The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
이 논문에서 우리는 2에 대한 대규모 대칭 부울 함수 클래스를 명시적으로 구성합니다.k 대수적 면역성을 갖는 변수 d, 여기서 정수 k 임의로 주어지고 d 은 주어진 접미사이다 k 이진 표현으로. 놔두면 d = k, 우리가 구축한 함수는 최대의 대수적 면역성을 달성합니다. 놀랍게도 2⌊ 통나무2k ⌋ + 2 2의 대칭 부울 함수k 이전 구성보다 훨씬 더 많은 최대 대수적 면역성을 갖는 변수가 구성됩니다. 우리의 구성을 기반으로 대수적 면역성을 갖춘 대칭 부울 함수의 하한은 다음과 같습니다. d 파생되어 2가 됩니다.⌊ 통나무2d ⌋ + 2(k-d+ 1). 우리가 아는 한, 이것이 이런 종류의 첫 번째 하한입니다.
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부
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
부
@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},}
부
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 -