On the number of rotation symmetric functions over

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• 作者：Shaojing  ; Fu^a ;   ; ^{fu_math@qq.com} ;   ; ^{shaojing1984@yahoo.cn} ; Chao  ; Li^b ;   ; ^c ; Longjiang  ; Qu^b ; Deshuai  ; Dong^b
• 关键词：Cryptography ; Rotation symmetry ; Nonlinearity ; Minimal function
• 刊名：Mathematical and Computer Modelling
• 出版年：2012
• 出版时间：January 2012
• 年：2012
• 卷：55
• 期：1-2
• 页码：142-150
• 全文大小：229 K

文摘

Rotation symmetric functions which are invariant under circular translation of indices are widely used as components of different cryptosystems. In this paper, we do some enumeration on rotation symmetric functions over . First, we prove that the construction and enumeration of balanced rotation symmetric functions over are equivalent to solving a specified equation system and enumerating the solutions, and then a lower bound on the number of balanced rotation symmetric functions over is given. Furthermore, we give a formula to count homogeneous rotation symmetric functions which solves the open problem in Li (2008)?.