Improvement of Faugère et al.'s method to solve ECDLP

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

Volumn 8231 LNCS, Issue , 2013, Pages 115-132

  Huang, Yun Ju ^a   Petit, Christophe ^b   Shinohara, Naoyuki ^c   Takagi, Tsuyoshi ^a  

^a KYUSHU UNIVERSITY   (Japan)

^b Microelectronics Laboratory   (Belgium)

^c NATIONAL INSTITUTE OF INFORMATION AND COMMUNICATIONS TECHNOLOGY   (Japan)

Author keywords

Discrete logarithm problem; Elliptic curve; Gr bner basis; Index calculus; Multivariable polynomial system

Indexed keywords

DISCRETE LOGARITHM PROBLEMS; ELLIPTIC CURVE; ELLIPTIC CURVE CRYPTOGRAPHY; ELLIPTIC CURVE DISCRETE LOGARITHM PROBLEMS; EXPERIMENTAL EVIDENCE; INDEX CALCULUS; MULTI-VARIABLE POLYNOMIALS; PAIRING BASED CRYPTOSYSTEMS;

COMPUTER PROGRAMMING; SECURITY OF DATA;

POLYNOMIALS;

EID: 84891939354     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-41383-4_8     Document Type: Conference Paper

References (18)

1. National Security Agency: The case for elliptic curve cryptography (January 2009), http://www.nsa.gov/business/programs/elliptic-curve.shtml
2. Shanks, D.: Class number, A theory of factorization, and genera. In: 1969 Number Theory Institute (Proc. Sympos. Pure Math., vol. XX, State Univ. New York, Stony Brook, N.Y., 1969), Providence, R.I., pp. 415-440 (1971)
3. Pollard, J.M.: A Monte Carlo method for factorization. BIT Numerical Mathematics 15(3), 331-334 (1975)
4. Brent, R.P.: An improved Monte Carlo factorization algorithm. BIT Numerical Mathematics 20, 176-184 (1980)
5. Pollard, J.M.: Kangaroos, monopoly and discrete logarithms. Journal of Cryptology 13, 437-447 (2000)
6. Diem, C.: An index calculus algorithm for plane curves of small degree. In: Hess, F., Pauli, S., Pohst, M. (eds.) ANTS 2006. LNCS, vol. 4076, pp. 543-557. Springer, Heidelberg (2006)
7. Gaudry, P.: Index calculus for abelian varieties of small dimension and the elliptic curve discrete logarithm problem. Journal of Symbolic Computation 44(12), 1690-1702 (2009)
8. Diem, C.: On the discrete logarithm problem in elliptic curves. Compositio Mathematica 147, 75-104 (2011)
9. Faugère, J.-C., Perret, L., Petit, C., Renault, G.: Improving the complexity of index calculus algorithms in elliptic curves over binary fields. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 27-44. Springer, Heidelberg (2012)
10. Petit, C., Quisquater, J.-J.: On polynomial systems arising from a Weil descent. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 451-466. Springer, Heidelberg (2012)
11. Joux, A., Vitse, V.: Elliptic curve discrete logarithm problem over small degree extension fields. Journal of Cryptology, 1-25 (2011)
12. Faugère, J.C., Gaudry, P., Huot, L., Renault, G.: Using symmetries in the index calculus for elliptic curves discrete logarithm. IACR Cryptology ePrint Archive 2012, 199 (2012)
13. Semaev, I.: Summation polynomials and the discrete logarithm problem on elliptic curves. IACR Cryptology ePrint Archive 2004, 31 (2004)
14. 4). Journal of Pure and Applied Algebra 139(1-3), 61-88 (1999)
15. 5). In: Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation, ISSAC 2002, pp. 75-83. ACM, New York (2002)
16. Faugère, J., Gianni, P., Lazard, D., Mora, T.: Efficient computation of zerodimensional Gröbner bases by change of ordering. Journal of Symbolic Computation 16(4), 329-344 (1993)
17. Joux, A., Vitse, V.: Cover and decomposition index calculus on elliptic curves made practical - application to a previously unreachable curve over Fp6. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 9-26. Springer, Heidelberg (2012)
18. Joux, A., Vitse, V.: A variant of the F4 algorithm. In: Kiayias, A. (ed.) CT-RSA 2011. LNCS, vol. 6558, pp. 356-375. Springer, Heidelberg (2011)