Technical history of discrete logarithms in small characteristic finite fields

Joux Antoine; Pierrot Cecile

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Technical history of discrete logarithms in small characteristic finite fields

机译：小特征有限域中离散对数的技术历史

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Due to its use in cryptographic protocols such as the Diffie-Hellman key exchange, the discrete logarithm problem attracted a considerable amount of attention in the past 40 years. In this paper, we summarize the key technical ideas and their evolution for the case of discrete logarithms in small characteristic finite fields. This road leads from the original belief that this problem was hard enough for cryptographic purpose to the current state of the art where the algorithms are so efficient and practical that the problem can no longer be considered for cryptographic use.

机译：由于在诸如Diffie-Hellman密钥交换之类的加密协议中使用，离散对数问题在过去40年中引起了相当大的关注。在本文中，我们总结了在小特征有限域中离散对数情况下的关键技术思想及其发展。这条路源于最初的信念，即该问题对于加密目的而言已经足够困难，而导致当前的现有技术水平（算法是如此高效和实用，以至于不能再将该问题考虑用于加密用途）。

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来源
《Designs, Codes and Crytography》 |2016年第1期|73-85|共13页
作者
Joux Antoine; Pierrot Cecile;
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作者单位

Univ Paris 06, Univ Paris 04, UMR 7606, LIP6, F-75005 Paris, France|UPMC, CryptoExperts, Paris, France|UPMC, Chaire Cryptol Fdn, Paris, France;

Univ Paris 06, Univ Paris 04, UMR 7606, LIP6, F-75005 Paris, France|CNRS, Paris, France|Direct Gen Armement, Paris, France;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Cryptography; Discrete logarithms; Finite fields;

机译：密码学;离散对数;有限域;

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专利

1. ON THE DISCRETE LOGARITHM PROBLEM IN FINITE FIELDS OF FIXED CHARACTERISTIC [J] . Granger Robert, Kleinjung Thorsten, Zumbraegel Jens Transactions of the American Mathematical Society . 2018,第5期

机译：在固定特性有限字段中的离散对数问题
2. COMPUTING DISCRETE LOGARITHMS IN CRYPTOGRAPHICALLY-INTERESTING CHARACTERISTIC-THREE FINITE FIELDS [J] . Adj Gora, Canales-Martinez Isaac, Cruz-Cortes Nareli, Advances in mathematics of communications . 2018,第4期

机译：在密码有趣的特征三个有限字段中计算离散对数
3. Discrete Logarithms in Small Characteristic Finite Fields: a Survey of Recent Advances (Invited Talk) [J] . Antoine Joux LIPIcs : Leibniz International Proceedings in Informatics . 2017,第4期

机译：小特征有限域中的离散对数：近期进展的调查（邀请演讲）
4. Improving the Polynomial time Precomputation of Frobenius Representation Discrete Logarithm Algorithms: Simplified Setting for Small Characteristic Finite Fields [C] . Antoine Joux, Cecile Pierrot International conference on the theory and application of cryptology and information security . 2014

机译：改进Frobenius表示离散对数算法的多项式时间预计算：小特征有限域的简化设置
5. On the discrete logarithm problem in the finite fields and on elliptic curves. [D] . Garefalakis, Theodoulos. 2000

机译：关于有限域和椭圆曲线上的离散对数问题。
6. Fast Parallel Molecular Algorithms for DNA-Based Computation: Solving the Elliptic Curve Discrete Logarithm Problem over GF(2n) [O] . Kenli Li, Shuting Zou, Jin Xv 2008

机译：基于DNA的快速并行分子算法：求解GF（2n）上的椭圆曲线离散对数问题
7. Technical history of discrete logarithms in small characteristic finite fields : The road from subexponential to quasi-polynomial complexity [O] . Joux, Antoine, Pierrot, Cécile 2016

机译：小特征有限域中离散对数的技术历史：从次指数到拟多项式复杂性的道路

Technical history of discrete logarithms in small characteristic finite fields

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