Fisher, Tom On binary quartics and the Cassels-Tate pairing. (English) Zbl 07600666 Res. Number Theory 8, No. 4, Paper No. 74, 13 p. (2022). Reviewer: Remke Kloosterman (Padova) MSC: 11G05 14H52 14Q05 PDF BibTeX XML Cite \textit{T. Fisher}, Res. Number Theory 8, No. 4, Paper No. 74, 13 p. (2022; Zbl 07600666) Full Text: DOI arXiv OpenURL
Castryck, Wouter; Decru, Thomas; Vercauteren, Frederik Radical isogenies. (English) Zbl 07666673 Moriai, Shiho (ed.) et al., Advances in cryptology – ASIACRYPT 2020. 26th international conference on the theory and application of cryptology and information security, Daejeon, South Korea, December 7–11, 2020. Proceedings. Part II. Cham: Springer. Lect. Notes Comput. Sci. 12492, 493-519 (2020). MSC: 94A60 PDF BibTeX XML Cite \textit{W. Castryck} et al., Lect. Notes Comput. Sci. 12492, 493--519 (2020; Zbl 07666673) Full Text: DOI OpenURL
Ionica, Sorina; Thomé, Emmanuel Isogeny graphs with maximal real multiplication. (English) Zbl 1457.11082 J. Number Theory 207, 385-422 (2020). Reviewer: WonTae Hwang (Seoul) MSC: 11G10 14K02 11G15 PDF BibTeX XML Cite \textit{S. Ionica} and \textit{E. Thomé}, J. Number Theory 207, 385--422 (2020; Zbl 1457.11082) Full Text: DOI arXiv OpenURL
van Bommel, Raymond; Holmes, David; Müller, J. Steffen Explicit arithmetic intersection theory and computation of Néron-Tate heights. (English) Zbl 1426.14006 Math. Comput. 89, No. 321, 395-410 (2020). Reviewer: Juan Tena Ayuso (Valladolid) MSC: 14G40 11G30 11G50 37P30 11G10 PDF BibTeX XML Cite \textit{R. van Bommel} et al., Math. Comput. 89, No. 321, 395--410 (2020; Zbl 1426.14006) Full Text: DOI arXiv OpenURL
van Beek, Monique; Fisher, Tom Computing the Cassels-Tate pairing on 3-isogeny Selmer groups via cubic norm equations. (English) Zbl 1417.11111 Acta Arith. 185, No. 4, 367-396 (2018). Reviewer: Noburo Ishii (Kyoto) MSC: 11G05 11Y40 PDF BibTeX XML Cite \textit{M. van Beek} and \textit{T. Fisher}, Acta Arith. 185, No. 4, 367--396 (2018; Zbl 1417.11111) Full Text: DOI arXiv OpenURL
Doss, Srinath; Kaondera-Shava, Roselyn An optimal Tate pairing computation using Jacobi quartic elliptic curves. (English) Zbl 1418.90254 J. Comb. Optim. 35, No. 4, 1086-1103 (2018). MSC: 90C30 PDF BibTeX XML Cite \textit{S. Doss} and \textit{R. Kaondera-Shava}, J. Comb. Optim. 35, No. 4, 1086--1103 (2018; Zbl 1418.90254) Full Text: DOI OpenURL
Kumar, Rajeev; Pal, S. K.; Arvind Pairing-friendly elliptic curves of embedding degree 1 and applications to cryptography. (English) Zbl 1425.94065 Ital. J. Pure Appl. Math. 38, 441-454 (2017). MSC: 94A60 11G20 14G50 11T71 PDF BibTeX XML Cite \textit{R. Kumar} et al., Ital. J. Pure Appl. Math. 38, 441--454 (2017; Zbl 1425.94065) Full Text: Link OpenURL
El Mrabet, Nadia (ed.); Joye, Marc (ed.) Guide to pairing-based cryptography. (English) Zbl 1371.94003 Chapman & Hall/CRC Cryptography and Network Security. Boca Raton, FL: CRC Press (ISBN 978-1-4987-2950-5/hbk; 978-1-315-37017-0/ebook). ix, 402 p., not consecutively paged (2017). Reviewer: Fernando Hernando (Castellón) MSC: 94-02 94A60 94-06 11T71 11G05 14G50 PDF BibTeX XML Cite \textit{N. El Mrabet} (ed.) and \textit{M. Joye} (ed.), Guide to pairing-based cryptography. Boca Raton, FL: CRC Press (2017; Zbl 1371.94003) Full Text: DOI OpenURL
Onuki, Hiroshi; Teruya, Tadanori; Kanayama, Naoki; Uchiyama, Shigenori Faster explicit formulae for computing pairings via elliptic nets and their parallel computation. (English) Zbl 1398.94149 Ogawa, Kazuto (ed.) et al., Advances in information and computer security. 11th international workshop on security, IWSEC 2016, Tokyo, Japan, September 12–14, 2016. Proceedings. Cham: Springer (ISBN 978-3-319-44523-6/pbk; 978-3-319-44524-3/ebook). Lecture Notes in Computer Science 9836, 319-334 (2016). MSC: 94A60 11G20 11Y16 14G50 PDF BibTeX XML Cite \textit{H. Onuki} et al., Lect. Notes Comput. Sci. 9836, 319--334 (2016; Zbl 1398.94149) Full Text: DOI OpenURL
Schneider, Peter; Venjakob, Otmar Coates-Wiles homomorphisms and Iwasawa cohomology for Lubin-Tate extensions. (English) Zbl 1409.11107 Loeffler, David (ed.) et al., Elliptic curves, modular forms and Iwasawa theory. In honour of John H. Coates’ 70th birthday, Cambridge, UK, March 2015. Proceedings of the conference and the workshop. Cham: Springer. Springer Proc. Math. Stat. 188, 401-468 (2016). MSC: 11S31 11S25 11S37 PDF BibTeX XML Cite \textit{P. Schneider} and \textit{O. Venjakob}, Springer Proc. Math. Stat. 188, 401--468 (2016; Zbl 1409.11107) Full Text: DOI arXiv OpenURL
Wang, Zhangjie Congruent elliptic curves with non-trivial Shafarevich-Tate groups. (English) Zbl 1410.11056 Sci. China, Math. 59, No. 11, 2145-2166 (2016). MSC: 11G05 11R11 11R29 PDF BibTeX XML Cite \textit{Z. Wang}, Sci. China, Math. 59, No. 11, 2145--2166 (2016; Zbl 1410.11056) Full Text: DOI arXiv OpenURL
Le, Duc-Phong; Tan, Chik How Further refinements of Miller’s algorithm on Edwards curves. (English) Zbl 1368.94110 Appl. Algebra Eng. Commun. Comput. 27, No. 3, 205-217 (2016). MSC: 94A60 14G50 11G07 PDF BibTeX XML Cite \textit{D.-P. Le} and \textit{C. H. Tan}, Appl. Algebra Eng. Commun. Comput. 27, No. 3, 205--217 (2016; Zbl 1368.94110) Full Text: DOI arXiv OpenURL
Duquesne, Sylvain; Ghammam, Loubna Memory-saving computation of the pairing final exponentiation on BN curves. (English) Zbl 1401.14138 Groups Complex. Cryptol. 8, No. 1, 75-90 (2016). MSC: 14G50 11G07 94A60 PDF BibTeX XML Cite \textit{S. Duquesne} and \textit{L. Ghammam}, Groups Complex. Cryptol. 8, No. 1, 75--90 (2016; Zbl 1401.14138) Full Text: DOI OpenURL
Fouotsa, Emmanuel; Ciss, Abdoul Aziz Faster Ate pairing computation on Selmer’s model of elliptic curves. (English) Zbl 1336.14021 Groups Complex. Cryptol. 8, No. 1, 55-67 (2016). MSC: 14G50 14H52 94A60 PDF BibTeX XML Cite \textit{E. Fouotsa} and \textit{A. A. Ciss}, Groups Complex. Cryptol. 8, No. 1, 55--67 (2016; Zbl 1336.14021) Full Text: DOI OpenURL
