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Analysis of the algebraic side channel attack

机译：代数侧通道攻击分析

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摘要

At CHES 2009, Renauld, Standaert and Veyrat-Charvillon introduced a new kind of attack called algebraic side-channel attacks (ASCA). They showed that side-channel information leads to effective algebraic attacks. These results are mostly experiments since strongly based on the use of a SAT solver. This article presents a theoretical study to explain and to characterize the algebraic phase of these attacks. We study more general algebraic attacks based on Grobner methods. We show that the complexity of the Grobner basis computations in these attacks depends on a new notion of algebraic immunity defined in this paper, and on the distribution of the leakage information of the cryptosystem. We also study two examples of common leakage models: the Hamming weight and the Hamming distance models. For instance, the study in the case of the Hamming weight model gives that the probability of obtaining at least 64 (resp. 130) linear relations is about 50% for the substitution layer of PRESENT (resp. AES). Moreover if the S-boxes are replaced by functions maximizing the new algebraic immunity criterion then the algebraic attacks (Grobner and SAT) are intractable. From this theoretical study, we also deduce an invariant which can be easily computed from a given S-box and provides a sufficient condition of weakness under an ASCA. This new invariant does not require any sophisticated algebraic techniques to be defined and computed. Thus, for cryptographic engineers without an advanced knowledge in algebra (e.g. Grobner basis techniques), this invariant may represent an interesting tool for rejecting weak S-boxes.
机译：在2009年CHES上，Renauld，Standaert和Veyrat-Charvillon提出了一种新型的攻击，称为代数边通道攻击（ASCA）。他们表明，旁通道信息会导致有效的代数攻击。这些结果主要是实验，因为强烈基于SAT求解器的使用。本文提出了一项理论研究，以解释和表征这些攻击的代数阶段。我们研究基于Grobner方法的更一般的代数攻击。我们表明，在这些攻击中，Grobner基计算的复杂性取决于本文定义的新的代数免疫概念，并取决于密码系统泄漏信息的分布。我们还研究了两个常见的泄漏模型示例：汉明权重和汉明距离模型。例如，对汉明权重模型的研究表明，对于PRESENT（resp。AES）的替换层，获得至少64（resp。130）线性关系的可能性约为50％。而且，如果用最大化新的代数免疫力准则的函数代替S-box，那么代数攻击（Grobner和SAT）就很棘手。从这一理论研究中，我们还推导出了可以很容易地从给定的S盒中计算出的不变量，并提供了ASCA下的弱点的充分条件。这个新的不变式不需要定义和计算任何复杂的代数技术。因此，对于在代数方面没有高级知识的加密工程师（例如Grobner基础技术），此不变式可能是拒绝弱S盒的有趣工具。

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  • 来源
    《Journal of cryptographic engineering》 |2012年第1期|p.45-62|共18页
  • 作者

    Claude Carlet; Jean-Charles Faugere; Christopher Goyet; Guenael Renault;

  • 作者单位

    Universite Paris 8, UMR LAGA, MTU team, 2, rue de la liberte, 93526 Saint-Denis Cedex 02, France;

    UPMC, Universite Paris 6, LIP6, INRIA, Centre Paris-Rocquencourt, PolSys Project-Team, CNRS, UMR 7606, LIP6,4, place Jussieu, 75252 Paris Cedex 5, France;

    UPMC, Universite Paris 6, LIP6, INRIA, Centre Paris-Rocquencourt, PolSys Project-Team, CNRS, UMR 7606, LIP6,4, place Jussieu, 75252 Paris Cedex 5, France,Thales Communications and Security, 160 Boulevard de Valmy,92700 Colombes, France;

    UPMC, Universite Paris 6, LIP6, INRIA, Centre Paris-Rocquencourt, PolSys Project-Team, CNRS, UMR 7606, LIP6,4, place Jussieu, 75252 Paris Cedex 5, France;

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  • 正文语种 eng
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  • 关键词

    algebraic side channel attack; grobner basis; algebraic immunity; block cipher;

    机译：代数侧通道攻击;基础知识;代数免疫分组密码;

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