Four-dimensional GLV via the Weil restriction

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 8269 LNCS, Issue PART 1, 2013, Pages 79-96

  Guillevic, Aurore ^a,b   Ionica, Sorina ^a  

^a ECOLE NORMALE SUPÉRIEURE   (France)

^b THALES COMMUNICATIONS   (France)

Author keywords

elliptic curves; genus 2 curves; GLV method; isogenies

Indexed keywords

ABELIAN VARIETIES; ELLIPTIC CURVE; ENDOMORPHISM RING; EXTENSION FIELD; GENUS 2 CURVES; GLV METHOD; ISOGENIES; SCALAR MULTIPLICATION;

CRYPTOGRAPHY; SECURITY OF DATA;

GEOMETRY;

EID: 84892409765     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-42033-7_5     Document Type: Conference Paper

References (20)

1. Bernstein, D., Lange, T.: Explicit-Formulas Database, http://www.hyperelliptic.org/EFD/
2. Bisson, G.: Endomorphism rings in cryptography. PhD thesis, Institut National Polytechnique de Lorraine (2011)
3. Bos, J.W., Costello, C., Hisil, H., Lauter, K.: Fast cryptography in genus 2. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 194-210. Springer, Heidelberg (2013)
4. Cheon, J.H.: Security analysis of the strong diffie-hellman problem. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 1-11. Springer, Heidelberg (2006)
5. Costello, C., Lauter, K.: Group Law Computations on Jacobians of Hyperelliptic Curves. In: Miri, A., Vaudenay, S. (eds.) SAC 2011. LNCS, vol. 7118, pp. 92-117. Springer, Heidelberg (2012)
6. Dewaghe, L.: Un corollaire aux formules de Vélu. Draft (1995)
7. Doche, C.: Exponentiation. In: Handbook of Elliptic and Hyperelliptic Curve Cryptography, ch. 9, pp. 145-168. Chapman and Hall/CRC, Taylor and Francis Group (2006)
8. Duursma, I., Kiyavash, N.: The vector decomposition problem for elliptic and hyperelliptic curves. Journal of the Ramanujan Mathematical Society 20(1), 59-76 (2005)
9. Freeman, D.M., Satoh, T.: Constructing pairing-friendly hyperelliptic curves using Weil restriction. Journal of Number Theory 131(5), 959-983 (2011)
10. Galbraith, S.D., Lin, X., Scott, M.: Endomorphisms for faster elliptic curve cryptography on a large class of curves. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 518-535. Springer, Heidelberg (2009)
11. Gallant, R.P., Lambert, R.J., Vanstone, S.A.: Faster point multiplication on elliptic curves with efficient endomorphisms. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 190-200. Springer, Heidelberg (2001)
12. Gaudry, P., Schost, É.: On the invariants of the quotients of the jacobian of a curve of genus 2. In: Bozta, S., Sphparlinski, I. (eds.) AAECC 2001. LNCS, vol. 2227, pp. 373-386. Springer, Heidelberg (2001)
13. 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)
14. Kohel, D.: Endomorphism rings of elliptic curves over finite fields. Ph.D. thesis, University of California at Berkeley (1996)
15. Leprévost, F., Morain, F.: Revêtements de courbes elliptiques à multiplication complexe par des courbes hyperelliptiques et sommes de caractères. Journal of Number Theory 64, 165-182 (1997), http://www.lix.polytechnique.fr/Labo/Francois.Morain/Articles/ LIX-RR-94-07-revetement.ps.gz
16. Longa, P., Sica, F.: Four dimensional Gallant-Lambert-Vanstone scalar multiplication. Journal of Cryptology, 1-36 (2013)
17. Quer, J.: Fields of definition of Q-curves. Journal de Théorie des Nombres de Bordeaux 13(1), 275-285 (2001)
18. Satoh, T.: Generating genus two hyperelliptic curves over large characteristic finite fields. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 536-553. Springer, Heidelberg (2009)
19. Smith, B.: Families of fast elliptic curves from Q-curves. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part I. LNCS, vol. 8269, pp. 61-78. Springer, Heidelberg (2013), http://eprint.iacr.org/2013/312
20. Vélu, J.: Isogenies entre courbes elliptiques. Comptes Rendus De l'Académie Des Sciences Paris, Série I-Mathèmatique, Série A 273, 238-241 (1971)