Hess, Florian; Massierer, Maike Tame class field theory for global function fields. (English) Zbl 1402.11134 J. Number Theory 162, 86-115 (2016). MSC: 11R37 11R58 11T71 PDF BibTeX XML Cite \textit{F. Hess} and \textit{M. Massierer}, J. Number Theory 162, 86--115 (2016; Zbl 1402.11134) Full Text: DOI arXiv OpenURL
Ivanov, M. A.; Vostokov, S. V. The skew-symmetric pairing on the Lubin-Tate formal module. (English) Zbl 1388.11079 Dieulefait, Luis (ed.) et al., Arithmetic and geometry. Proceedings of the research conference of the trimester, Bonn, Germany, April 15–19, 2013. Cambridge: Cambridge University Press (ISBN 978-1-107-46254-0/pbk; 978-1-316-10687-7/ebook). London Mathematical Society Lecture Note Series 420, 255-263 (2015). MSC: 11S31 11G07 PDF BibTeX XML Cite \textit{M. A. Ivanov} and \textit{S. V. Vostokov}, Lond. Math. Soc. Lect. Note Ser. 420, 255--263 (2015; Zbl 1388.11079) OpenURL
Enge, Andreas Bilinear pairings on elliptic curves. (English) Zbl 1335.14001 Enseign. Math. (2) 61, No. 1-2, 211-243 (2015). Reviewer: Andrea Bandini (Parma) MSC: 14-02 11-02 14H52 14Q05 11Y40 PDF BibTeX XML Cite \textit{A. Enge}, Enseign. Math. (2) 61, No. 1--2, 211--243 (2015; Zbl 1335.14001) Full Text: DOI arXiv OpenURL
Sohn, Gyoyong Weaknesses of the Tate pairing on generalized Hessian curves. (English) Zbl 1333.94047 Proc. Jangjeon Math. Soc. 18, No. 4, 571-578 (2015). Reviewer: Juan Tena Ayuso (Valladolid) MSC: 94A60 14G50 14H52 PDF BibTeX XML Cite \textit{G. Sohn}, Proc. Jangjeon Math. Soc. 18, No. 4, 571--578 (2015; Zbl 1333.94047) OpenURL
Kim, Sungwook; Cheon, Jung Hee Fixed argument pairing inversion on elliptic curves. (English) Zbl 1329.94068 Des. Codes Cryptography 77, No. 1, 143-152 (2015). MSC: 94A60 11T71 14G50 PDF BibTeX XML Cite \textit{S. Kim} and \textit{J. H. Cheon}, Des. Codes Cryptography 77, No. 1, 143--152 (2015; Zbl 1329.94068) Full Text: DOI OpenURL
Lubicz, David; Robert, Damien A generalisation of Miller’s algorithm and applications to pairing computations on abelian varieties. (English) Zbl 1304.14056 J. Symb. Comput. 67, 68-92 (2015). Reviewer: Juan Tena Ayuso (Valladolid) MSC: 14K15 14K25 14G15 14H52 94A60 PDF BibTeX XML Cite \textit{D. Lubicz} and \textit{D. Robert}, J. Symb. Comput. 67, 68--92 (2015; Zbl 1304.14056) Full Text: DOI OpenURL
Li, Liangze; Wu, Hongfeng; Zhang, Fan Pairing computation on Edwards curves with high-degree twists. (English) Zbl 1347.94042 Lin, Dongdai (ed.) et al., Information security and cryptology. 9th international conference, Inscrypt 2013, Guangzhou, China, November 27–30, 2013. Revised selected papers. Cham: Springer (ISBN 978-3-319-12086-7/pbk; 978-3-319-12087-4/ebook). Lecture Notes in Computer Science 8567, 185-200 (2014). MSC: 94A60 14G50 PDF BibTeX XML Cite \textit{L. Li} et al., Lect. Notes Comput. Sci. 8567, 185--200 (2014; Zbl 1347.94042) Full Text: DOI OpenURL
Holmes, David An Arakelov-theoretic approach to naïve heights on hyperelliptic Jacobians. (English) Zbl 1338.11059 New York J. Math. 20, 927-957 (2014). Reviewer: Paul Vojta (Berkeley) MSC: 11G50 11G30 14G40 PDF BibTeX XML Cite \textit{D. Holmes}, New York J. Math. 20, 927--957 (2014; Zbl 1338.11059) Full Text: arXiv EMIS OpenURL
Duquesne, Sylvain; El Mrabet, Nadia; Fouotsa, Emmanuel Efficient computation of pairings on Jacobi quartic elliptic curves. (English) Zbl 1311.14032 J. Math. Cryptol. 8, No. 4, 331-362 (2014). Reviewer: Guillermo Matera (Buenos Aires) MSC: 14H52 11G20 68W40 94A60 PDF BibTeX XML Cite \textit{S. Duquesne} et al., J. Math. Cryptol. 8, No. 4, 331--362 (2014; Zbl 1311.14032) Full Text: DOI HAL OpenURL
Fisher, Tom; Newton, Rachel Computing the Cassels-Tate pairing on the 3-Selmer group of an elliptic curve. (English) Zbl 1314.11042 Int. J. Number Theory 10, No. 7, 1881-1907 (2014). Reviewer: Noburo Ishii (Kyoto) MSC: 11G05 11G07 16H05 PDF BibTeX XML Cite \textit{T. Fisher} and \textit{R. Newton}, Int. J. Number Theory 10, No. 7, 1881--1907 (2014; Zbl 1314.11042) Full Text: DOI arXiv OpenURL
Chen, BingLong; Zhao, Chang-An Self-pairings on supersingular elliptic curves with embedding degree three. (English) Zbl 1308.14038 Finite Fields Appl. 28, 79-93 (2014). Reviewer: Juan Tena Ayuso (Valladolid) MSC: 14H52 11G20 94A60 PDF BibTeX XML Cite \textit{B. Chen} and \textit{C.-A. Zhao}, Finite Fields Appl. 28, 79--93 (2014; Zbl 1308.14038) Full Text: DOI OpenURL
Tran, Christophe Formulae for computation of Tate pairing on hyperelliptic curve using hyperelliptic nets. (English) Zbl 1288.94084 Pointcheval, David (ed.) et al., Progress in cryptology – AFRICACRYPT 2014. 7th international conference on cryptology in Africa, Marrakesh, Morocco, May 28–30, 2014. Proceedings. Berlin: Springer (ISBN 978-3-319-06733-9/pbk). Lecture Notes in Computer Science 8469, 199-214 (2014). MSC: 94A60 14G50 68W40 PDF BibTeX XML Cite \textit{C. Tran}, Lect. Notes Comput. Sci. 8469, 199--214 (2014; Zbl 1288.94084) Full Text: DOI OpenURL
Nesteruk, V. I. On the Kolyvagin’s formula, the Tate pairing associated to an isogeny, the local Artin map and the Hilberts symbol. (Ukrainian. English, Russian summaries) Zbl 1382.11042 Carpathian Math. Publ. 5, No. 1, 94-101 (2013). MSC: 11G05 14K02 PDF BibTeX XML Cite \textit{V. I. Nesteruk}, Carpathian Math. Publ. 5, No. 1, 94--101 (2013; Zbl 1382.11042) Full Text: DOI OpenURL
Nesteruk, Volodymyr On the Tate pairing associated to an isogeny between abelian varieties over pseudofinite field. (English) Zbl 1316.14086 Algebra Discrete Math. 16, No. 1, 103-106 (2013). MSC: 14K02 14H05 11G10 PDF BibTeX XML Cite \textit{V. Nesteruk}, Algebra Discrete Math. 16, No. 1, 103--106 (2013; Zbl 1316.14086) OpenURL
