An L(1/3 + ε) Algorithm for the discrete logarithm problem for low degree curves

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

Volumn 4515 LNCS, Issue , 2007, Pages 379-393

  Enge, Andreas ^a   Gaudry, Pierrick ^b  

^a ECOLE POLYTECHNIQUE   (France)

^b LORIA   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL EFFICIENCY; CURVE FITTING; JACOBIAN MATRICES;

DISCRETE LOGARITHM COMPUTATION; DISCRETE LOGARITHM PROBLEMS; SUBEXPONENTIAL COMPLEXITY;

PROBLEM SOLVING;

EID: 38049153000     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-72540-4_22     Document Type: Conference Paper

References (16)

1. L. M. Adleman, J. DeMarrais, and M.-D. Huang. A subexponential algorithm for discrete logarithms over the rational subgroup of the jacobians of large genus hyperelliptic curves over finite fields. In L. Adleman and M.-D. Huang, editors, ANTS-I, volume 877 of Lecture Notes in Comput. Sci., pages 28-40. Springer-Verlag, 1994.
2. R. L. Bender and C Pomerance. Rigorous discrete logarithm computations in finite fields via smooth polynomials. In D. A. Buell and J. T. Teitelbaum, editors, Computational Perspectives on Number Theory: Proceedings of a Conference in Honor of A.O.L. Atkin, volume 7 of Studies in Advanced Mathematics, pages 221-232. American Mathematical Society, 1998.
3. J.-M. Couveignes. Algebraic groups and discrete logarithm. In Public-key cryptography and computational number theory, pages 17-27. de Gruyter, 2001.
4. C Diem. An index calculus algorithm for plane curves of small degree. In F. Heß, S. Pauli, and M. Pohst, editors, ANTS-VII, volume 4076 of Lecture Notes in Comput. Sci., pages 543-557. Springer-Verlag, 2006.
5. A. Enge. Computing discrete logarithms in high-genus hyperelliptic Jacobians in provably subexponential time. Math. Comp., 71:729-742, 2002.
6. A. Enge and P. Gaudry. A general framework for subexponential discrete logarithm algorithms. Acta Arith., 102:83-103, 2002.
7. A. Enge and A. Stein. Smooth ideals in hyperelliptic function fields. Math. Comp., 71:1219-1230, 2002.
8. P. Gaudry. An algorithm for solving the discrete log problem on hyperelliptic curves. In B. Preneel, editor, Advances in Cryptology - EUROCRYPT 2000, volume 1807 of Lecture Notes in Comput. Sei., pages 19-34. Springer-Verlag, 2000.
9. P. Gaudry, E. Thomé, N. Thériault, and C. Diem. A double large prime variation for small genus hyperelliptic index calculus. Math. Comp., 76:475-492, 2007.
10. G. Haché. Construction effective de codes géomé triques. PhD thesis, Université de Paris VI, 1996.
11. J. L. Haffner and K. S. McCurley. A rigorous subexponential algorithm for computation of class groups. J. Amer. Math. Soc., 2(4):837-850, 1989.
12. F. Heß. Computing Riemann-Roch spaces in algebraic function fields and related topics. J. Symbolic Comput., 33:425-445, 2002.
13. F. Heß. Computing relations in divisor class groups of algebraic curves over finite fields. Preprint, 2004.
14. E. Manstavičius. Semigroup elements free of large prime factors. In F. Schweiger and E. Manstavičius, editors, New Trends in Probability and Statistic, pages 135-153, 1992.
15. V. Müller, A. Stein, and C. Thiel. Computing discrete logarithms in real quadratic congruence function fields of large genus. Math. Comp., 68(226):807-822, 1999.
16. A. Storjohann. Algorithms for Matrix Canonical Forms. PhD thesis, Eidgenössische Technische Hochschule Zürich, 2000.