRN. International Mathematics Research Notices 2 Mathematical Research Letters 1 Journal of Algebra 1 Journal of Number Theory 1 Monatshefte für Mathematik 1 Pacific Journal of Mathematics 1 Proceedings of the American Mathematical Society 1 Transactions of the American Mathematical Society 1 Acta Applicandae Mathematicae 1 Journal of the European Mathematical Society (JEMS)
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#### Fields

 23 Number theory (11-XX) 12 Mathematical logic and foundations (03-XX) 8 Algebraic geometry (14-XX) 7 Information and communication theory, circuits (94-XX) 2 Computer science (68-XX) 1 History and biography (01-XX) 1 Field theory and polynomials (12-XX)

#### Citations contained in zbMATH

21 Publications have been cited 99 times in 76 Documents Cited by Year
A CRT algorithm for constructing genus 2 curves over finite fields. Zbl 1270.11060
Eisenträger, Kirsten; Lauter, Kristin
2009
Hilbert’s tenth problem for algebraic function fields of characteristic 2. Zbl 1057.11067
Eisenträger, Kirsten
2003
Fast elliptic curve arithmetic and improved Weil pairing evaluation. Zbl 1038.11079
Eisenträger, Kirsten; Lauter, Kristin; Montgomery, Peter L.
2003
Descent on elliptic curves and Hilbert’s tenth problem. Zbl 1267.11120
Eisenträger, Kirsten; Everest, Graham
2009
Weak instances of PLWE. Zbl 1336.94045
Eisenträger, Kirsten; Hallgren, Sean; Lauter, Kristin
2014
Hilbert’s Tenth problem for function fields of varieties over number fields and $$p$$-adic fields. Zbl 1152.11050
Eisenträger, Kirsten
2007
Hilbert’s tenth problem for function fields of varieties over $$\mathbb{C}$$. Zbl 1109.11061
Eisenträger, Kirsten
2004
A quantum algorithm for computing the unit group of an arbitrary degree number field. Zbl 1315.68134
Eisenträger, Kirsten; Hallgren, Sean; Kitaev, Alexei; Song, Fang
2014
Undecidability in function fields of positive characteristic. Zbl 1242.11100
Eisenträger, Kirsten; Shlapentokh, Alexandra
2009
Supersingular isogeny graphs and endomorphism rings: reductions and solutions. Zbl 1415.94426
Eisenträger, Kirsten; Hallgren, Sean; Lauter, Kristin; Morrison, Travis; Petit, Christophe
2018
Hilbert’s tenth problem and Mazur’s conjectures in complementary subrings of number fields. Zbl 1294.11088
Eisenträger, Kirsten; Everest, Graham; Shlapentokh, Alexandra
2011
As easy as $$\mathbb {Q}$$: Hilbert’s tenth problem for subrings of the rationals and number fields. Zbl 1427.11142
Eisenträger, Kirsten; Miller, Russell; Park, Jennifer; Shlapentokh, Alexandra
2017
Improved Weil and Tate pairings for elliptic and hyperelliptic curves. Zbl 1116.11042
Eisenträger, Kirsten; Lauter, Kristin; Montgomery, Peter L.
2004
The work of Kim and Roush on questions of decidability in algebra and number theory. Zbl 1318.11163
Eisenträger, Kirsten
2013
Hilbert’s tenth problem for function fields of varieties over algebraically closed fields of positive characteristic. Zbl 1270.11126
Eisenträger, Kirsten
2012
Pairings on hyperelliptic curves. Zbl 1214.14021
Balakrishnan, Jennifer; Belding, Juliana; Chisholm, Sarah; Eisenträger, Kirsten; Stange, Katherine E.; Teske, Edlyn
2011
Universally and existentially definable subsets of global fields. Zbl 07020777
Eisenträger, Kirsten; Morrison, Travis
2018
Hilbert’s tenth problem over function fields of positive characteristic not containing the algebraic closure of a finite field. Zbl 1416.11171
Eisenträger, Kirsten; Shlapentokh, Alexandra
2017
Algorithms for ray class groups and Hilbert class fields. Zbl 1288.68070
