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Construction and Counting of 1-Resilient Rotation Symmetric Boolean Functions on pq Variables
Jiao DU Qiaoyan WEN Jie ZHANG Shanqi PANG
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2013/07/01
Online ISSN: 1745-1337
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Cryptography and Information Security
cryptology, rotation symmetric, characteristic matrix, correlation immune, resilient function,
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In this letter, a property of the characteristic matrix of the Rotation Symmetric Boolean Functions (RSBFs) is characterized, and a sufficient and necessary condition for RSBFs being 1st correlation-immune (1-CI for simplicity) is obtained. This property is applied to construct resilient RSBFs of order 1 (1-resilient for simplicity) on pq variables, where p and q are both prime consistently in this letter. The results show that construction and counting of 1-resilient RSBFs on pq variables are equivalent to solving an equation system and counting the solutions. At last, the counting of all 1-resilient RSBFs on pq variables is also proposed.