Constructing Rotation Symmetric Boolean Functions with Maximum Algebraic Immunity on an Odd Number of Variables

Jie PENG; Haibin KAN

doi:10.1587/transfun.E95.A.1056

Constructing Rotation Symmetric Boolean Functions with Maximum Algebraic Immunity on an Odd Number of Variables

Jie PENG, Haibin KAN

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It is well known that Boolean functions used in stream and block ciphers should have high algebraic immunity to resist algebraic attacks. Up to now, there have been many constructions of Boolean functions achieving the maximum algebraic immunity. In this paper, we present several constructions of rotation symmetric Boolean functions with maximum algebraic immunity on an odd number of variables which are not symmetric, via a study of invertible cyclic matrices over the binary field. In particular, we generalize the existing results and introduce a new method to construct all the rotation symmetric Boolean functions that differ from the majority function on two orbits. Moreover, we prove that their nonlinearities are upper bounded by .

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E95-A No.6 pp.1056-1064

Publication Date: 2012/06/01

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Online ISSN: 1745-1337

DOI: 10.1587/transfun.E95.A.1056

Type of Manuscript: PAPER

Category: Cryptography and Information Security

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Jie PENG, Haibin KAN, "Constructing Rotation Symmetric Boolean Functions with Maximum Algebraic Immunity on an Odd Number of Variables" in IEICE TRANSACTIONS on Fundamentals, vol. E95-A, no. 6, pp. 1056-1064, June 2012, doi: 10.1587/transfun.E95.A.1056.
Abstract: It is well known that Boolean functions used in stream and block ciphers should have high algebraic immunity to resist algebraic attacks. Up to now, there have been many constructions of Boolean functions achieving the maximum algebraic immunity. In this paper, we present several constructions of rotation symmetric Boolean functions with maximum algebraic immunity on an odd number of variables which are not symmetric, via a study of invertible cyclic matrices over the binary field. In particular, we generalize the existing results and introduce a new method to construct all the rotation symmetric Boolean functions that differ from the majority function on two orbits. Moreover, we prove that their nonlinearities are upper bounded by .
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E95.A.1056/_p

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@ARTICLE{e95-a_6_1056,
author={Jie PENG, Haibin KAN, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Constructing Rotation Symmetric Boolean Functions with Maximum Algebraic Immunity on an Odd Number of Variables},
year={2012},
volume={E95-A},
number={6},
pages={1056-1064},
abstract={It is well known that Boolean functions used in stream and block ciphers should have high algebraic immunity to resist algebraic attacks. Up to now, there have been many constructions of Boolean functions achieving the maximum algebraic immunity. In this paper, we present several constructions of rotation symmetric Boolean functions with maximum algebraic immunity on an odd number of variables which are not symmetric, via a study of invertible cyclic matrices over the binary field. In particular, we generalize the existing results and introduce a new method to construct all the rotation symmetric Boolean functions that differ from the majority function on two orbits. Moreover, we prove that their nonlinearities are upper bounded by .},
keywords={},
doi={10.1587/transfun.E95.A.1056},
ISSN={1745-1337},
month={June},}

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TY - JOUR
TI - Constructing Rotation Symmetric Boolean Functions with Maximum Algebraic Immunity on an Odd Number of Variables
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1056
EP - 1064
AU - Jie PENG
AU - Haibin KAN
PY - 2012
DO - 10.1587/transfun.E95.A.1056
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E95-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 2012
AB - It is well known that Boolean functions used in stream and block ciphers should have high algebraic immunity to resist algebraic attacks. Up to now, there have been many constructions of Boolean functions achieving the maximum algebraic immunity. In this paper, we present several constructions of rotation symmetric Boolean functions with maximum algebraic immunity on an odd number of variables which are not symmetric, via a study of invertible cyclic matrices over the binary field. In particular, we generalize the existing results and introduce a new method to construct all the rotation symmetric Boolean functions that differ from the majority function on two orbits. Moreover, we prove that their nonlinearities are upper bounded by .
ER -