A Low-Memory Parallel Version of Matsuo, Chao, and Tsujii’s Algorithm

  • Pierrick Gaudry
  • Éric Schost
Conference paper

DOI: 10.1007/978-3-540-24847-7_15

Part of the Lecture Notes in Computer Science book series (LNCS, volume 3076)
Cite this paper as:
Gaudry P., Schost É. (2004) A Low-Memory Parallel Version of Matsuo, Chao, and Tsujii’s Algorithm. In: Buell D. (eds) Algorithmic Number Theory. ANTS 2004. Lecture Notes in Computer Science, vol 3076. Springer, Berlin, Heidelberg

Abstract

We present an algorithm based on the birthday paradox, which is a low-memory parallel counterpart to the algorithm of Matsuo, Chao and Tsujii. This algorithm computes the group order of the Jacobian of a genus 2 curve over a finite field for which the characteristic polynomial of the Frobenius endomorphism is known modulo some integer. The main tool is a 2-dimensional pseudo-random walk that allows to heuristically choose random elements in a 2-dimensional space. We analyze the expected running time based on heuristics that we validate by computer experiments. Compared with the original algorithm by Matsuo, Chao and Tsujii, we lose a factor of about 3 in running time, but the memory requirement drops from several GB to almost nothing. Our method is general and can be applied in other contexts to transform a baby-step giant-step approach into a low memory algorithm.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Pierrick Gaudry
    • 1
  • Éric Schost
    • 2
  1. 1.Laboratoire LIXÉcole polytechniquePalaiseauFrance
  2. 2.Laboratoire STIXÉcole polytechniquePalaiseauFrance

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