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A New Test Statistic for Key Recovery Attacks Using Multiple Linear Approximations

  • Subhabrata Samajder
  • Palash Sarkar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10311)

Abstract

The log-likelihood ratio (LLR) and the chi-squared distribution based test statistics have been proposed in the literature for performing statistical analysis of key recovery attacks on block ciphers. A limitation of the LLR test statistic is that its application requires the full knowledge of the corresponding distribution. Previous work using the chi-squared approach required approximating the distribution of the relevant test statistic by chi-squared and normal distributions. Problematic issues regarding such approximations have been reported in the literature. Perhaps more importantly, both the LLR and the chi-squared based methods are applicable only if the success probability \(P_S\) is greater than 0.5. On the other hand, an attack with success probability less than 0.5 is also of considerable interest. This work proposes a new test statistic for key recovery attacks which has the following features. Its application does not require the full knowledge of the underlying distribution; it is possible to carry out an analysis using this test statistic without using any approximations; the method applies for all values of the success probability. The statistical analysis of the new test statistic follows the hypothesis testing framework and uses Hoeffding’s inequalities to bound the probabilities of Type-I and Type-II errors.

Keywords

Multiple linear cryptanalyis LLR statistic Chi-squared statistic Hoeffding inequality 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Applied Statistics UnitIndian Statistical InstituteKolkataIndia

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