The Exact Fast Algebraic Immunity of Two Subclasses of the Majority Function

Deng TANG  Rong LUO  Xiaoni DU  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E99-A   No.11   pp.2084-2088
Publication Date: 2016/11/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E99.A.2084
Type of Manuscript: LETTER
Category: Cryptography and Information Security
stream cipher,  Boolean function,  algebraic attack,  fast algebraic immunity,  

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To resist algebraic and fast algebraic attacks, Boolean functions used in stream ciphers should have optimal algebraic immunity and good fast algebraic immunity. One challenge of cryptographic Boolean functions is to determine their ability to resist fast algebraic attacks, which can be measured by their fast algebraic immunities. In this letter, we determine the exact values of fast algebraic immunity of the majority function of 2m and 2m+1 variables. This is the first time that the exact values of the fast algebraic immunity of an infinite class of symmetric Boolean functions with optimal algebraic immunity are determined.