A Note on “On the Construction of Boolean Functions with Optimal Algebraic Immunity”
Summary :
In this note, we go further on the “basis exchange” idea presented in [2] by using Mobious inversion. We show that the matrix S1(f)S0(f)-1 has a nice form when f is chosen to be the majority function, where S1(f) is the matrix with row vectors υk(α) for all α ∈ 1f and S0(f)=S1(f ⊕ 1). And an exact counting for Boolean functions with maximum algebraic immunity by exchanging one point in on-set with one point in off-set of the majority function is given. Furthermore, we present a necessary condition according to weight distribution for Boolean functions to achieve algebraic immunity not less than a given number.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E94-A No.9 pp.1877-1880
- Publication Date
- 2011/09/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E94.A.1877
- Type of Manuscript
- LETTER
- Category
- Cryptography and Information Security
Authors
Keyword
Latest Issue
Copyrights notice of machine-translated contents
The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.
Cite this
Copy
Yuan LI, Haibin KAN, Kokichi FUTATSUGI, "A Note on “On the Construction of Boolean Functions with Optimal Algebraic Immunity”" in IEICE TRANSACTIONS on Fundamentals,
vol. E94-A, no. 9, pp. 1877-1880, September 2011, doi: 10.1587/transfun.E94.A.1877.
Abstract: In this note, we go further on the “basis exchange” idea presented in [2] by using Mobious inversion. We show that the matrix S1(f)S0(f)-1 has a nice form when f is chosen to be the majority function, where S1(f) is the matrix with row vectors υk(α) for all α ∈ 1f and S0(f)=S1(f ⊕ 1). And an exact counting for Boolean functions with maximum algebraic immunity by exchanging one point in on-set with one point in off-set of the majority function is given. Furthermore, we present a necessary condition according to weight distribution for Boolean functions to achieve algebraic immunity not less than a given number.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E94.A.1877/_p
Copy
@ARTICLE{e94-a_9_1877,
author={Yuan LI, Haibin KAN, Kokichi FUTATSUGI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Note on “On the Construction of Boolean Functions with Optimal Algebraic Immunity”},
year={2011},
volume={E94-A},
number={9},
pages={1877-1880},
abstract={In this note, we go further on the “basis exchange” idea presented in [2] by using Mobious inversion. We show that the matrix S1(f)S0(f)-1 has a nice form when f is chosen to be the majority function, where S1(f) is the matrix with row vectors υk(α) for all α ∈ 1f and S0(f)=S1(f ⊕ 1). And an exact counting for Boolean functions with maximum algebraic immunity by exchanging one point in on-set with one point in off-set of the majority function is given. Furthermore, we present a necessary condition according to weight distribution for Boolean functions to achieve algebraic immunity not less than a given number.},
keywords={},
doi={10.1587/transfun.E94.A.1877},
ISSN={1745-1337},
month={September},}
Copy
TY - JOUR
TI - A Note on “On the Construction of Boolean Functions with Optimal Algebraic Immunity”
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1877
EP - 1880
AU - Yuan LI
AU - Haibin KAN
AU - Kokichi FUTATSUGI
PY - 2011
DO - 10.1587/transfun.E94.A.1877
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E94-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2011
AB - In this note, we go further on the “basis exchange” idea presented in [2] by using Mobious inversion. We show that the matrix S1(f)S0(f)-1 has a nice form when f is chosen to be the majority function, where S1(f) is the matrix with row vectors υk(α) for all α ∈ 1f and S0(f)=S1(f ⊕ 1). And an exact counting for Boolean functions with maximum algebraic immunity by exchanging one point in on-set with one point in off-set of the majority function is given. Furthermore, we present a necessary condition according to weight distribution for Boolean functions to achieve algebraic immunity not less than a given number.
ER -
English
