New Construction of Even-variable Rotation Symmetric Boolean Functions with Optimum Algebraic Immunity

Chen, Yindong; Xiang, Hongyan; Zhang, Yanan

doi:10.14257/ijsia.2014.8.1.29

Cited by 4 publications

(3 citation statements)

References 18 publications

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“…−2 when n is even. Late in 2014, Chen et al [21] proposed a construction of even-variable RSBFs with optimal algebraic immunity based on Su's method, and the nonlinearity is…”

Section: +2mentioning

confidence: 99%

Constructing Odd-Variable Rotation Symmetric Boolean Functions With Optimal AI and Higher Nonlinearity

et al. 2019

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As a part of the field of cryptography, rotation symmetric Boolean functions have rich cryptographic significance. In this paper, based on the knowledge of integer compositions, we present a new construction of odd-variable rotation symmetric Boolean functions with optimal algebraic immunity. The nonlinearity of the new rotation symmetric Boolean functions is much better than that of the previously ones with optimal algebraic immunity. And the algebraic degree of the function class is also much high. Moreover, it is shown that our new functions have almost optimal fast algebraic immunity within the range of variable numbers that ordinary computers can calculate.

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“…−2 when n is even. Late in 2014, Chen et al [21] proposed a construction of even-variable RSBFs with optimal algebraic immunity based on Su's method, and the nonlinearity is…”

Section: +2mentioning

confidence: 99%

Constructing Odd-Variable Rotation Symmetric Boolean Functions With Optimal AI and Higher Nonlinearity

et al. 2019

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“…The drawback of the construction is the high complexity of the computation for the value of f(x). Chen [12] presented a new category of even-variable rotation symmetric Boolean functions with optimum AI, in which there are altogether 4 3…”

Section:  mentioning

confidence: 99%

A Proof of Constructions for Balanced Boolean Function with Optimum Algebraic Immunity

Chen

Tian²,

Zhang³

2015

IJSIA

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“…, both of which are later improved in [32]- [34]. However, the constructions of [31]- [33] totally ignore the fast algebraic attack.…”

Section: Introductionmentioning

confidence: 99%

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

Chen

Liao

et al. 2019

IEEE Access

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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 − 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.

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New Construction of Even-variable Rotation Symmetric Boolean Functions with Optimum Algebraic Immunity

Abstract: Abstract

Cited by 4 publications

References 18 publications

Constructing Odd-Variable Rotation Symmetric Boolean Functions With Optimal AI and Higher Nonlinearity

Constructing Odd-Variable Rotation Symmetric Boolean Functions With Optimal AI and Higher Nonlinearity

A Proof of Constructions for Balanced Boolean Function with Optimum Algebraic Immunity

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

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