On the Construction of Balanced Boolean Functions with Strict Avalanche Criterion and Optimal Algebraic Immunity

Deng TANG  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E102-A   No.9   pp.1321-1325
Publication Date: 2019/09/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E102.A.1321
Type of Manuscript: LETTER
Category: Cryptography and Information Security
Keyword: 
Boolean function,  balancedness,  algebraic immunity,  strict avalanche criterion,  nonlinearity,  

Full Text: FreePDF(248.7KB)


Summary: 
Boolean functions used in the filter model of stream ciphers should have balancedness, large nonlinearity, optimal algebraic immunity and high algebraic degree. Besides, one more criterion called strict avalanche criterion (SAC) can be also considered. During the last fifteen years, much work has been done to construct balanced Boolean functions with optimal algebraic immunity. However, none of them has the SAC property. In this paper, we first present a construction of balanced Boolean functions with SAC property by a slight modification of a known method for constructing Boolean functions with SAC property and consider the cryptographic properties of the constructed functions. Then we propose an infinite class of balanced functions with optimal algebraic immunity and SAC property in odd number of variables. This is the first time that such kind of functions have been constructed. The algebraic degree and nonlinearity of the functions in this class are also determined.