Abstract
Structural and Statistical Analysis of Multidimensional Linear Approximations of Random Functions and Permutations
Highlights
The new models given in this paper are realistic, accurate and easy to use
The affine linear cryptanalysis was proposed to allow removing trivial approximations and, at the same time, admitting a solid statistical model. We identify another type of multidimensional linear approximation, called Davies-Meyer approximation, which has similar advantages, and present full statistical models for both the affine and the Davies-Meyer type of multidimensional linear approximations
In this paper we presented a model which captures the statistical behaviour of the capacity of multidimensional linear approximations computed for a permutation and a sample of plaintext, when the permutation and the sample of distinct
Summary
The new models given in this paper are realistic, accurate and easy to use They are backed up by standard statistical tools such as Pearson’s χ2 test and finite population correction and demonstrated to work accurately using practical examples. A) Modelling linear key-recovery attacks: Linear cryptanalysis is a statistical method used for distinguishing a block cipher from a random permutation and can be extended to keyrecovery attacks of practical block ciphers It makes use of the nonrandom behaviour of certain linear approximations of the cipher. The wrong-key hypothesis in linear cryptanalysis, as well as in other statistical attacks, is based on a statistical model of the family of random permutations, when the target cipher is a block cipher, or a model of the family of random functions in some other cases such as stream ciphers. The right-key hypothesis is derived from a statistical model that captures the probability distributions and their parameters of the linear approximations in the case of the cipher
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