Lattice basis reduction, Jacobi sums and hyperelliptic cryptosystems

Bulletin of the Australian Mathematical Society

Volumn 58, Issue 1, 1998, Pages 147-154

  Buhler, Joe ^a   Koblitz, Neal ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032147416     PISSN: 00049727     EISSN: None     Source Type: Journal    
DOI: 10.1017/s000497270003207x     Document Type: Article

References (11)

1. L.M. Adleman, J. DeMarrais and M. Huang, 'A subexponential algorithm for discrete logarithms over the rational subgroup of the jacobians of large genus hyperelliptic curves over finite fields', in Algorithmic Number Theory, Lecture Notes Comput. Sci. 877 (Springer-Verlag, Berlin, Heidelberg, New York, 1994), pp. 28-40.
2. J. Buchmann and H.C. Williams, 'On principal ideal testing in algebraic number fields', J. Symbolic Comput. 4 (1987), 11-19.
3. H. Cohen, A course in computational algebraic number theory (Springer-Verlag, Berlin, Heidelberg, New York, 1993).
4. G. Frey and H. Rück, 'A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves', Math. Comp. 62 (1994), 865-874.
5. C.F. Gauss, Werke (Zweiter Band, Göttingen, 1976).
6. K. Ireland and M.I. Rosen, A classical introduction to modern number theory, (2nd edition) (Springer-Verlag, Berlin, Heidelberg, New York, 1990).
7. N. Koblitz, 'Hyperelliptic cryptosystems', J. Cryptology 1 (1989), 139-150.
8. A.K. Lenstra, H.W. Lenstra, Jr. and L. Lovász, 'Factoring polynomials with rational coefficients', Math. Ann. 261 (1982), 515-534.
9. H.W. Lenstra, Jr., 'Euclid's algorithm in cyclotomic fields', J. London Math. Soc. 10 (1975), 457-465.
10. A. Menezes, T. Okamoto and S.A. Vanstone, 'Reducing elliptic curve logarithms to logarithms in a finite field', IEEE Trans. Inform. Theory 39 (1993), 1639-1646.
11. A. Weil, 'Numbers of solutions of equations in finite fields', Bull. Amer. Math. Soc. 55 (1949), 497-508.