Analysis of the number of even-variable boolean functions with maximum algebraic immunity

Algebraic Immunity has been considered as one of significant properties for Boolean functions, and possessing maximum algebraic immunity (MAI) is a necessary criteria for Boolean functions used in stream ciphers against algebraic attacks. However, for a given number of variables, the accurate number...

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Published in:CIICT 2012 : Symposium on ICT and Energy Efficiency and Workshop on Information Theory and Security : 4-5 July 2012 pp. 93 - 97
Main Authors: Xiong, Xiaowen, Ma, Chi, Yang, Xia
Format: Conference Proceeding
Language:English
Published: Stevenage, UK IET 2012
The Institution of Engineering & Technology
Subjects:
Algebra
Cryptography
Cryptography theory
Boolean functions
MAI
maximum algebraic immunity
algebraic attacks
cryptography
even-variable Boolean function analysis
stream ciphers
Boolean function enumeration
ISBN:9781849195478, 1849195471
Online Access:Get full text
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Summary:Algebraic Immunity has been considered as one of significant properties for Boolean functions, and possessing maximum algebraic immunity (MAI) is a necessary criteria for Boolean functions used in stream ciphers against algebraic attacks. However, for a given number of variables, the accurate number of Boolean functions with MAI is not known, and the best known bound on the number also seems weak. In this paper, we investigate the enumeration of Boolean functions with MAI, and provide a new lower bound on the number of even-variable Boolean functions with MAI, this lower bound is better than the previous ones.
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ISBN:9781849195478
1849195471
DOI:10.1049/cp.2012.1869