Statistical Model of Correlation Difference and Related-Key Linear Cryptanalysis

The goal of this work is to propose a related-key model for linear cryptanalysis. We start by giving the mean and variance of the difference of sampled correlations of two Boolean functions when using the same sample of inputs to compute both correlations. This result is further extended to determi...

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Autor principal:	Kaisa Nyberg
Formato:	article
Lenguaje:	EN
Publicado:	Ruhr-Universität Bochum 2021
Materias:	block cipher linear cryptanalysis related-key attack statistical model Computer engineering. Computer hardware TK7885-7895
Acceso en línea:	https://doaj.org/article/88fc87ecc6ba463cb165ec33d49fd73c
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id	oai:doaj.org-article:88fc87ecc6ba463cb165ec33d49fd73c
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spelling	oai:doaj.org-article:88fc87ecc6ba463cb165ec33d49fd73c2021-12-03T14:38:29ZStatistical Model of Correlation Difference and Related-Key Linear Cryptanalysis10.46586/tosc.v2021.i4.124-1372519-173Xhttps://doaj.org/article/88fc87ecc6ba463cb165ec33d49fd73c2021-12-01T00:00:00Zhttps://tosc.iacr.org/index.php/ToSC/article/view/9331https://doaj.org/toc/2519-173X The goal of this work is to propose a related-key model for linear cryptanalysis. We start by giving the mean and variance of the difference of sampled correlations of two Boolean functions when using the same sample of inputs to compute both correlations. This result is further extended to determine the mean and variance of the difference of correlations of a pair of Boolean functions taken over a random data sample of fixed size and over a random pair of Boolean functions. We use the properties of the multinomial distribution to achieve these results without independence assumptions. Using multivariate normal approximation of the multinomial distribution we obtain that the distribution of the difference of related-key correlations is approximately normal. This result is then applied to existing related-key cryptanalyses. We obtain more accurate right-key and wrong-key distributions and remove artificial assumptions about independence of sampled correlations. We extend this study to using multiple linear approximations and propose a Χ2-type statistic, which is proven to be Χ2 distributed if the linear approximations are independent. We further examine this statistic for multidimensional linear approximation and discuss why removing the assumption about independence of linear approximations does not work in the related-key setting the same way as in the single-key setting. Kaisa NybergRuhr-Universität Bochumarticleblock cipherlinear cryptanalysisrelated-key attackstatistical modelComputer engineering. Computer hardwareTK7885-7895ENIACR Transactions on Symmetric Cryptology, Vol 2021, Iss 4 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	block cipher linear cryptanalysis related-key attack statistical model Computer engineering. Computer hardware TK7885-7895
spellingShingle	block cipher linear cryptanalysis related-key attack statistical model Computer engineering. Computer hardware TK7885-7895 Kaisa Nyberg Statistical Model of Correlation Difference and Related-Key Linear Cryptanalysis
description	The goal of this work is to propose a related-key model for linear cryptanalysis. We start by giving the mean and variance of the difference of sampled correlations of two Boolean functions when using the same sample of inputs to compute both correlations. This result is further extended to determine the mean and variance of the difference of correlations of a pair of Boolean functions taken over a random data sample of fixed size and over a random pair of Boolean functions. We use the properties of the multinomial distribution to achieve these results without independence assumptions. Using multivariate normal approximation of the multinomial distribution we obtain that the distribution of the difference of related-key correlations is approximately normal. This result is then applied to existing related-key cryptanalyses. We obtain more accurate right-key and wrong-key distributions and remove artificial assumptions about independence of sampled correlations. We extend this study to using multiple linear approximations and propose a Χ2-type statistic, which is proven to be Χ2 distributed if the linear approximations are independent. We further examine this statistic for multidimensional linear approximation and discuss why removing the assumption about independence of linear approximations does not work in the related-key setting the same way as in the single-key setting.
format	article
author	Kaisa Nyberg
author_facet	Kaisa Nyberg
author_sort	Kaisa Nyberg
title	Statistical Model of Correlation Difference and Related-Key Linear Cryptanalysis
title_short	Statistical Model of Correlation Difference and Related-Key Linear Cryptanalysis
title_full	Statistical Model of Correlation Difference and Related-Key Linear Cryptanalysis
title_fullStr	Statistical Model of Correlation Difference and Related-Key Linear Cryptanalysis
title_full_unstemmed	Statistical Model of Correlation Difference and Related-Key Linear Cryptanalysis
title_sort	statistical model of correlation difference and related-key linear cryptanalysis
publisher	Ruhr-Universität Bochum
publishDate	2021
url	https://doaj.org/article/88fc87ecc6ba463cb165ec33d49fd73c
work_keys_str_mv	AT kaisanyberg statisticalmodelofcorrelationdifferenceandrelatedkeylinearcryptanalysis
_version_	1718373160210923520

Statistical Model of Correlation Difference and Related-Key Linear Cryptanalysis

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