Eisenträger, Kirsten; Hallgren, Sean
2010
Computing the Cassels pairing on Kolyvagin classes in the Shafarevich-Tate group. Zbl 1186.94436
Eisenträger, Kirsten; Jetchev, Dimitar; Lauter, Kristin
2008
Integrality at a prime for global fields and the perfect closure of global fields of characteristic $$p > 2$$. Zbl 1137.11358
Eisenträger, Kirsten
2005
Supersingular isogeny graphs and endomorphism rings: reductions and solutions. Zbl 1415.94426
Eisenträger, Kirsten; Hallgren, Sean; Lauter, Kristin; Morrison, Travis; Petit, Christophe
2018
Universally and existentially definable subsets of global fields. Zbl 07020777
Eisenträger, Kirsten; Morrison, Travis
2018
As easy as $$\mathbb {Q}$$: Hilbert’s tenth problem for subrings of the rationals and number fields. Zbl 1427.11142
Eisenträger, Kirsten; Miller, Russell; Park, Jennifer; Shlapentokh, Alexandra
2017
Hilbert’s tenth problem over function fields of positive characteristic not containing the algebraic closure of a finite field. Zbl 1416.11171
Eisenträger, Kirsten; Shlapentokh, Alexandra
2017
Weak instances of PLWE. Zbl 1336.94045
Eisenträger, Kirsten; Hallgren, Sean; Lauter, Kristin
2014
A quantum algorithm for computing the unit group of an arbitrary degree number field. Zbl 1315.68134
Eisenträger, Kirsten; Hallgren, Sean; Kitaev, Alexei; Song, Fang
2014
The work of Kim and Roush on questions of decidability in algebra and number theory. Zbl 1318.11163
Eisenträger, Kirsten
2013
Hilbert’s tenth problem for function fields of varieties over algebraically closed fields of positive characteristic. Zbl 1270.11126
Eisenträger, Kirsten
2012
Hilbert’s tenth problem and Mazur’s conjectures in complementary subrings of number fields. Zbl 1294.11088
Eisenträger, Kirsten; Everest, Graham; Shlapentokh, Alexandra
2011
Pairings on hyperelliptic curves. Zbl 1214.14021
Balakrishnan, Jennifer; Belding, Juliana; Chisholm, Sarah; Eisenträger, Kirsten; Stange, Katherine E.; Teske, Edlyn
2011
Algorithms for ray class groups and Hilbert class fields. Zbl 1288.68070
Eisenträger, Kirsten; Hallgren, Sean
2010
A CRT algorithm for constructing genus 2 curves over finite fields. Zbl 1270.11060
Eisenträger, Kirsten; Lauter, Kristin
2009
Descent on elliptic curves and Hilbert’s tenth problem. Zbl 1267.11120
Eisenträger, Kirsten; Everest, Graham
2009
Undecidability in function fields of positive characteristic. Zbl 1242.11100
Eisenträger, Kirsten; Shlapentokh, Alexandra
2009
Computing the Cassels pairing on Kolyvagin classes in the Shafarevich-Tate group. Zbl 1186.94436
Eisenträger, Kirsten; Jetchev, Dimitar; Lauter, Kristin
2008
Hilbert’s Tenth problem for function fields of varieties over number fields and $$p$$-adic fields. Zbl 1152.11050
Eisenträger, Kirsten
2007
Integrality at a prime for global fields and the perfect closure of global fields of characteristic $$p > 2$$. Zbl 1137.11358
Eisenträger, Kirsten
2005
Hilbert’s tenth problem for function fields of varieties over $$\mathbb{C}$$. Zbl 1109.11061
Eisenträger, Kirsten
2004
Improved Weil and Tate pairings for elliptic and hyperelliptic curves. Zbl 1116.11042
Eisenträger, Kirsten; Lauter, Kristin; Montgomery, Peter L.
2004
Hilbert’s tenth problem for algebraic function fields of characteristic 2. Zbl 1057.11067
Eisenträger, Kirsten
2003
Fast elliptic curve arithmetic and improved Weil pairing evaluation. Zbl 1038.11079
Eisenträger, Kirsten; Lauter, Kristin; Montgomery, Peter L.
2003
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#### Cited by 124 Authors