Ionica, Sorina Pairing-based algorithms for Jacobians of genus 2 curves with maximal endomorphism ring. (English) Zbl 1297.11052 J. Number Theory 133, No. 11, 3755-3770 (2013). MSC: 11G05 11T71 14H45 PDF BibTeX XML Cite \textit{S. Ionica}, J. Number Theory 133, No. 11, 3755--3770 (2013; Zbl 1297.11052) Full Text: DOI arXiv OpenURL
Nesteruk, V. I. On the Kolyvagin formula for elliptic curves with good reductions over pseudolocal fields. (English) Zbl 1303.11071 Mat. Stud. 39, No. 1, 16-20 (2013). MSC: 11G20 11G07 14H52 PDF BibTeX XML Cite \textit{V. I. Nesteruk}, Mat. Stud. 39, No. 1, 16--20 (2013; Zbl 1303.11071) OpenURL
Lashermes, Ronan; Fournier, Jacques; Goubin, Louis Inverting the final exponentiation of Tate pairings on ordinary elliptic curves using faults. (English) Zbl 1353.94058 Bertoni, Guido (ed.) et al., Cryptographic hardware and embedded systems – CHES 2013. 15th international workshop, Santa Barbara, CA, USA, August 20–23, 2013. Proceedings. Berlin: Springer (ISBN 978-3-642-40348-4/pbk). Lecture Notes in Computer Science 8086, 365-382 (2013). MSC: 94A60 PDF BibTeX XML Cite \textit{R. Lashermes} et al., Lect. Notes Comput. Sci. 8086, 365--382 (2013; Zbl 1353.94058) Full Text: DOI OpenURL
Galbraith, Steven D.; Zhao, Chang-An Self-pairings on hyperelliptic curves. (English) Zbl 1273.14051 J. Math. Cryptol. 7, No. 1, 31-42 (2013); erratum 8, No. 1, 93 (2014). MSC: 14G50 94A60 11T71 11G20 14Q05 PDF BibTeX XML Cite \textit{S. D. Galbraith} and \textit{C.-A. Zhao}, J. Math. Cryptol. 7, No. 1, 31--42 (2013; Zbl 1273.14051) Full Text: DOI OpenURL
Wu, Hongfeng; Feng, Rongquan Efficient self-pairing on ordinary elliptic curves. (English) Zbl 1382.94169 Chan, T-H. Hubert (ed.) et al., Theory and applications of models of computation. 10th international conference, TAMC 2013, Hong Kong, China, May 20–22, 2013. Proceedings. Berlin: Springer (ISBN 978-3-642-38235-2/pbk). Lecture Notes in Computer Science 7876, 282-293 (2013). MSC: 94A60 11T71 14G50 PDF BibTeX XML Cite \textit{H. Wu} and \textit{R. Feng}, Lect. Notes Comput. Sci. 7876, 282--293 (2013; Zbl 1382.94169) Full Text: DOI OpenURL
Duquesne, Sylvain; Fouotsa, Emmanuel Tate pairing computation on Jacobi’s elliptic curves. (English) Zbl 1305.94044 Abdalla, Michel (ed.) et al., Pairing-based cryptography – Pairing 2012. 5th international conference, Cologne, Germany, May 16–18, 2012. Revised selected papers. Berlin: Springer (ISBN 978-3-642-36333-7/pbk). Lecture Notes in Computer Science 7708, 254-269 (2013). MSC: 94A60 14G50 68W40 PDF BibTeX XML Cite \textit{S. Duquesne} and \textit{E. Fouotsa}, Lect. Notes Comput. Sci. 7708, 254--269 (2013; Zbl 1305.94044) Full Text: DOI OpenURL
Uchida, Yukihiro; Uchiyama, Shigenori The Tate-Lichtenbaum pairing on a hyperelliptic curve via hyperelliptic nets. (English) Zbl 1305.94080 Abdalla, Michel (ed.) et al., Pairing-based cryptography – Pairing 2012. 5th international conference, Cologne, Germany, May 16–18, 2012. Revised selected papers. Berlin: Springer (ISBN 978-3-642-36333-7/pbk). Lecture Notes in Computer Science 7708, 218-233 (2013). MSC: 94A60 14G50 68W40 PDF BibTeX XML Cite \textit{Y. Uchida} and \textit{S. Uchiyama}, Lect. Notes Comput. Sci. 7708, 218--233 (2013; Zbl 1305.94080) Full Text: DOI Link OpenURL
Li, Liangze; Zhang, Fan Tate pairing computation on generalized Hessian curves. (English) Zbl 1333.94043 Lee, Dong Hoon (ed.) et al., Information security applications. 13th international workshop, WISA 2012, Jeju Island, Korea, August 16–18, 2012. Revised selected papers. Berlin: Springer (ISBN 978-3-642-35415-1/pbk). Lecture Notes in Computer Science 7690, 111-123 (2012). MSC: 94A60 14H50 14H52 PDF BibTeX XML Full Text: DOI OpenURL
Zhang, Xusheng; Chen, Shan; Lin, Dongdai Fast Tate pairing computation on twisted Jacobi intersections curves. (English) Zbl 1292.94163 Wu, Chuan-Kun (ed.) et al., Information security and cryptology. 7th international conference, Inscrypt 2011, Beijing, China, November 30–December 3, 2011. Revised selected papers. Berlin: Springer (ISBN 978-3-642-34703-0/pbk). Lecture Notes in Computer Science 7537, 210-226 (2012). MSC: 94A60 14G50 PDF BibTeX XML Cite \textit{X. Zhang} et al., Lect. Notes Comput. Sci. 7537, 210--226 (2012; Zbl 1292.94163) Full Text: DOI OpenURL
Sohn, Gyoyong The robust arithmetic of finite field for fault-tolerant Tate pairing with binary field. (English) Zbl 1268.14024 Adv. Stud. Contemp. Math., Kyungshang 22, No. 4, 499-505 (2012). MSC: 14G50 94B40 PDF BibTeX XML Cite \textit{G. Sohn}, Adv. Stud. Contemp. Math., Kyungshang 22, No. 4, 499--505 (2012; Zbl 1268.14024) OpenURL
Heß, Florian; Stein, Andreas; Stein, Sandra; Lochter, Manfred The magic of elliptic curves and public-key cryptography. (English) Zbl 1273.94349 Jahresber. Dtsch. Math.-Ver. 114, No. 2, 59-88 (2012). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 94A60 11T71 11Y16 14G50 14H52 94-03 PDF BibTeX XML Cite \textit{F. Heß} et al., Jahresber. Dtsch. Math.-Ver. 114, No. 2, 59--88 (2012; Zbl 1273.94349) Full Text: DOI OpenURL
Poonen, Bjorn; Rains, Eric Random maximal isotropic subspaces and Selmer groups. (English) Zbl 1294.11097 J. Am. Math. Soc. 25, No. 1, 245-269 (2012). Reviewer: Sungkon Chang (Savannah) MSC: 11G10 11G05 11G30 14G25 14K15 PDF BibTeX XML Cite \textit{B. Poonen} and \textit{E. Rains}, J. Am. Math. Soc. 25, No. 1, 245--269 (2012; Zbl 1294.11097) Full Text: DOI arXiv OpenURL
Eom, Soo-Kyung; Lee, Hyang-Sook; Park, Cheol-Min Optimal pairing computation over families of pairing-friendly elliptic curves. (English) Zbl 1266.94021 Appl. Algebra Eng. Commun. Comput. 22, No. 4, 235-248 (2011). Reviewer: Andreas Stein (Oldenburg) MSC: 94A60 11T71 14G15 14G50 PDF BibTeX XML Cite \textit{S.-K. Eom} et al., Appl. Algebra Eng. Commun. Comput. 22, No. 4, 235--248 (2011; Zbl 1266.94021) Full Text: DOI OpenURL
