Deterministic encoding and hashing to odd hyperelliptic curves

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

Volumn 6487 LNCS, Issue , 2010, Pages 265-277

  Fouque, Pierre Alain ^a   Tibouchi, Mehdi ^a  

^a ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

Deterministic Encoding; Hashing; Hyperelliptic Curve Cryptography

Indexed keywords

BIJECTIONS; DETERMINISTIC ENCODING; EFFICIENT ENCODING; ELGAMAL ENCRYPTION; HASHING; HYPERELLIPTIC CURVE; HYPERELLIPTIC CURVE CRYPTOGRAPHY; JACOBIANS; RATIONAL POINTS; SUPERSINGULAR ELLIPTIC CURVE;

HASH FUNCTIONS; RATIONAL FUNCTIONS;

ENCODING (SYMBOLS);

EID: 78650262752     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-17455-1_17     Document Type: Conference Paper

References (29)

1. Baek, J., Zheng, Y.: Identity-based threshold decryption. In: Bao, et al. (eds.) [2], pp. 262-276
2. Bao, F., Deng, R., Zhou, J. (eds.): PKC 2004. LNCS, vol. 2947. Springer, Heidelberg (2004)
3. Boldyreva, A.: Threshold signatures, multisignatures and blind signatures based on the gap-diffie-hellman-group signature scheme. In: Desmedt (ed.) [11], pp. 31-46
4. Boneh, D., Franklin, M.K.: Identity-based encryption from the weil pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213-229. Springer, Heidelberg (2001)
5. Boneh, D., Gentry, C., Lynn, B., Shacham, H.: Aggregate and verifiably encrypted signatures from bilinear maps. In: EUROCRYPT, pp. 416-432 (2003)
6. Boneh, D., Lynn, B., Shacham, H.: Short signatures from the weil pairing. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 514-532. Springer, Heidelberg (2001) (Pubitemid 33371204)
7. Boyd, C., Montague, P., Nguyen, K.Q.: Elliptic curve based password authenticated key exchange protocols. In: Varadharajan, V., Mu, Y. (eds.) ACISP 2001. LNCS, vol. 2119, pp. 487-501. Springer, Heidelberg (2001)
8. Boyen, X.: Multipurpose identity-based signcryption (a swiss army knife for identity-based cryptography). In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 383-399. Springer, Heidelberg (2003)
9. Brier, E., Coron, J.-S., Icart, T., Madore, D., Randriam, H., Tibouchi, M.: Efficient indifferentiable hashing into ordinary elliptic curves. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 237-254. Springer, Heidelberg (2010)
10. Cha, J.C., Cheon, J.H.: An identity-based signature from gap diffie-hellman groups. In: Desmedt (ed.) [11], pp. 18-30
11. Desmedt, Y. (ed.): PKC 2003. LNCS, vol. 2567. Springer, Heidelberg (2002)
12. Farashahi, R.R., Fouque, P.-A., Shparlinski, I., Tibouchi, M., Voloch, F.: Indifferentiable deterministic hashing to elliptic and hyperelliptic curves. Preprint (2010),
13. Freeman, D.M., Satoh, T.: Constructing pairing-friendly hyperelliptic curves using weil restriction. Cryptology ePrint Archive, Report 2009/103 (2009),
14. 5+ax over finite prime fields. In: Matsui, M., Zuccherato, R.J. (eds.) SAC 2003. LNCS, vol. 3006, pp. 26-41. Springer, Heidelberg (2003)
15. Gentry, C., Silverberg, A.: Hierarchical id-based cryptography. In: Zheng (ed.) [29], pp. 548-566
16. Haneda, M., Kawazoe, M., Takahashi, T.: Suitable curves for genus-4 HCC over prime fields. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 539-550. Springer, Heidelberg (2005)
17. Horwitz, J., Lynn, B.: Toward hierarchical identity-based encryption. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 466-481. Springer, Heidelberg (2002)
18. Icart, T.: How to hash into elliptic curves. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 303-316. Springer, Heidelberg (2009)
19. Joux, A.: The weil and tate pairings as building blocks for public key cryptosystems. In: Fieker, C., Kohel, D.R. (eds.) ANTS 2002. LNCS, vol. 2369, pp. 20-32. Springer, Heidelberg (2002)
20. Kammerer, J.-G., Lercier, R., Renault, G.: Encoding points on hyperelliptic curves over finite fields in deterministic polynomial time. CoRR, abs/1005.1454 (2010)
21. 5 + ax. In: Galbraith, S.D., Paterson, K.G. (eds.) Pairing 2008. LNCS, vol. 5209, pp. 164-177. Springer, Heidelberg (2008)
22. Kohel, D.R., Shparlinski, I.: On exponential sums and group generators for elliptic curves over finite fields. In: Bosma, W. (ed.) ANTS 2000. LNCS, vol. 1838, pp. 395-404. Springer, Heidelberg (2000)
23. Libert, B., Quisquater, J.-J.: Efficient signcryption with key privacy from gap diffiehellman groups. In: Bao, et al. (eds.) [2], pp. 187-200
24. Menezes, A.J., Wu, Y.-H., Zuccherato, R.J.: An elementary introduction to hyperelliptic curves. In: Koblitz, N. (ed.) Algebraic Aspects of Cryptography. Algorithms and Computation in Mathematics, vol. 3, pp. 155-178. Springer, Heidelberg (1998)
25. 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 (2010)
26. Shallue, A., van de Woestijne, C.: Construction of rational points on elliptic curves over finite fields. In: Hess, F., Pauli, S., Pohst, M.E. (eds.) ANTS 2006. LNCS, vol. 4076, pp. 510-524. Springer, Heidelberg (2006)
27. Ulas, M.: Rational points on certain hyperelliptic curves over finite fields. Bull. Polish Acad. Sci. Math. 55(2), 97-104 (2007)
28. Zhang, F., Kim, K.: Id-based blind signature and ring signature from pairings. In: Zheng (ed.) [29], pp. 533-547
29. Zheng, Y. (ed.): ASIACRYPT 2002. LNCS, vol. 2501. Springer, Heidelberg (2002)