Annihilators and Algebraic Immunity of Symmetric Boolean Functions

Jie PENG; Haibin KAN

doi:10.1587/transfun.E94.A.1434

Annihilators and Algebraic Immunity of Symmetric Boolean Functions

Jie PENG, Haibin KAN

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In this paper, we deal with the algebraic immunity of the symmetric Boolean functions. The algebraic immunity is a property which measures the resistance against the algebraic attacks on symmetric ciphers. It is well known that the algebraic immunity of the symmetric Boolean functions is completely determined by a narrow class of annihilators with low degree which is denoted by G(n,). We study and determine the weight support of part of these functions. Basing on this, we obtain some relations between the algebraic immunity of a symmetric Boolean function and its simplified value vector. For applications, we put forward an upper bound on the number of the symmetric Boolean functions with algebraic immunity at least d and prove that the algebraic immunity of the symmetric palindromic functions is not high.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E94-A No.6 pp.1434-1440

Publication Date: 2011/06/01

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Online ISSN: 1745-1337

DOI: 10.1587/transfun.E94.A.1434

Type of Manuscript: PAPER

Category: Cryptography and Information Security

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Jie PENG, Haibin KAN, "Annihilators and Algebraic Immunity of Symmetric Boolean Functions" in IEICE TRANSACTIONS on Fundamentals, vol. E94-A, no. 6, pp. 1434-1440, June 2011, doi: 10.1587/transfun.E94.A.1434.
Abstract: In this paper, we deal with the algebraic immunity of the symmetric Boolean functions. The algebraic immunity is a property which measures the resistance against the algebraic attacks on symmetric ciphers. It is well known that the algebraic immunity of the symmetric Boolean functions is completely determined by a narrow class of annihilators with low degree which is denoted by G(n,). We study and determine the weight support of part of these functions. Basing on this, we obtain some relations between the algebraic immunity of a symmetric Boolean function and its simplified value vector. For applications, we put forward an upper bound on the number of the symmetric Boolean functions with algebraic immunity at least d and prove that the algebraic immunity of the symmetric palindromic functions is not high.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E94.A.1434/_p

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@ARTICLE{e94-a_6_1434,
author={Jie PENG, Haibin KAN, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Annihilators and Algebraic Immunity of Symmetric Boolean Functions},
year={2011},
volume={E94-A},
number={6},
pages={1434-1440},
abstract={In this paper, we deal with the algebraic immunity of the symmetric Boolean functions. The algebraic immunity is a property which measures the resistance against the algebraic attacks on symmetric ciphers. It is well known that the algebraic immunity of the symmetric Boolean functions is completely determined by a narrow class of annihilators with low degree which is denoted by G(n,). We study and determine the weight support of part of these functions. Basing on this, we obtain some relations between the algebraic immunity of a symmetric Boolean function and its simplified value vector. For applications, we put forward an upper bound on the number of the symmetric Boolean functions with algebraic immunity at least d and prove that the algebraic immunity of the symmetric palindromic functions is not high.},
keywords={},
doi={10.1587/transfun.E94.A.1434},
ISSN={1745-1337},
month={June},}

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TY - JOUR
TI - Annihilators and Algebraic Immunity of Symmetric Boolean Functions
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1434
EP - 1440
AU - Jie PENG
AU - Haibin KAN
PY - 2011
DO - 10.1587/transfun.E94.A.1434
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E94-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 2011
AB - In this paper, we deal with the algebraic immunity of the symmetric Boolean functions. The algebraic immunity is a property which measures the resistance against the algebraic attacks on symmetric ciphers. It is well known that the algebraic immunity of the symmetric Boolean functions is completely determined by a narrow class of annihilators with low degree which is denoted by G(n,). We study and determine the weight support of part of these functions. Basing on this, we obtain some relations between the algebraic immunity of a symmetric Boolean function and its simplified value vector. For applications, we put forward an upper bound on the number of the symmetric Boolean functions with algebraic immunity at least d and prove that the algebraic immunity of the symmetric palindromic functions is not high.
ER -