Ogura, Naoki; Kanayama, Naoki; Uchiyama, Shigenori; Okamoto, Eiji Cryptographic pairings based on elliptic nets. (English) Zbl 1344.94068 Iwata, Tetsu (ed.) et al., Advances in information and computer security. 6th international workshop, IWSEC 2011, Tokyo, Japan, November 8–10, 2011. Proceedings. Berlin: Springer (ISBN 978-3-642-25140-5/pbk). Lecture Notes in Computer Science 7038, 65-78 (2011). MSC: 94A60 14G50 PDF BibTeX XML Cite \textit{N. Ogura} et al., Lect. Notes Comput. Sci. 7038, 65--78 (2011; Zbl 1344.94068) Full Text: DOI OpenURL
Menares, Ricardo Correspondences in Arakelov geometry and applications to the case of Hecke operators on modular curves. (English) Zbl 1338.14029 Manuscr. Math. 136, No. 3-4, 501-543 (2011). MSC: 14G40 11G18 11G40 11G50 PDF BibTeX XML Cite \textit{R. Menares}, Manuscr. Math. 136, No. 3--4, 501--543 (2011; Zbl 1338.14029) Full Text: DOI arXiv OpenURL
Bruin, Peter The Tate pairing for abelian varieties over finite fields. (English. French summary) Zbl 1246.11123 J. Théor. Nombres Bordx. 23, No. 2, 323-328 (2011). Reviewer: Xiao Xiao (Utica) MSC: 11G10 11G20 PDF BibTeX XML Cite \textit{P. Bruin}, J. Théor. Nombres Bordx. 23, No. 2, 323--328 (2011; Zbl 1246.11123) Full Text: DOI Numdam EuDML OpenURL
Zhang, Lijun; Wang, Kunpeng; Wang, Hong; Ye, Dingfeng Another elliptic curve model for faster pairing computation. (English) Zbl 1305.94085 Bao, Feng (ed.) et al., Information security practice and experience. 7th international conference, ISPEC 2011, Guangzhou, China, May 30 – June 1, 2011. Proceedings. Berlin: Springer (ISBN 978-3-642-21030-3/pbk). Lecture Notes in Computer Science 6672, 432-446 (2011). MSC: 94A60 14G50 68W10 PDF BibTeX XML Cite \textit{L. Zhang} et al., Lect. Notes Comput. Sci. 6672, 432--446 (2011; Zbl 1305.94085) Full Text: DOI OpenURL
Tang, Chunming; Qi, Yanfeng; Xu, Maozhi Implementing optimal pairings over Brezing-Weng elliptic curves with \(k=18\). (Chinese. English summary) Zbl 1240.14004 Acta Sci. Nat. Univ. Pekin. 46, No. 5, 743-748 (2010). MSC: 14H52 94A60 11T71 PDF BibTeX XML Cite \textit{C. Tang} et al., Acta Sci. Nat. Univ. Pekin. 46, No. 5, 743--748 (2010; Zbl 1240.14004) OpenURL
Nesteruk, Volodymyr On nondegeneracy of Tate pairing for curves over complete discrete valuation fields with pseudofinite residue fields. (Ukrainian. English summary) Zbl 1240.11072 Visn. L’viv. Univ., Ser. Mekh.-Mat. 72, 195-200 (2010). MSC: 11G20 PDF BibTeX XML Cite \textit{V. Nesteruk}, Visn. L'viv. Univ., Ser. Mekh.-Mat. 72, 195--200 (2010; Zbl 1240.11072) OpenURL
Huang, Ming-Deh; Raskind, Wayne A multilinear generalization of the Tate pairing. (English) Zbl 1216.14021 McGuire, Gary (ed.) et al., Finite fields. Theory and applications. Proceedings of the 9th international conference on finite fields and applications, Dublin, Ireland, July 13–17, 2009. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4786-2/pbk). Contemporary Mathematics 518, 255-263 (2010). MSC: 14G50 11T71 94A60 11G10 11G20 15A69 PDF BibTeX XML Cite \textit{M.-D. Huang} and \textit{W. Raskind}, Contemp. Math. 518, 255--263 (2010; Zbl 1216.14021) OpenURL
Estibals, Nicolas Compact hardware for computing the Tate pairing over 128-bit-security supersingular curves. (English) Zbl 1273.14050 Joye, Marc (ed.) et al., Pairing-based cryptography – Pairing 2010. 4th international conference, Yamanaka Hot Spring, Japan, December 13–15, 2010. Proceedings. Berlin: Springer (ISBN 978-3-642-17454-4/pbk). Lecture Notes in Computer Science 6487, 397-416 (2010). MSC: 14G50 94A60 PDF BibTeX XML Cite \textit{N. Estibals}, Lect. Notes Comput. Sci. 6487, 397--416 (2010; Zbl 1273.14050) Full Text: DOI Link OpenURL
Beuchat, Jean-Luc; González-Díaz, Jorge E.; Mitsunari, Shigeo; Okamoto, Eiji; Rodríguez-Henríquez, Francisco; Teruya, Tadanori High-speed software implementation of the optimal ate pairing over Barreto-Naehrig curves. (English) Zbl 1287.94054 Joye, Marc (ed.) et al., Pairing-based cryptography – Pairing 2010. 4th international conference, Yamanaka Hot Spring, Japan, December 13–15, 2010. Proceedings. Berlin: Springer (ISBN 978-3-642-17454-4/pbk). Lecture Notes in Computer Science 6487, 21-39 (2010). MSC: 94A60 11T71 14G50 68N99 PDF BibTeX XML Cite \textit{J.-L. Beuchat} et al., Lect. Notes Comput. Sci. 6487, 21--39 (2010; Zbl 1287.94054) Full Text: DOI OpenURL
Joye, Marc; Tibouchi, Mehdi; Vergnaud, Damien Huff’s model for elliptic curves. (English) Zbl 1260.11087 Hanrot, Guillaume (ed.) et al., Algorithmic number theory. 9th international symposium, ANTS-IX, Nancy, France, July 19–23, 2010. Proceedings. Berlin: Springer (ISBN 978-3-642-14517-9/pbk). Lecture Notes in Computer Science 6197, 234-250 (2010). MSC: 11Y16 PDF BibTeX XML Cite \textit{M. Joye} et al., Lect. Notes Comput. Sci. 6197, 234--250 (2010; Zbl 1260.11087) Full Text: DOI Link OpenURL
Ismail, Abdulwahed M.; Said, Mohamad Rushdan Md; Atan, Kamel Ariffin Mohd; Rakhimov, Isamiddin S. Bilinear pairing computation using the extended double-base chains algorithm. (English) Zbl 1214.68150 Int. J. Math. Anal., Ruse 4, No. 17-20, 929-941 (2010). MSC: 68P25 94A60 PDF BibTeX XML Cite \textit{A. M. Ismail} et al., Int. J. Math. Anal., Ruse 4, No. 17--20, 929--941 (2010; Zbl 1214.68150) Full Text: Link OpenURL
Costello, Craig; Stebila, Douglas Fixed argument pairings. (English) Zbl 1285.94050 Abdalla, Michel (ed.) et al., Progress in cryptology – LATINCRYPT 2010. First international conference on cryptology and information security in Latin America, Puebla, Mexico, August 8–11, 2010. Proceedings. Berlin: Springer (ISBN 978-3-642-14711-1/pbk). Lecture Notes in Computer Science 6212, 92-108 (2010). MSC: 94A60 PDF BibTeX XML Cite \textit{C. Costello} and \textit{D. Stebila}, Lect. Notes Comput. Sci. 6212, 92--108 (2010; Zbl 1285.94050) Full Text: DOI Link OpenURL
Thorne, Jack On the Tate-Shafarevich groups of certain elliptic curves. (English) Zbl 1223.11081 J. Number Theory 130, No. 9, 2092-2098 (2010). Reviewer: Jannis A. Antoniadis (Iraklion) MSC: 11G40 11G05 PDF BibTeX XML Cite \textit{J. Thorne}, J. Number Theory 130, No. 9, 2092--2098 (2010; Zbl 1223.11081) Full Text: DOI OpenURL
