Catching Kangaroos in Function Fields
نویسندگان
چکیده
1. Introduction In this paper we generalize the parallelized lambda method for computing invariants in real qua-dratic function elds. A basic such invariant is the regulator, which plays an important role in cryptosystems based on real quadratic function elds. For example, in the key-exchange protocol by Scheidler, Stein and Williams SSW96], the regulator provides a measure for the key space; moreover, computation of the regulator is an instance of solving the discrete logarithm problem in real quadratic function elds. Pollard's lambda method Pol78], also called the method of catching kangaroos, was originally developed to compute discrete logarithms in Z=pZand has been canonically generalized to solve the discrete logarithm problem in any nite abelian group. The key ingredient for the lambda method is that we know that the discrete logarithm lies in a given interval a; b; then the expected running time is O(p b ? a) group operations. Van Oorschot and Wiener vOW99] have shown that
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