Enumeration of Homogeneous Rotation Symmetric Functions over Fp

Authors:
Shaojing Fu;Chao Li;Bing Sun
Affiliations:
Department of Mathematics and System Science Science College, National University of Defence Technology, Hunan, China 410073;Department of Mathematics and System Science Science College, National University of Defence Technology, Hunan, China 410073 and National Mobile Communications Research Laboratory, Southeast Unive ...;Department of Mathematics and System Science Science College, National University of Defence Technology, Hunan, China 410073
Venue:
CANS '08 Proceedings of the 7th International Conference on Cryptology and Network Security
Year:
2008

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Abstract

Rotation symmetric functions have been used as components of different cryptosystems. Functions in this class are invariant under circular translation of indices. In this paper, we will do some enumeration on homogeneous rotation symmetric functions over F p . A formula for counting homogeneous rotation symmetric functions over F p is presented when gcd(n ,d ) is a prime power, where n is the number of input variables and d is the algebraic degree of the function, which demonstrates that we solved one of the problems in [7].