Costello, Craig; Boyd, Colin; Gonzalez Nieto, Juan Manuel; Wong, Kenneth Koon-Ho Delaying mismatched field multiplications in pairing computations. (English) Zbl 1245.11126 Hasan, M. Anwar (ed.) et al., Arithmetic of finite fields. Third international workshop, WAIFI 2010, Istanbul, Turkey, June 27–30, 2010. Proceedings. Berlin: Springer (ISBN 978-3-642-13796-9/pbk). Lecture Notes in Computer Science 6087, 196-214 (2010). MSC: 11Y16 11T71 94A60 PDF BibTeX XML Cite \textit{C. Costello} et al., Lect. Notes Comput. Sci. 6087, 196--214 (2010; Zbl 1245.11126) Full Text: DOI Link OpenURL
Sohn, Gyoyong; Lee, Sang-Hyuk; Dafa-Alla, Anour F. A. Robust finite field arithmetic for fault-tolerant Tate pairing. (English) Zbl 1192.94136 Proc. Jangjeon Math. Soc. 13, No. 1, 77-87 (2010). MSC: 94B40 14G50 PDF BibTeX XML Cite \textit{G. Sohn} et al., Proc. Jangjeon Math. Soc. 13, No. 1, 77--87 (2010; Zbl 1192.94136) OpenURL
Costello, Craig; Lange, Tanja; Naehrig, Michael Faster pairing computations on curves with high-degree twists. (English) Zbl 1279.94069 Nguyen, Phong Q. (ed.) et al., Public key cryptography – PKC 2010. 13th international conference on practice and theory in public key cryptography, Paris, France, May 26–28, 2010. Proceedings. Berlin: Springer (ISBN 978-3-642-13012-0/pbk). Lecture Notes in Computer Science 6056, 224-242 (2010). MSC: 94A60 14G50 PDF BibTeX XML Cite \textit{C. Costello} et al., Lect. Notes Comput. Sci. 6056, 224--242 (2010; Zbl 1279.94069) Full Text: DOI OpenURL
Costello, Craig; Boyd, Colin; González Nieto, Juan Manuel; Wong, Kenneth Koon-Ho Avoiding full extension field arithmetic in pairing computations. (English) Zbl 1284.11160 Bernstein, Daniel J. (ed.) et al., Progress in cryptology – AFRICACRYPT 2010. Third international conference on cryptology in Africa, Stellenbosch, South Africa, May 3–6, 2010. Proceedings. Berlin: Springer (ISBN 978-3-642-12677-2/pbk). Lecture Notes in Computer Science 6055, 203-224 (2010). MSC: 11T71 11Y16 12F05 94A60 PDF BibTeX XML Cite \textit{C. Costello} et al., Lect. Notes Comput. Sci. 6055, 203--224 (2010; Zbl 1284.11160) Full Text: DOI Link OpenURL
Beuchat, Jean-Luc; Doi, Hiroshi; Fujita, Kaoru; Inomata, Atsuo; Ith, Piseth; Kanaoka, Akira; Katouno, Masayoshi; Mambo, Masahiro; Okamoto, Eiji; Okamoto, Takeshi; Shiga, Takaaki; Shirase, Masaaki; Soga, Ryuji; Takagi, Tsuyoshi; Vithanage, Ananda; Yamamoto, Hiroyasu FPGA and ASIC implementations of the \(\eta _T\) pairing in characteristic three. (English) Zbl 1192.68235 Comput. Electr. Eng. 36, No. 1, 73-87 (2010). MSC: 68P25 68M99 PDF BibTeX XML Cite \textit{J.-L. Beuchat} et al., Comput. Electr. Eng. 36, No. 1, 73--87 (2010; Zbl 1192.68235) Full Text: DOI OpenURL
Feng, Rongquan; Wu, Hongfeng Efficient pairing computation on curves. (English) Zbl 1235.14022 Dong, Chongying (ed.) et al., Recent developments in algebra and related areas. Papers of the international conference on algebra and related areas, Tsinghua University, Beijing, China, August 18–20, 2007. Dedicated to Zhexian Wan in honor of his 80th birthday. Somerville, MA: International Press; Beijing: Higher Education Press (ISBN 978-1-57146-135-3/pbk). Advanced Lectures in Mathematics (ALM) 8, 99-110 (2009). MSC: 14G50 14H52 94A60 PDF BibTeX XML Cite \textit{R. Feng} and \textit{H. Wu}, Adv. Lect. Math. (ALM) 8, 99--110 (2009; Zbl 1235.14022) OpenURL
Paugam, Frédéric Spectral symmetries of zeta functions. (Symétries spectrales des fonctions zêtas.) (French. English summary) Zbl 1214.11095 J. Théor. Nombres Bordx. 21, No. 3, 711-718 (2009). Reviewer: Paul-Olivier Dehaye (Zürich) MSC: 11M26 11F66 11M36 11R42 11S40 11F72 58J50 58B34 PDF BibTeX XML Cite \textit{F. Paugam}, J. Théor. Nombres Bordx. 21, No. 3, 711--718 (2009; Zbl 1214.11095) Full Text: DOI arXiv Numdam EuDML OpenURL
Beuchat, Jean-Luc; López-Trejo, Emmanuel; Martínez-Ramos, Luis; Mitsunari, Shigeo; Rodríguez-Henríquez, Francisco Multi-core implementation of the Tate pairing over supersingular elliptic curves. (English) Zbl 1287.94055 Garay, Juan A. (ed.) et al., Cryptology and network security. 8th international conference, CANS 2009, Kanazawa, Japan, December 12–14, 2009. Proceedings. Berlin: Springer (ISBN 978-3-642-10432-9/pbk). Lecture Notes in Computer Science 5888, 413-432 (2009). MSC: 94A60 14G50 PDF BibTeX XML Cite \textit{J.-L. Beuchat} et al., Lect. Notes Comput. Sci. 5888, 413--432 (2009; Zbl 1287.94055) Full Text: DOI OpenURL
Beuchat, Jean-Luc; Detrey, Jérémie; Estibals, Nicolas; Okamoto, Eiji; Rodríguez-Henríquez, Francisco Hardware accelerator for the Tate pairing in characteristic three based on Karatsuba-Ofman multipliers. (English) Zbl 1290.94043 Clavier, Christophe (ed.) et al., Cryptographic hardware and embedded systems – CHES 2009. 11th international workshop Lausanne, Switzerland, September 6–9, 2009. Proceedings. Berlin: Springer (ISBN 978-3-642-04137-2/pbk). Lecture Notes in Computer Science 5747, 225-239 (2009). MSC: 94A60 68P25 14G50 PDF BibTeX XML Cite \textit{J.-L. Beuchat} et al., Lect. Notes Comput. Sci. 5747, 225--239 (2009; Zbl 1290.94043) Full Text: DOI OpenURL
Fan, Xinxin; Gong, Guang; Jao, David Efficient pairing computation on genus 2 curves in projective coordinates. (English) Zbl 1256.94049 Avanzi, Roberto Maria (ed.) et al., Selected areas in cryptography. 15th international workshop, SAC 2008, Sackville, New Brunswick, Canada, August 14–15. Revised selected papers. Berlin: Springer (ISBN 978-3-642-04158-7/pbk). Lecture Notes in Computer Science 5381, 18-34 (2009). MSC: 94A60 11G20 14G50 PDF BibTeX XML Cite \textit{X. Fan} et al., Lect. Notes Comput. Sci. 5381, 18--34 (2009; Zbl 1256.94049) Full Text: DOI OpenURL
