Index Calculus Attack for Hyperelliptic Curves of Small Genus

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

Volumn 2894, Issue , 2003, Pages 75-92

  Thériault, Nicolas ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

GEOMETRY; SECURITY OF DATA;

DISCRETE LOGARITHM PROBLEMS; HYPER-ELLIPTIC CURVES; INDEX CALCULUS; JACOBIANS; MEMORY SPACE; RHO METHODS; RUNNING TIME; SQUARE-ROOT ALGORITHMS;

CALCULATIONS;

EID: 0345058968     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-40061-5_5     Document Type: Article

References (13)

1. L. M. Adleman, J. DeMarrais, M.-D. Huang, A subexponential algorithm for discrete logarithms over hyperelliptic curves of large genus over GF(q), Theoret. Comput. Sci., 226, no. 1-2, pp. 7-18, 1999.
2. D. G. Cantor, Computing in the Jacobian of an hyperelliptic curve, Math. Comp., 48(177), pp. 95-101, 1987.
3. A. Enge, Computing discrete logarithms in high-genus hyperelliptic jacobians in provably subexponential time, Math. Comp., 71, no. 238, pp. 729-742, 2002.
4. A. Enge, P. Gaudry, A general framework for subexponential discrete logarithm algorithms, Acta Arith., 102, no. 1, pp. 83-103, 2002.
5. A. Enge, A. Stein, Smooth ideals in hyperelliptic function fields, Math. Comp., 71, no. 239, pp. 1219-1230, 2002.
6. T. Garefalakis, D. Panario, The index calculus method using non-smooth polynomials, Math. Comp., 70, no 235, pp. 1253-1264, 2001.
7. P. Gaudry, Algorithmique des courbes hyperelliptiques et applications à la cryptologie, Thèse de doctorat de l'École polytechnique, 2000
8. P. Gaudry, An algorithm for solving the discrete log problem on hyperelliptic curves, Advances in cryptology - EUROCRYPT 2000, Springer-Verlag, LNCS 1807, pp. 19-34, 2000.
9. M. Girault, R. Cohen, M. Campana, A generalized birthday attack, Advances in Cryptology - EUROCRYPT '88, Springer-Verlag, LNCS 330, pp. 129-156, 1988.
10. N. Koblitz, Hyperelliptic cryptosystems, J. of Cryptology, 1, pp. 139-150, 1989.
11. B. A. LaMacchia, A. M. Odlyzko, Solving large sparse linear systems over finite fields, Advances in Cryptology - CRYPTO '90, Springer-Verlag, LNCS 537, pp. 109-133, 1990.
12. V. Müller, A. Stein, C. Thiel, Computing discrete logarithms in real quadratic congruence function fields of large genus, Math. Comp., 68, no. 226, pp. 807-822, 1999.
13. D. H. Wiedemann, Solving sparse linear equations over finite fields, IEEE Trans. Inform. Theory, IT-32, no. 1, pp.54-62, 1986.