Ordinary Pairing-Friendly Genus 2 Hyperelliptic Curves with Absolutely Simple Jacobians

FOTIADIS, Georgios; Konstantinou, Elisavet

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Ordinary Pairing-Friendly Genus 2 Hyperelliptic Curves with Absolutely Simple Jacobians

FOTIADIS, Georgios; Konstantinou, Elisavet

2017 • In International Conference on Mathematical Aspects of Computer and Information Sciences

Peer reviewed

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https://hdl.handle.net/10993/39268

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Détails

Disciplines :

Sciences informatiques

Auteur, co-auteur :

FOTIADIS, Georgios ; University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT)

Konstantinou, Elisavet; University of the Aegean > Department of Information & Communication Systems Engineering > Assistant Professor

Co-auteurs externes :

yes

Langue du document :

Anglais

Titre :

Ordinary Pairing-Friendly Genus 2 Hyperelliptic Curves with Absolutely Simple Jacobians

Date de publication/diffusion :

21 décembre 2017

Nom de la manifestation :

7th International Conference on Mathematical Aspects of Computer and Information Sciences

Organisateur de la manifestation :

SBA Research

Lieu de la manifestation :

Vienna, Autriche

Date de la manifestation :

from 15-11-2017 to 17-11-2017

Manifestation à portée :

International

Titre de l'ouvrage principal :

International Conference on Mathematical Aspects of Computer and Information Sciences

Maison d'édition :

Springer

ISBN/EAN :

978-3-319-72453-9

Collection et n° de collection :

Lecture Notes in Computer Science, vol 10693

Pagination :

409-424

Peer reviewed :

Peer reviewed

Disponible sur ORBilu :

depuis le 03 avril 2019

Statistiques

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190 (dont 0 Unilu)

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Bibliographie

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Bernstein, D.: Elliptic vs. hyperelliptic, Part 1. Talk at ECC 2006 (2006).
Brezing, F., Weng, A.: Elliptic curves suitable for pairing based cryptography. Des. Codes Cryptogr. 37(1), 133–141 (2005). https://doi.org/10.1007/s10623-004-3808-4. Springer.
Cantor, D.G.: Computing in the Jacobian of a hyperelliptic curve. Math. Comput. 48(177), 95–101 (1987). https://doi.org/10.1090/S0025-5718-1987-0866101-0.
Cohen, H., Frey, G., Avanzi, R., Doche, C., Lange, T., Nguyen, K., Vercauteren, F.: Handbook of Elliptic and Hyperelliptic Curve Cryptography. Discrete Mathematics and its Applications. Chapman & Hall/CRC Press, Boca Raton (2006).
Dryło, R.: Constructing pairing-friendly genus 2 curves with split Jacobian. In: Galbraith, S., Nandi, M. (eds.) INDOCRYPT 2012. LNCS, vol. 7668, pp. 431–453. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-34931-7_25.
El Mrabet, N., Joye, M.: Guide to Pairing-Based Cryptography. CRC Press, Boca Raton (2017).
Freeman, D.: A generalized Brezing-Weng algorithm for constructing pairing-friendly ordinary abelian varieties. In: Galbraith, S.D., Paterson, K.G. (eds.) Pairing 2008. LNCS, vol. 5209, pp. 146–163. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85538-5_11.
Freeman, D., Stevenhagen, P., Streng, M.: Abelian varieties with prescribed embedding degree. In: van der Poorten, A.J., Stein, A. (eds.) ANTS 2008. LNCS, vol. 5011, pp. 60–73. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-79456-1_3.
Freeman, D.M., Satoh, S.: Constructing pairing-friendly hyperelliptic curves using Weil restriction. J. Number Theor. 131(5), 959–983 (2011). https://doi.org/10.1016/j.jnt.2010.06.003. Elsevier.
Frey, G., Lange, T.: Fast bilinear maps from the Tate-Lichtenbaum pairing on hyperelliptic curves. In: Hess, F., Pauli, S., Pohst, M. (eds.) ANTS 2006. LNCS, vol. 4076, pp. 466–479. Springer, Heidelberg (2006). https://doi.org/10.1007/11792086_33.
Guillevic, A., Vergnaud, D.: Genus 2 hyperelliptic curve families with explicit jacobian order evaluation and pairing-friendly constructions. In: Abdalla, M., Lange, T. (eds.) Pairing 2012. LNCS, vol. 7708, pp. 234–253. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36334-4_16.
Howe, E.W., Zhu, H.J.: On the existence of absolutely simple abelian varieties of a given dimension over an arbitrary field. J. Number Theor. 92(1), 139–163 (2002). https://doi.org/10.1006/jnth.2001.2697. Elsevier.
Kim, T., Jeong, J.: Extended tower number field sieve with application to finite fields of arbitrary composite extension degree. In: Fehr, S. (ed.) PKC 2017. LNCS, vol. 10174, pp. 388–408. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-662-54365-8_16.
Kachisa, E.J.: Generating more Kawazoe-Takahashi genus 2 pairing-friendly hyperelliptic curves. In: Joye, M., Miyaji, A., Otsuka, A. (eds.) Pairing 2010. LNCS, vol. 6487, pp. 312–326. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17455-1_20.
Kawazoe, M., Takahashi, T.: Pairing-friendly hyperelliptic curves with ordinary Jacobians of type y2=x5+axy2=x5+ax. In: Galbraith, S.D., Paterson, K.G. (eds.) Pairing 2008. LNCS, vol. 5209, pp. 164–177. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85538-5_12.
Kim, T., Barbulescu, R.: Extended tower number field sieve: a new complexity for the medium prime case. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9814, pp. 543–571. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53018-4_20.
Koblitz, N.: Hyperelliptic cryptosystems. J. Cryptol. 1(3), 139–150 (1989). https://doi.org/10.1007/BF02252872. Springer.
Lange, T.: Elliptic vs. hyperelliptic, Part 2. Talk at ECC 2006 (2006).
Lauter, K., Shang, N.: Generating pairing-friendly parameters for the CM construction of genus 2 curves over prime fields. Des. Codes Cryptogr. 67(3), 341–355 (2013). https://doi.org/10.1007/s10623-012-9611-8. Springer.
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Weng, A.: Constructing hyperelliptic curves of genus 2 suitable for cryptography. Math. Comput. 72(241), 435–458 (2002). https://doi.org/10.1090/S0025-5718-02-01422-9. American Mathematical Society.