Scott, Michael; Benger, Naomi; Charlemagne, Manuel; Dominguez Perez, Luis J.; Kachisa, Ezekiel J. Fast hashing to \(G _{2}\) on pairing-friendly curves. (English) Zbl 1248.94094 Shacham, Hovav (ed.) et al., Pairing-based cryptography – Pairing 2009. Third international conference Palo Alto, CA, USA, August 12–14, 2009. Proceedings. Berlin: Springer (ISBN 978-3-642-03297-4/pbk). Lecture Notes in Computer Science 5671, 102-113 (2009). MSC: 94A60 14G50 PDF BibTeX XML Cite \textit{M. Scott} et al., Lect. Notes Comput. Sci. 5671, 102--113 (2009; Zbl 1248.94094) Full Text: DOI OpenURL
Costello, Craig; Hisil, Huseyin; Boyd, Colin; Gonzalez Nieto, Juan; Wong, Kenneth Koon-Ho Faster pairings on special Weierstrass curves. (English) Zbl 1248.94062 Shacham, Hovav (ed.) et al., Pairing-based cryptography – Pairing 2009. Third international conference Palo Alto, CA, USA, August 12–14, 2009. Proceedings. Berlin: Springer (ISBN 978-3-642-03297-4/pbk). Lecture Notes in Computer Science 5671, 89-101 (2009). MSC: 94A60 14G50 PDF BibTeX XML Cite \textit{C. Costello} et al., Lect. Notes Comput. Sci. 5671, 89--101 (2009; Zbl 1248.94062) Full Text: DOI Link OpenURL
Scott, Michael; Benger, Naomi; Charlemagne, Manuel; Dominguez Perez, Luis J.; Kachisa, Ezekiel J. On the final exponentiation for calculating pairings on ordinary elliptic curves. (English) Zbl 1248.94093 Shacham, Hovav (ed.) et al., Pairing-based cryptography – Pairing 2009. Third international conference Palo Alto, CA, USA, August 12–14, 2009. Proceedings. Berlin: Springer (ISBN 978-3-642-03297-4/pbk). Lecture Notes in Computer Science 5671, 78-88 (2009). MSC: 94A60 14G50 PDF BibTeX XML Cite \textit{M. Scott} et al., Lect. Notes Comput. Sci. 5671, 78--88 (2009; Zbl 1248.94093) Full Text: DOI OpenURL
Sharma, Aribam Chandrakant Non existence of finite \(\Lambda\)-submodules of dual Selmer groups over a cyclotomic \(\mathbb Z_p\)-extension. (English) Zbl 1233.11113 J. Ramanujan Math. Soc. 24, No. 1, 75-85 (2009). Reviewer: Andrzej Dąbrowski (Szczecin) MSC: 11R23 11F70 PDF BibTeX XML Cite \textit{A. C. Sharma}, J. Ramanujan Math. Soc. 24, No. 1, 75--85 (2009; Zbl 1233.11113) OpenURL
Keller, Maurice; Ronan, Robert; Byrne, Andrew; Murphy, Colin; Marnane, William Hardware implementation of pairings. (English) Zbl 1159.68442 Joye, Marc (ed.) et al., Identity-based cryptography. Amsterdam: IOP Press (ISBN 978-1-58603-947-9/hbk). Cryptology and Information Security Series 2, 207-225 (2009). MSC: 68P25 68M07 94A60 PDF BibTeX XML Cite \textit{M. Keller} et al., in: Identity-based cryptography. Amsterdam: IOP Press. 207--225 (2009; Zbl 1159.68442) OpenURL
Hankerson, Darrel; Menezes, Alfred; Scott, Michael Software implementation of pairings. (English) Zbl 1159.68439 Joye, Marc (ed.) et al., Identity-based cryptography. Amsterdam: IOP Press (ISBN 978-1-58603-947-9/hbk). Cryptology and Information Security Series 2, 188-206 (2009). MSC: 68P25 14H52 94A60 PDF BibTeX XML Cite \textit{D. Hankerson} et al., in: Identity-based cryptography. Amsterdam: IOP Press. 188--206 (2009; Zbl 1159.68439) OpenURL
Menezes, Alfred An introduction to pairing-based cryptography. (English) Zbl 1180.94058 Luengo, Ignacio (ed.), Recent trends in cryptography. UIMP-RSME Santaló summer school, July 11–15, 2005, Universidad Internacional Menéndez Pelayo, Santander, Spain. Providence, RI: American Mathematical Society (AMS); Madrid: Real Sociedad Matemática Española (ISBN 978-0-8218-3984-3/pbk). Contemporary Mathematics 477, 47-65 (2009). MSC: 94A60 14G50 PDF BibTeX XML Cite \textit{A. Menezes}, Contemp. Math. 477, 47--65 (2009; Zbl 1180.94058) OpenURL
Beuchat, Jean-Luc; Brisebarre, Nicolas; Detrey, Jérémie; Okamoto, Eiji; Rodríguez-Henríquez, Francisco A comparison between hardware accelerators for the modified Tate pairing over \(\mathbb{F}_{2^m}\) and \(\mathbb{F}_{3^m}\). (English) Zbl 1186.94424 Galbraith, Steven D. (ed.) et al., Pairing-based cryptography – Pairing 2008. Second international conference, Egham, UK, September 1–3, 2008. Proceedings. Berlin: Springer (ISBN 978-3-540-85503-3/pbk). Lecture Notes in Computer Science 5209, 297-315 (2008). MSC: 94A60 PDF BibTeX XML Cite \textit{J.-L. Beuchat} et al., Lect. Notes Comput. Sci. 5209, 297--315 (2008; Zbl 1186.94424) Full Text: DOI OpenURL
Fan, Xinxin; Gong, Guang; Jao, David Speeding up pairing computations on genus 2 hyperelliptic curves with efficiently computable automorphisms. (English) Zbl 1186.94438 Galbraith, Steven D. (ed.) et al., Pairing-based cryptography – Pairing 2008. Second international conference, Egham, UK, September 1–3, 2008. Proceedings. Berlin: Springer (ISBN 978-3-540-85503-3/pbk). Lecture Notes in Computer Science 5209, 243-264 (2008). MSC: 94A60 11T71 11Y16 PDF BibTeX XML Cite \textit{X. Fan} et al., Lect. Notes Comput. Sci. 5209, 243--264 (2008; Zbl 1186.94438) Full Text: DOI OpenURL
Ionica, Sorina; Joux, Antoine Another approach to pairing computation in Edwards coordinates. (English) Zbl 1203.94104 Roy Chowdhury, Dipanwita (ed.) et al., Progress in cryptology – INDOCRYPT 2008. 9th international conference on cryptology in India, Kharagpur, India, December 14–17, 2008. Proceedings. Berlin: Springer (ISBN 978-3-540-89753-8/pbk). Lecture Notes in Computer Science 5365, 400-413 (2008). MSC: 94A60 11T71 PDF BibTeX XML Cite \textit{S. Ionica} and \textit{A. Joux}, Lect. Notes Comput. Sci. 5365, 400--413 (2008; Zbl 1203.94104) Full Text: DOI OpenURL
Zhao, Chanan; Zhang, Fangguo; Huang, Jiwu Efficient Tate pairing computation using double-base chains. (English) Zbl 1210.94098 Sci. China, Ser. F 51, No. 8, 1096-1105 (2008). MSC: 94A60 14G50 PDF BibTeX XML Cite \textit{C. Zhao} et al., Sci. China, Ser. F 51, No. 8, 1096--1105 (2008; Zbl 1210.94098) Full Text: DOI OpenURL