 8 Lauter, Kristin Estella 8 Shlapentokh, Alexandra 7 Eisenträger, Kirsten 4 Streng, Marco 3 Galbraith, Steven D. 3 Hisil, Huseyin 3 Miller, Russell G. 3 Stange, Katherine E. 2 Carter, Gary 2 Costello, Craig 2 Dawson, Edward 2 Ducas, Léo 2 Ionica, Sorina 2 Jetchev, Dimitar P. 2 Khleborodov, Denis 2 Mahé, Valéry 2 Morrison, Travis 2 Park, Jennifer 2 Pasten, Hector V. 2 Poonen, Bjorn 2 Vercauteren, Frederik 2 Wesolowski, Benjamin 2 Wong, Kenneth Koon-Ho 1 Albrecht, Martin R. 1 Anand, R. Sai 1 Appleby, Marcus 1 Bai, Shi 1 Bank, Efrat 1 Bauch, Jens-Dietrich 1 Bernstein, Daniel Julius 1 Biasse, Jean-François 1 Bisson, Gaetan 1 Boneh, Dan 1 Bos, Joppe W. 1 Boyle, Mike 1 Bradford, Jeremy 1 Brooks, Ernest Hunter 1 Camacho-Navarro, Catalina 1 Castryck, Wouter 1 Chen, Hao 1 Chen, Teyu 1 Cho, Sungmin 1 Cramer, Ronald John Fitzgerald 1 de Valence, Henry 1 Demeyer, Jeroen 1 Dewal, M. L. 1 Dimitrov, Vassil S. 1 Ding, Jintai 1 Dittmann, Philip 1 Flammia, Steven T. 1 Glass, Darren B. 1 Gonzales, Alex Capuñay 1 Goren, Eyal Z. 1 Gu, Chunsheng 1 Gupta, Sangeeta 1 Harasawa, Ryuichi 1 Hayashida, Daiki 1 Hong, Seokhie 1 Horng, Gwoboa 1 Huang, Jiwu 1 Iliashenko, Ilia 1 Imbert, Laurent 1 Ingram, Patrick 1 Kang, Bo Gyeong 1 Kılıçer, Pınar 1 Kim, Taehyun 1 Koenigsmann, Jochen 1 Kramer, Kenneth B. 1 Krashen, Daniel 1 Kudo, Aichi 1 Kudo, Momonari 1 Lange, Tanja 1 Liu, Chao-Liang 1 Lorenzo García, Elisa 1 Lyubashevsky, Vadim 1 Mazur, Barry 1 McConnell, Gary 1 McGuire, Gary 1 Menezes, Alfred J. 1 Mishra, Pradeep Kumar 1 Moret-Bailly, Laurent 1 Mosca, Michele 1 Naehrig, Michael 1 O’Connor, Laura Hitt 1 Okumura, Shinya 1 Parent, Alex 1 Park, Je Hong 1 Park, Youngho 1 Peikert, Chris 1 Perlega, Stefan 1 Petit, Christophe 1 Pheidas, Thanases 1 Qi, Yanfeng 1 Reynolds, Jonathan 1 Rötteler, Martin 1 Rubin, Karl Cooper 1 Sakzad, Amin 1 Seo, Seog Chung 1 Shang, Ning 1 Sharif, Shahed ...and 24 more Authors
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#### Cited in 37 Serials

 9 Journal of Number Theory 4 Mathematics of Computation 3 Israel Journal of Mathematics 2 Information Processing Letters 2 Annales de l’Institut Fourier 2 Applied Mathematics and Computation 2 Inventiones Mathematicae 2 Monatshefte für Mathematik 2 Transactions of the American Mathematical Society 2 Acta Applicandae Mathematicae 2 Annals of Pure and Applied Logic 2 Journal of Cryptology 2 Japan Journal of Industrial and Applied Mathematics 2 Designs, Codes and Cryptography 2 Journal of the European Mathematical Society (JEMS) 2 Journal of Mathematical Cryptology 1 Archiv der Mathematik 1 Canadian Journal of Mathematics 1 Compositio Mathematica 1 Functiones et Approximatio. Commentarii Mathematici 1 Information Sciences 1 Journal of Algebra 1 Proceedings of the American Mathematical Society 1 Applicable Algebra in Engineering, Communication and Computing 1 Journal of Algebraic Geometry 1 Finite Fields and their Applications 1 Advances in Computational Mathematics 1 LMS Journal of Computation and Mathematics 1 Journal of the Australian Mathematical Society 1 Sādhanā 1 Quantum Information Processing 1 Foundations of Physics 1 Science in China. Series F 1 International Journal of Number Theory 1 Algebra & Number Theory 1 Research in Number Theory 1 SIAM Journal on Applied Algebra and Geometry
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#### Cited in 11 Fields

 51 Number theory (11-XX) 29 Information and communication theory, circuits (94-XX) 25 Algebraic geometry (14-XX) 16 Mathematical logic and foundations (03-XX) 9 Computer science (68-XX) 5 Field theory and polynomials (12-XX) 4 Quantum theory (81-XX) 1 History and biography (01-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Functional analysis (46-XX) 1 Convex and discrete geometry (52-XX)