Lattice basis reduction, Jacobi sums and hyperelliptic cryptosystems
- 1 August 1998
- journal article
- research article
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
- Vol. 58 (1) , 147-154
- https://doi.org/10.1017/s000497270003207x
Abstract
Using the LLL-algorithm for finding short vectors in lattices, we show how to compute a Jacobi sum for the prime field Fp in Q(e2πi/n) in time O(log3p), where n is small and fixed, p is large, and p = 1 (mod n). This result is useful in the construction of hyperelliptic cryptosystems.This publication has 1 reference indexed in Scilit:
- A Remark Concerning m-Divisibility and the Discrete Logarithm in the Divisor Class Group of CurvesMathematics of Computation, 1994