Lee, Eunjeong; Lee, Yoonjin Tate pairing computation on the divisors of hyperelliptic curves of genus 2. (English) Zbl 1209.11106 J. Korean Math. Soc. 45, No. 4, 1057-1073 (2008). MSC: 11T71 14G50 94A60 14G15 PDF BibTeX XML Cite \textit{E. Lee} and \textit{Y. Lee}, J. Korean Math. Soc. 45, No. 4, 1057--1073 (2008; Zbl 1209.11106) Full Text: DOI OpenURL
Lee, Eunjeong; Lee, Hyang-Sook; Lee, Yoonjin Eta pairing computation on general divisors over hyperelliptic curves \(y^2=x^p - x+d\). (English) Zbl 1143.14020 J. Symb. Comput. 43, No. 6-7, 452-474 (2008). Reviewer: Juan Tena Ayuso (Valladolid) MSC: 14G15 14H40 94A60 PDF BibTeX XML Cite \textit{E. Lee} et al., J. Symb. Comput. 43, No. 6--7, 452--474 (2008; Zbl 1143.14020) Full Text: DOI OpenURL
Naehrig, Michael; Barreto, Paulo S. L. M.; Schwabe, Peter On compressible pairings and their computation. (English) Zbl 1142.94353 Vaudenay, Serge (ed.), Progress in cryptology – AFRICACRYPT 2008. First international conference on cryptology in Africa, Casablanca, Morocco, June 11–14, 2008. Proceedings. Berlin: Springer (ISBN 978-3-540-68159-5/pbk). Lecture Notes in Computer Science 5023, 371-388 (2008). MSC: 94A60 PDF BibTeX XML Cite \textit{M. Naehrig} et al., Lect. Notes Comput. Sci. 5023, 371--388 (2008; Zbl 1142.94353) Full Text: DOI OpenURL
Washington, Lawrence C. Elliptic curves. Number theory and cryptography. 2nd ed. (English) Zbl 1200.11043 Boca Raton, FL: Chapman and Hall/CRC (ISBN 978-1-4200-7146-7/hbk). xviii, 513 p. (2008). MSC: 11G20 11G05 11-01 14G50 94A60 11T71 11G50 14G10 PDF BibTeX XML Cite \textit{L. C. Washington}, Elliptic curves. Number theory and cryptography. 2nd ed. Boca Raton, FL: Chapman and Hall/CRC (2008; Zbl 1200.11043) OpenURL
Hu, Lei Compression of Tate pairings on elliptic curves. (Chinese. English summary) Zbl 1174.94361 J. Softw. 18, No. 7, 1799-1805 (2007). MSC: 94A60 68P25 14G50 PDF BibTeX XML Cite \textit{L. Hu}, J. Softw. 18, No. 7, 1799--1805 (2007; Zbl 1174.94361) OpenURL
Scott, Michael Implementing cryptographic pairings. (English) Zbl 1148.94432 Takagi, Tsuyoshi (ed.) et al., Pairing-based cryptography – Pairing 2007. First international conference, Tokyo, Japan, July 2–4, 2007. Proceedings. Berlin: Springer (ISBN 978-3-540-73488-8/pbk). Lecture Notes in Computer Science 4575, 177-196 (2007). MSC: 94A60 11T71 PDF BibTeX XML Cite \textit{M. Scott}, Lect. Notes Comput. Sci. 4575, 177--196 (2007; Zbl 1148.94432) OpenURL
Gorla, Elisa; Puttmann, Christoph; Shokrollahi, Jamshid Explicit formulas for efficient multiplication in \(\mathbb{F}_{3^{6m}}\). (English) Zbl 1154.11348 Adams, Carlisle (ed.) et al., Selected areas in cryptography. 14th international workshop, SAC 2007, Ottawa, Canada, August 16–17, 2007. Revised selected papers. Berlin: Springer (ISBN 978-3-540-77359-7/pbk). Lecture Notes in Computer Science 4876, 173-183 (2007). MSC: 11Y16 11T71 PDF BibTeX XML Cite \textit{E. Gorla} et al., Lect. Notes Comput. Sci. 4876, 173--183 (2007; Zbl 1154.11348) Full Text: DOI OpenURL
Granger, R.; Hess, F.; Oyono, R.; Thériault, N.; Vercauteren, F. Ate pairing on hyperelliptic curves. (English) Zbl 1141.94356 Naor, Moni (ed.), Advances in cryptology – EUROCRYPT 2007. 26th annual international conference on the theory and applications of cryptographic techniques, Barcelona, Spain, May 20–24, 2007. Proceedings. Berlin: Springer (ISBN 978-3-540-72539-8/pbk). Lecture Notes in Computer Science 4515, 430-447 (2007). MSC: 94A60 PDF BibTeX XML Cite \textit{R. Granger} et al., Lect. Notes Comput. Sci. 4515, 430--447 (2007; Zbl 1141.94356) Full Text: DOI OpenURL
Lee, Eunjeong; Lee, Hyang-Sook; Lee, Yoonjin Eta pairing computation on general divisors over hyperelliptic curves \(y ^{2} = x ^{7} - x \pm 1\). (English) Zbl 1151.94533 Takagi, Tsuyoshi (ed.) et al., Pairing-based cryptography – Pairing 2007. First international conference, Tokyo, Japan, July 2–4, 2007. Proceedings. Berlin: Springer (ISBN 978-3-540-73488-8/pbk). Lecture Notes in Computer Science 4575, 349-366 (2007). MSC: 94A60 11T71 11Y16 PDF BibTeX XML Cite \textit{E. Lee} et al., Lect. Notes Comput. Sci. 4575, 349--366 (2007; Zbl 1151.94533) Full Text: DOI OpenURL
Stange, Katherine E. The Tate pairing via elliptic nets. (English) Zbl 1151.94570 Takagi, Tsuyoshi (ed.) et al., Pairing-based cryptography – Pairing 2007. First international conference, Tokyo, Japan, July 2–4, 2007. Proceedings. Berlin: Springer (ISBN 978-3-540-73488-8/pbk). Lecture Notes in Computer Science 4575, 329-348 (2007). MSC: 94A60 14G50 14Q05 68W40 PDF BibTeX XML Cite \textit{K. E. Stange}, Lect. Notes Comput. Sci. 4575, 329--348 (2007; Zbl 1151.94570) Full Text: DOI OpenURL
Ó hÉigeartaigh, Colm; Scott, Michael Pairing calculation on supersingular genus 2 curves. (English) Zbl 1161.94423 Biham, Eli (ed.) et al., Selected areas in cryptography. 13th international workshop, SAC 2006, Montreal, Canada, August 17–18, 2006. Revised selected papers. Berlin: Springer (ISBN 978-3-540-74461-0/pbk). Lecture Notes in Computer Science 4356, 302-316 (2007). MSC: 94A60 14G50 11T71 PDF BibTeX XML Cite \textit{C. Ó hÉigeartaigh} and \textit{M. Scott}, Lect. Notes Comput. Sci. 4356, 302--316 (2007; Zbl 1161.94423) Full Text: DOI OpenURL
Feng, Rongquan; Wu, Hongfeng Encapsulated scalar multiplications and line functions in the computation of Tate pairing. (English) Zbl 1198.94092 Cai, Jin-Yi (ed.) et al., Theory and applications of models of computation. 4th international conference, TAMC 2007, Shanghai, China, May 22–25, 2007. Proceedings. Berlin: Springer (ISBN 978-3-540-72503-9/pbk). Lecture Notes in Computer Science 4484, 159-170 (2007). MSC: 94A60 14G15 14G50 14Q05 PDF BibTeX XML Cite \textit{R. Feng} and \textit{H. Wu}, Lect. Notes Comput. Sci. 4484, 159--170 (2007; Zbl 1198.94092) Full Text: DOI OpenURL
