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The discrete logarithm problem is an important computing problem in modern cryptography. Solving massive discrete logarithm problems is a nature need and appears in many application scenarios. In this paper, we propose the dynamic index calculus algorithm to solve massive discrete logarithm problems fast. We utilize the information generated in the process of solving previous discrete logarithm problems to accelerate the calculation of subsequent discrete logarithm problems. In particular, we utilize factorizations generated in solving previous discrete logarithm problems to expand factor base so that the calculation of subsequent discrete logarithm problems is accelerated. Empirical experiment results indicate that our algorithm can solve massive discrete logarithm problems twice as fast as the state-of-the-art algorithm.

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Dynamically Expanding Factor Base of Index Calculus Algorithm to Solve Massive Discrete Logarithm Problems Faster

  • 会议论文

  • 发表日期：

    2026年

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  • Yichen Hao,
  • Wen Huang,
  • Zhishuo Zhang,
  • Weixin Zhao,
  • Jian Peng,
  • Yongjian Liao

摘要

The discrete logarithm problem is an important computing problem in modern cryptography. Solving massive discrete logarithm problems is a nature need and appears in many application scenarios. In this paper, we propose the dynamic index calculus algorithm to solve massive discrete logarithm problems fast. We utilize the information generated in the process of solving previous discrete logarithm problems to accelerate the calculation of subsequent discrete logarithm problems. In particular, we utilize factorizations generated in solving previous discrete logarithm problems to expand factor base so that the calculation of subsequent discrete logarithm problems is accelerated. Empirical experiment results indicate that our algorithm can solve massive discrete logarithm problems twice as fast as the state-of-the-art algorithm.