Constructing Higher Nonlinear Odd-Variable RSBFs With Optimal AI and Almost Optimal FAI

Yindong Chen; Limin Lin; Lumin Liao; Jie Ruan; Fei Guo; Weihong Cai

doi:10.1109/ACCESS.2019.2939296

IEEE Access (Jan 2019)

Constructing Higher Nonlinear Odd-Variable RSBFs With Optimal AI and Almost Optimal FAI

Yindong Chen,
Limin Lin,
Lumin Liao,
Jie Ruan,
Fei Guo,
Weihong Cai

Affiliations

Yindong Chen: ORCiD; Department of Computer Science, Shantou University, Shantou, China
Limin Lin: Department of Computer Science, Shantou University, Shantou, China
Lumin Liao: Department of Computer Science, Shantou University, Shantou, China
Jie Ruan: Department of Computer Science, Shantou University, Shantou, China
Fei Guo: 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.2019.2939296
Journal volume & issue: Vol. 7
pp. 133335 – 133341

Abstract

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Rotation symmetric Boolean functions (RSBFs) are nowadays studied a lot because of its easy operations and good performance in cryptosystem. This paper constructs a new class of odd-variable RSBFs with optimal algebraic immunity (AI). The nonlinearity of the new function, $2^{n-1}-\binom {n-1}{k}+2^{k-4}(k-3)(k-2)$ , is the highest among all existing RSBFs with optimal AI and known nonlinearity, and its algebraic degree is also almost highest. Besides, the class of functions have almost optimal fast algebraic immunity (FAI) at least for $n < 17$ , which is actually the highest possible value for the designated number of variables.

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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