Geodesic
Matrix formula for the spectrum of output distribution of block cipher scheme and statistical criterion based on this formula
Prikladnaâ diskretnaâ matematika, no. 2 (2016), pp. 33-48.

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Arbitrary block iterative cipher scheme with random independent binary input and output vectors is considered. A matrix formula for the spectrum of the scheme output distribution is obtained by means of the pseudo-Boolean linear representation of the iterative vector-function. Based on this formula, a statistical criterion of the hypothesis testing that binary vectors are obtained as an output of the scheme against the hypothesis of their uniform distribution is given. Asymptotic type I and type II errors are calculated. An experimental comparison of the criterion with the “Bookstack” test (and its proposed modification) is done during the construction of a distinguishing attack on the mini-models of the block cipher PRESENT (with block size 12 bits and the number of rounds $R\le10$).
Keywords: binary vector-function, block iterative cipher scheme, spectrum of distribution, distinguishing attack, the “Bookstack” test. 
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O. V. Denisov; R. A. Bylina. Matrix formula for the spectrum of output distribution of block cipher scheme and statistical criterion based on this formula. Prikladnaâ diskretnaâ matematika, no. 2 (2016), pp. 33-48. http://geodesic.mathdoc.fr/item/PDM_2016_2_a2/

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