Abstract
Vectorial functions (i.e. mappings from F 2 n into F 2 m, also called S-boxes) can be used in pseudo-random generators with multiple outputs. The notion of maximum correlation of these S-boxes to linear functions, introduced by Zhang and Chan, plays a central role in the resistance of the resulting stream ciphers to correlation attacks. It can be related to a notion of “unrestricted nonlinearity”. We obtain a new lower bound on the overall maximum correlation to linear functions of vectorial functions which results in an upper bound on the unrestricted nonlinearity. We compare it with the known upper bounds on the nonlinearity (which are also valid for the unrestricted nonlinearity of balanced functions). We study its tightness and we exhibit a class of balanced functions whose nonlinearity and unrestricted nonlinearity are high relatively to the upper-bounds.
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Carlet, C., Prouff, E. (2004). On a New Notion of Nonlinearity Relevant to Multi-output Pseudo-random Generators. In: Matsui, M., Zuccherato, R.J. (eds) Selected Areas in Cryptography. SAC 2003. Lecture Notes in Computer Science, vol 3006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24654-1_21
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DOI: https://doi.org/10.1007/978-3-540-24654-1_21
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