A Lower Bound of Fast Algebraic Immunity of a Class of 1-Resilient Boolean Functions

Yindong Chen; Liu Zhang; Jianlong Xu; Weihong Cai

doi:10.1109/ACCESS.2019.2926765

IEEE Access (Jan 2019)

A Lower Bound of Fast Algebraic Immunity of a Class of 1-Resilient Boolean Functions

Yindong Chen,
Liu Zhang,
Jianlong Xu,
Weihong Cai

Affiliations

Yindong Chen: ORCiD; Department of Computer Science, Shantou University, Shantou, China
Liu Zhang: Department of Computer Science, Shantou University, Shantou, China
Jianlong Xu: ORCiD; Department of Computer Science, Shantou University, Shantou, China
Weihong Cai: Department of Computer Science, Shantou University, Shantou, China

DOI: https://doi.org/10.1109/ACCESS.2019.2926765
Journal volume & issue: Vol. 7
pp. 90145 – 90151

Abstract

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Boolean functions should possess high fast algebraic immunity when used in stream ciphers in order to stand up to fast algebraic attacks. However, in previous research, the fast algebraic immunity of Boolean functions was usually calculated by the computer. In 2017, Tang, Carlet, and Tang first mathematically proved that every function belonging to a class of 1-resilient Boolean functions has the fast algebraic immunity no less than n - 6. Inspired by the Tang's method, we also demonstrate that the fast algebraic immunity of another class of the 1-resilient Boolean functions is no less than n - 6. Meanwhile, we also prove some combinator facts originated from the Tu-Deng Conjecture.

Published in IEEE Access

ISSN: 2169-3536 (Online)
Publisher: IEEE
Country of publisher: United States
LCC subjects: Technology: Electrical engineering. Electronics. Nuclear engineering
Website: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639

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