Paper 2010/617
Computing Discrete Logarithms in an Interval
Steven D. Galbraith and John M. Pollard and Raminder S. Ruprai
Abstract
The discrete logarithm problem in an interval of size $N$ in a group $G$ is: Given $g, h \in G$ and an integer $ N$ to find an integer $0 \le n \le N$, if it exists, such that $h = g^n$. 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 $(2 + o(1)) \sqrt{N}$ group operations. We present two new low-storage algorithms for the discrete logarithm problem in an interval of size $N$. 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 $(1.714 + o(1)) \sqrt{N}$ 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 $(1.660 + o(1)) \sqrt{N}$ group operations. We give experimental results that show that the methods do work close to that predicted by the theoretical analysis.
Metadata
- Available format(s)
- Category
- Public-key cryptography
- Publication info
- Published elsewhere. Submitted
- Keywords
- discrete logarithm problem (DLP)
- Contact author(s)
- S Galbraith @ math auckland ac nz
- History
- 2018-11-23: revised
- 2010-12-08: received
- See all versions
- Short URL
- https://ia.cr/2010/617
- License
-
CC BY