IEICE TRANSACTIONS on Fundamentals
Constructing Even-Variable Symmetric Boolean Functions with High Algebraic Immunity
Summary :
In this paper, we explicitly construct a large class of symmetric Boolean functions on 2k variables with algebraic immunity not less than d, where integer k is given arbitrarily and d is a given suffix of k in binary representation. If let d = k, our constructed functions achieve the maximum algebraic immunity. Remarkably, 2⌊ log2k ⌋ + 2 symmetric Boolean functions on 2k variables with maximum algebraic immunity are constructed, which are much more than the previous constructions. Based on our construction, a lower bound of symmetric Boolean functions with algebraic immunity not less than d is derived, which is 2⌊ log2d ⌋ + 2(k-d+1). As far as we know, this is the first lower bound of this kind.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E94-A No.1 pp.362-366
- Publication Date
- 2011/01/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E94.A.362
- Type of Manuscript
- PAPER
- Category
- Cryptography and Information Security
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Keyword
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Yuan LI, Hui WANG, Haibin KAN, "Constructing Even-Variable Symmetric Boolean Functions with High Algebraic Immunity" in IEICE TRANSACTIONS on Fundamentals,
vol. E94-A, no. 1, pp. 362-366, January 2011, doi: 10.1587/transfun.E94.A.362.
Abstract: In this paper, we explicitly construct a large class of symmetric Boolean functions on 2k variables with algebraic immunity not less than d, where integer k is given arbitrarily and d is a given suffix of k in binary representation. If let d = k, our constructed functions achieve the maximum algebraic immunity. Remarkably, 2⌊ log2k ⌋ + 2 symmetric Boolean functions on 2k variables with maximum algebraic immunity are constructed, which are much more than the previous constructions. Based on our construction, a lower bound of symmetric Boolean functions with algebraic immunity not less than d is derived, which is 2⌊ log2d ⌋ + 2(k-d+1). As far as we know, this is the first lower bound of this kind.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E94.A.362/_p
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@ARTICLE{e94-a_1_362,
author={Yuan LI, Hui WANG, Haibin KAN, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Constructing Even-Variable Symmetric Boolean Functions with High Algebraic Immunity},
year={2011},
volume={E94-A},
number={1},
pages={362-366},
abstract={In this paper, we explicitly construct a large class of symmetric Boolean functions on 2k variables with algebraic immunity not less than d, where integer k is given arbitrarily and d is a given suffix of k in binary representation. If let d = k, our constructed functions achieve the maximum algebraic immunity. Remarkably, 2⌊ log2k ⌋ + 2 symmetric Boolean functions on 2k variables with maximum algebraic immunity are constructed, which are much more than the previous constructions. Based on our construction, a lower bound of symmetric Boolean functions with algebraic immunity not less than d is derived, which is 2⌊ log2d ⌋ + 2(k-d+1). As far as we know, this is the first lower bound of this kind.},
keywords={},
doi={10.1587/transfun.E94.A.362},
ISSN={1745-1337},
month={January},}
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TY - JOUR
TI - Constructing Even-Variable Symmetric Boolean Functions with High Algebraic Immunity
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 362
EP - 366
AU - Yuan LI
AU - Hui WANG
AU - Haibin KAN
PY - 2011
DO - 10.1587/transfun.E94.A.362
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E94-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2011
AB - In this paper, we explicitly construct a large class of symmetric Boolean functions on 2k variables with algebraic immunity not less than d, where integer k is given arbitrarily and d is a given suffix of k in binary representation. If let d = k, our constructed functions achieve the maximum algebraic immunity. Remarkably, 2⌊ log2k ⌋ + 2 symmetric Boolean functions on 2k variables with maximum algebraic immunity are constructed, which are much more than the previous constructions. Based on our construction, a lower bound of symmetric Boolean functions with algebraic immunity not less than d is derived, which is 2⌊ log2d ⌋ + 2(k-d+1). As far as we know, this is the first lower bound of this kind.
ER -
English
