Cryptology ePrint Archive: Report 2013/673

Traps to the BGJT-Algorithm for Discrete Logarithms

Qi Cheng and Daqing Wan and Jincheng Zhuang

Abstract: In the recent breakthrough paper by Barbulescu, Gaudry, Joux and Thom{\'e}, a quasi-polynomial time algorithm (QPA) is proposed for the discrete logarithm problem over finite fields of small characteristic. The time complexity analysis of the algorithm is based on several heuristics presented in their paper. We show that some of the heuristics are problematic in their original forms, in particular, when the field is not a Kummer extension. We believe that the basic idea behind the new approach should still work, and propose a fix to the algorithm in non-Kummer cases, without altering the quasi-polynomial time complexity. The modified algorithm is also heuristic. Further study is required in order to fully understand the effectiveness of the new approach.

Category / Keywords: public-key cryptography / discrete logarithm problem

Date: received 20 Oct 2013

Contact author: qcheng at cs ou edu

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Version: 20131024:084212 (All versions of this report)

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