Time-Memory Analysis of Parallel Collision Search Algorithms

  • Monika Trimoska Laboratoire MIS, Université de Picardie Jules Verne, Amiens, France
  • Sorina Ionica Laboratoire MIS, Université de Picardie Jules Verne, Amiens, France
  • Gilles Dequen Laboratoire MIS, Université de Picardie Jules Verne, Amiens, France
Keywords: discrete logarithm, parallelism, collision, elliptic curves, meet-in-the-middle, attack, trade-off, radix tree

Abstract

Parallel versions of collision search algorithms require a significant amount of memory to store a proportion of the points computed by the pseudo-random walks. Implementations available in the literature use a hash table to store these points and allow fast memory access. We provide theoretical evidence that memory is an important factor in determining the runtime of this method. We propose to replace the traditional hash table by a simple structure, inspired by radix trees, which saves space and provides fast look-up and insertion. In the case of many-collision search algorithms, our variant has a constant-factor improved runtime. We give benchmarks that show the linear parallel performance of the attack on elliptic curves discrete logarithms and improved running times for meet-in-the-middle applications.

Published
2021-02-23
How to Cite
Trimoska, M., Ionica, S., & Dequen, G. (2021). Time-Memory Analysis of Parallel Collision Search Algorithms. IACR Transactions on Cryptographic Hardware and Embedded Systems, 2021(2), 254-274. https://doi.org/10.46586/tches.v2021.i2.254-274
Section
Articles