4 research outputs found
Computing Discrete Logarithms in an Interval
The discrete logarithm problem in an interval of size in a group is: Given and an integer to find an integer , if it exists, such that . Previously the best low-storage algorithm to solve this problem was the van Oorschot and Wiener version of the Pollard kangaroo method. The heuristic average case running time of this method is group operations.
We present two new low-storage algorithms for the discrete logarithm problem in an interval of size . The first algorithm is based on the Pollard kangaroo method, but uses 4 kangaroos instead of the usual two. We explain why this algorithm has heuristic average case expected running time of group operations. The second algorithm is based on the Gaudry-Schost algorithm and the ideas of our first algorithm. We explain why this algorithm has heuristic average case expected running time of group operations. We give experimental results that show that the methods do work close to that predicted by the theoretical analysis.
This is a revised version since the published paper that contains a corrected proof of Theorem 6 (the statement of Theorem 6 is unchanged). We thank Ravi Montenegro for pointing out the errors