Characterisations of extended resiliency and extended immunity of s-boxes

Authors:
Josef Pieprzyk;Xian-Mo Zhang;Jovan Dj. Golić
Affiliations:
Centre for Advanced Computing – Algorithms and Cryptography, Department of Computing, Macquarie University, Sydney, Australia;Centre for Advanced Computing – Algorithms and Cryptography, Department of Computing, Macquarie University, Sydney, Australia;Telecom Italia Lab, Telecom Italia, Turin, Italy
Venue:
ICISC'05 Proceedings of the 8th international conference on Information Security and Cryptology
Year:
2005

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Abstract

New criteria of extended resiliency and extended immunity of vectorial Boolean functions, such as S-boxes for stream or block ciphers, were recently introduced. They are related to a divide-and-conquer approach to algebraic attacks by conditional or unconditional equations. Classical resiliency turns out to be a special case of extended resiliency and as such requires more conditions to be satisfied. In particular, the algebraic degrees of classically resilient S-boxes are restricted to lower values. In this paper, extended immunity and extended resiliency of S-boxes are studied and many characterisations and properties of such S-boxes are established. The new criteria are shown to be necessary and sufficient for resistance against the divide-and-conquer algebraic attacks by conditional or unconditional equations.