On the group generated by the round functions of translation based ciphers over arbitrary finite fields

R. Aragona; A. Caranti; F. Dalla Volta; M. Sala

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On the group generated by the round functions of translation based ciphers over arbitrary finite fields

机译：关于任意有限域上基于平移密码的舍入函数产生的群

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摘要

We define a translation based cipher over an arbitrary finite field, and study the permutation group generated by the round functions of such a cipher. We show that under certain cryptographic assumptions this group is primitive. Moreover, a minor strengthening of our assumptions allows us to prove that such a group is the symmetric or the alternating group; this improves upon a previous result for the case of characteristic two.

机译：我们在任意有限域上定义基于平移的密码，并研究由该密码的舍入函数生成的置换组。我们证明，在某些密码学假设下，该组是原始的。此外，我们的假设稍有加强，就可以证明这一组是对称组或交替组；对于特征二的情况，这改进了先前的结果。

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来源
《Finite fields and their applications》 |2014年第1期|293-305|共13页
作者
R. Aragona; A. Caranti; F. Dalla Volta; M. Sala;
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作者单位

Department of Mathematics, University of Trento, Via Sommarive 14,38123 Trento, Italy;

Department of Mathematics, University of Trento, Via Sommarive 14,38123 Trento, Italy;

Department of Mathematics and Applications, University of Milano-Bicocca, Via R. Cozzi 53,20126 Milano, Italy;

Department of Mathematics, University of Trento, Via Sommarive 14,38123 Trento, Italy;

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正文语种 eng
中图分类
关键词
Cryptosystems; Groups generated by round functions; Primitive groups; O'Nan-Scott; Wreath products; Affine groups;

机译：密码系统;圆形函数生成的组;原始群体;奥南·斯科特;花环产品;仿射组;

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1. The group generated by the round functions of a GOST-like cipher [J] . Aragona R., Caranti A., Sala M. Annali di matematica pura ed applicata . 2017,第1期

机译：由GOST-LICK密码的圆形功能生成的组
2. An application of the O'Nan-Scott theorem to the group generated by the round functions of an AES-like cipher [J] . A. Caranti, Francesca Dalla Volta, M. Sala Designs, Codes and Crytography . 2009,第3期

机译：O'Nan-Scott定理在类AES密码的舍入函数生成的组中的应用
3. An application of the O’Nan-Scott theorem to the group generated by the round functions of an AES-like cipher [J] . A. Caranti, Francesca Dalla Volta, M. Sala Designs, Codes and Cryptography . 2009,第3期

机译：O’Nan-Scott定理在类AES密码的舍入函数生成的组上的应用
4. Power Analysis Based Reverse Engineering on the Secret Round Function of Block Ciphers [C] . Ming Tang, Zhenlong Qiu, Weijie Li, International Conference on Data and Knowledge Engineering . 2012

机译：基于功率分析基于封闭晶体秘密圆形功能的逆向工程
5. Expanding the waverider design space using arbitrary generating flowfields. [D] . Ferguson, Frederick. 1993

机译：使用任意生成的流场来扩展Waverider设计空间。
6. A Finite Field Method for Calculating Molecular Polarizability Tensors for Arbitrary Multipole Rank [O] . Dennis M. Elking, Lalith Perera, Robert Duke, -1

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7. 3 ON THE GROUP GENERATED BY THE ROUND FUNCTIONS OF TRANSLATION BASED CIPHERS OVER ARBITRARY FINITE FIELDS [O] . R. Aragona, A. Caranti, F. Dalla Volta, 2016

机译：3关于任意有限域上基于翻译的密码子的圆函数所产生的群
8. Determining the Instantaneous Axis of Translation from Optic Flow Generated by Arbitrary Sensor Motion [R] . Rieger, J. H., Lawton, D. T. 1983

机译：从任意传感器运动产生的光流确定平移瞬时轴

On the group generated by the round functions of translation based ciphers over arbitrary finite fields

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