On the Nonlinearity and Affine Equivalence Classes of C-F Functions
Summary :
Since 2008, three different classes of Boolean functions with optimal algebraic immunity have been proposed by Carlet and Feng [2], Wang et al.[8] and Chen et al.[3]. We call them C-F functions, W-P-K-X functions and C-T-Q functions for short. In this paper, we propose three affine equivalent classes of Boolean functions containing C-F functions, W-P-K-X functions and C-T-Q functions as a subclass, respectively. Based on the affine equivalence relation, we construct more classes of Boolean functions with optimal algebraic immunity. Moreover, we deduce a new lower bound on the nonlinearity of C-F functions, which is better than all the known ones.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E99-A No.6 pp.1251-1254
- Publication Date
- 2016/06/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E99.A.1251
- Type of Manuscript
- LETTER
- Category
- Cryptography and Information Security
Authors
Lei SUN
Nankai University
Fangwei FU
Nankai University
Xuang GUANG
Nankai University
Keyword
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Lei SUN, Fangwei FU, Xuang GUANG, "On the Nonlinearity and Affine Equivalence Classes of C-F Functions" in IEICE TRANSACTIONS on Fundamentals,
vol. E99-A, no. 6, pp. 1251-1254, June 2016, doi: 10.1587/transfun.E99.A.1251.
Abstract: Since 2008, three different classes of Boolean functions with optimal algebraic immunity have been proposed by Carlet and Feng [2], Wang et al.[8] and Chen et al.[3]. We call them C-F functions, W-P-K-X functions and C-T-Q functions for short. In this paper, we propose three affine equivalent classes of Boolean functions containing C-F functions, W-P-K-X functions and C-T-Q functions as a subclass, respectively. Based on the affine equivalence relation, we construct more classes of Boolean functions with optimal algebraic immunity. Moreover, we deduce a new lower bound on the nonlinearity of C-F functions, which is better than all the known ones.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E99.A.1251/_p
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@ARTICLE{e99-a_6_1251,
author={Lei SUN, Fangwei FU, Xuang GUANG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On the Nonlinearity and Affine Equivalence Classes of C-F Functions},
year={2016},
volume={E99-A},
number={6},
pages={1251-1254},
abstract={Since 2008, three different classes of Boolean functions with optimal algebraic immunity have been proposed by Carlet and Feng [2], Wang et al.[8] and Chen et al.[3]. We call them C-F functions, W-P-K-X functions and C-T-Q functions for short. In this paper, we propose three affine equivalent classes of Boolean functions containing C-F functions, W-P-K-X functions and C-T-Q functions as a subclass, respectively. Based on the affine equivalence relation, we construct more classes of Boolean functions with optimal algebraic immunity. Moreover, we deduce a new lower bound on the nonlinearity of C-F functions, which is better than all the known ones.},
keywords={},
doi={10.1587/transfun.E99.A.1251},
ISSN={1745-1337},
month={June},}
Copy
TY - JOUR
TI - On the Nonlinearity and Affine Equivalence Classes of C-F Functions
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1251
EP - 1254
AU - Lei SUN
AU - Fangwei FU
AU - Xuang GUANG
PY - 2016
DO - 10.1587/transfun.E99.A.1251
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E99-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 2016
AB - Since 2008, three different classes of Boolean functions with optimal algebraic immunity have been proposed by Carlet and Feng [2], Wang et al.[8] and Chen et al.[3]. We call them C-F functions, W-P-K-X functions and C-T-Q functions for short. In this paper, we propose three affine equivalent classes of Boolean functions containing C-F functions, W-P-K-X functions and C-T-Q functions as a subclass, respectively. Based on the affine equivalence relation, we construct more classes of Boolean functions with optimal algebraic immunity. Moreover, we deduce a new lower bound on the nonlinearity of C-F functions, which is better than all the known ones.
ER -
English