Keller, Maurice; Ronan, Robert; Marnane, William; Murphy, Colin Hardware architectures for the Tate pairing over GF\((2^{m})\). (English) Zbl 1124.68003 Comput. Electr. Eng. 33, No. 5-6, 392-406 (2007). MSC: 68M07 68P25 PDF BibTeX XML Cite \textit{M. Keller} et al., Comput. Electr. Eng. 33, No. 5--6, 392--406 (2007; Zbl 1124.68003) Full Text: DOI OpenURL
Barreto, Paulo S. L. M.; Galbraith, Steven D.; Ó hÉigeartaigh, Colm; Scott, Michael Efficient pairing computation on supersingular abelian varieties. (English) Zbl 1142.14307 Des. Codes Cryptography 42, No. 3, 239-271 (2007). MSC: 14G50 94A60 11T71 PDF BibTeX XML Cite \textit{P. S. L. M. Barreto} et al., Des. Codes Cryptography 42, No. 3, 239--271 (2007; Zbl 1142.14307) Full Text: DOI OpenURL
Smart, N. P.; Vercauteren, F. On computable isomorphisms in efficient asymmetric pairing-based systems. (English) Zbl 1123.94009 Discrete Appl. Math. 155, No. 4, 538-547 (2007). MSC: 94A60 14G50 PDF BibTeX XML Cite \textit{N. P. Smart} and \textit{F. Vercauteren}, Discrete Appl. Math. 155, No. 4, 538--547 (2007; Zbl 1123.94009) Full Text: DOI OpenURL
Whelan, Claire; Scott, Mike Side channel analysis of practical pairing implementations: which path is more secure? (English) Zbl 1295.94155 Nguyen, Phong Q. (ed.), Progress in cryptology – VIETCRYPT 2006. First international conference on cryptology in Vietnam, Hanoi, Vietnam, September 25–28, 2006. Revised selected papers. Berlin: Springer (ISBN 978-3-540-68799-3/pbk). Lecture Notes in Computer Science 4341, 99-114 (2006). MSC: 94A60 PDF BibTeX XML Cite \textit{C. Whelan} and \textit{M. Scott}, Lect. Notes Comput. Sci. 4341, 99--114 (2006; Zbl 1295.94155) Full Text: DOI OpenURL
Kang, Bo Gyeong; Park, Je Hong On the relationship between squared pairings and plain pairings. (English) Zbl 1191.68279 Inf. Process. Lett. 97, No. 6, 219-224 (2006). MSC: 68P25 PDF BibTeX XML Cite \textit{B. G. Kang} and \textit{J. H. Park}, Inf. Process. Lett. 97, No. 6, 219--224 (2006; Zbl 1191.68279) Full Text: DOI OpenURL
Page, Daniel; Vercauteren, Frederik A fault attack on pairing-based cryptography. (English) Zbl 1189.94046 IEEE Trans. Comput. 55, No. 9, 1075-1080 (2006). MSC: 94A60 PDF BibTeX XML Cite \textit{D. Page} and \textit{F. Vercauteren}, IEEE Trans. Comput. 55, No. 9, 1075--1080 (2006; Zbl 1189.94046) Full Text: DOI OpenURL
Frey, Gerhard; Lange, Tanja Fast bilinear maps from the Tate-Lichtenbaum pairing on hyperelliptic curves. (English) Zbl 1143.94345 Hess, Florian (ed.) et al., Algorithmic number theory. 7th international symposium, ANTS-VII, Berlin, Germany, July 23–28, 2006. Proceedings. Berlin: Springer (ISBN 3-540-36075-1/pbk). Lecture Notes in Computer Science 4076, 466-479 (2006). MSC: 94A60 11T71 14G50 PDF BibTeX XML Cite \textit{G. Frey} and \textit{T. Lange}, Lect. Notes Comput. Sci. 4076, 466--479 (2006; Zbl 1143.94345) Full Text: DOI OpenURL
Blake, Ian F.; Murty, V. Kumar; Xu, Guangwu Refinements of Miller’s algorithm for computing the Weil/Tate pairing. (English) Zbl 1093.68037 J. Algorithms 58, No. 2, 134-149 (2006). MSC: 14G50 94A60 PDF BibTeX XML Cite \textit{I. F. Blake} et al., J. Algorithms 58, No. 2, 134--149 (2006; Zbl 1093.68037) Full Text: DOI OpenURL
Kerins, T.; Marnane, W. P.; Popovici, E. M.; Barreto, P. S. L. M. Efficient hardware for the Tate pairing calculation in characteristic three. (English) Zbl 1319.94070 Rao, Josyula R. (ed.) et al., Cryptographic hardware and embedded systems – CHES 2005. 7th international workshop, Edinburgh, UK, August 29–September 1, 2005. Proceedings. Berlin: Springer (ISBN 978-3-540-28474-1/pbk). Lecture Notes in Computer Science 3659, 412-426 (2005). MSC: 94A60 68P25 14G50 PDF BibTeX XML Cite \textit{T. Kerins} et al., Lect. Notes Comput. Sci. 3659, 412--426 (2005; Zbl 1319.94070) Full Text: DOI OpenURL
Scott, Michael Faster pairings using an elliptic curve with an efficient endomorphism. (English) Zbl 1153.94429 Maitra, Subhamoy (ed.) et al., Progress in cryptology – INDOCRYPT 2005. 6th international conference on cryptology in India, Bangalore, India, December 10–12, 2005, Proceedings. Berlin: Springer (ISBN 978-3-540-30805-8/pbk). Lecture Notes in Computer Science 3797, 258-269 (2005). MSC: 94A60 14G50 PDF BibTeX XML Cite \textit{M. Scott}, Lect. Notes Comput. Sci. 3797, 258--269 (2005; Zbl 1153.94429) Full Text: DOI OpenURL
Chatterjee, Sanjit; Sarkar, Palash; Barua, Rana Efficient computation of Tate pairing in projective coordinate over general characteristic fields. (English) Zbl 1133.94310 Park, Choonsik (ed.) et al., Information security and cryptology – ICISC 2004. 7th international conference, Seoul, Korea, December 2–3, 2004. Revised Selected Papers. Berlin: Springer (ISBN 978-3-540-26226-8/pbk). Lecture Notes in Computer Science 3506, 168-181 (2005). MSC: 94A60 68W30 PDF BibTeX XML Cite \textit{S. Chatterjee} et al., Lect. Notes Comput. Sci. 3506, 168--181 (2005; Zbl 1133.94310) Full Text: DOI OpenURL
Kwon, Soonhak Efficient Tate pairing computation for elliptic curves over binary fields. (English) Zbl 1127.94348 Boyd, Colin (ed.) et al., Information security and privacy. 10th Australasian conference, ACISP 2005, Brisbane, Australia, July 4–6, 2005. Proceedings. Berlin: Springer (ISBN 3-540-26547-3/pbk). Lecture Notes in Computer Science 3574, 134-145 (2005). MSC: 94A60 14G50 PDF BibTeX XML Cite \textit{S. Kwon}, Lect. Notes Comput. Sci. 3574, 134--145 (2005; Zbl 1127.94348) Full Text: DOI OpenURL
McCullagh, Noel; Barreto, Paulo S. L. M. A new two-party identity-based authenticated key agreement. (English) Zbl 1079.94563 Menezes, Alfred (ed.), Topics in cryptology – CT-RSA 2005. The cryptographers’ track at the RSA conference 2005, San Francisco, CA, USA, February 14–18, 2005. Proceedings. Berlin: Springer (ISBN 3-540-24399-2/pbk). Lecture Notes in Computer Science 3376, 262-274 (2005). MSC: 94A60 PDF BibTeX XML Cite \textit{N. McCullagh} and \textit{P. S. L. M. Barreto}, Lect. Notes Comput. Sci. 3376, 262--274 (2005; Zbl 1079.94563) Full Text: DOI OpenURL