Asymptotic Distributions for S-Box Heterogeneous Differential Probabilities

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dc.contributor.authorYakovliev, S. V.
dc.contributor.authorBakhtigozin, V. Yu.
dc.date.accessioned2020-10-12T12:31:11Z
dc.date.available2020-10-12T12:31:11Z
dc.date.issued2019
dc.description.abstractenWe study asymptotic behavior of heterogeneous differentials, i.e. pairs of S-box input and output differences when «differences» are calculated with respect to non-equal Abelian operations. We prove that probabilities of any fixed (+, ⊕)-differential asymptotically follow Poisson distribution with parameter 1 or ½ dependent on the order of input difference in corresponding group, when S-box is taken randomly and uniformly from a set of all possible n-bit bijective mappings. These results generalize and complete the Hawkes and O‘Connor research about asymptotic distribution of homogeneous differentials. Besides, we examine the convergence of exact differential probabilities to their asymptotic estimations. Experimental evaluations show that discrepancy is low even for small size n of S-box; for n ≥ 6 it is less than 5 · 10^-4.uk
dc.format.pagerangePp. 37-41uk
dc.identifier.citationYakovliev, S. V. Asymptotic Distributions for S-Box Heterogeneous Differential Probabilities / S. V. Yakovliev, V. Yu. Bakhtigozin // Theoretical and Applied Cybersecurity : scientific journal. – 2019. – Vol. 1, Iss. 1. – Pp. 37–41. – Bibliogr.: 14 ref.uk
dc.identifier.doihttps://doi.org/10.20535/tacs.2664-29132019.1.169029
dc.identifier.urihttps://ela.kpi.ua/handle/123456789/36721
dc.language.isoenuk
dc.publisherIgor Sikorsky Kyiv Polytechnic Instituteuk
dc.publisher.placeKyivuk
dc.sourceTheoretical and Applied Cybersecurity : scientific journal, 2019, Vol. 1, No. 1uk
dc.subjectdifferential cryptanalysisuk
dc.subjectS-Boxuk
dc.subjectheterogeneous differentialuk
dc.subject.udc004.056.55:519.2uk
dc.titleAsymptotic Distributions for S-Box Heterogeneous Differential Probabilitiesuk
dc.typeArticleuk

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Theoretical and Applied Cybersecurity: scientific journal, Vol. 1, No. 1