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Lattice basis reduction, Jacobi sums and hyperelliptic cryptosystems

Published online by Cambridge University Press:  17 April 2009

Joe Buhler  and
Neal Koblitz
Joe Buhler
Affiliation:
Department of Mathematics, Reed College, Portland OR 97202-8199, United States of America e-mail: jpb@reed.edu
Neal Koblitz
Affiliation:
Department of Mathematics, Box 354350, University of Washington, Seattle WA 98195, United States of America e-mail: koblitz@math.washington.edu
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Abstract

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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 58 , Issue 1 , August 1998 , pp. 147 - 154
Copyright
Copyright © Australian Mathematical Society 1998

References

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