IEICE TRANSACTIONS on Fundamentals
Balanced Boolean Functions of σƒ>22n+2n+3(n≥4)
Summary :
The global avalanche characteristics measure the overall avalanche properties of Boolean functions, an n-variable balanced Boolean function of the sum-of-square indicator reaching σƒ=22n+2n+3 is an open problem. In this paper, we prove that there does not exist a balanced Boolean function with σƒ=22n+2n+3 for n≥4, if the hamming weight of one decomposition function belongs to the interval Q*. Some upper bounds on the order of propagation criterion of balanced Boolean functions with n (3≤n≤100) variables are given, if the number of vectors of propagation criterion is equal and less than 7·2n-3-1. Two lower bounds on the sum-of-square indicator for balanced Boolean functions with optimal autocorrelation distribution are obtained. Furthermore, the relationship between the sum-of-squares indicator and nonlinearity of balanced Boolean functions is deduced, the new nonlinearity improves the previously known nonlinearity.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E98-A No.6 pp.1313-1319
- Publication Date
- 2015/06/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E98.A.1313
- Type of Manuscript
- LETTER
- Category
- Cryptography and Information Security
Authors
Yu ZHOU
Science and Technology on Communication Security Laboratory
Lin WANG
Science and Technology on Communication Security Laboratory
Weiqiong WANG
Chang'an University
Xiaoni DU
Northwest Normal University
Keyword
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Yu ZHOU, Lin WANG, Weiqiong WANG, Xiaoni DU, "Balanced Boolean Functions of σƒ>22n+2n+3(n≥4)" in IEICE TRANSACTIONS on Fundamentals,
vol. E98-A, no. 6, pp. 1313-1319, June 2015, doi: 10.1587/transfun.E98.A.1313.
Abstract: The global avalanche characteristics measure the overall avalanche properties of Boolean functions, an n-variable balanced Boolean function of the sum-of-square indicator reaching σƒ=22n+2n+3 is an open problem. In this paper, we prove that there does not exist a balanced Boolean function with σƒ=22n+2n+3 for n≥4, if the hamming weight of one decomposition function belongs to the interval Q*. Some upper bounds on the order of propagation criterion of balanced Boolean functions with n (3≤n≤100) variables are given, if the number of vectors of propagation criterion is equal and less than 7·2n-3-1. Two lower bounds on the sum-of-square indicator for balanced Boolean functions with optimal autocorrelation distribution are obtained. Furthermore, the relationship between the sum-of-squares indicator and nonlinearity of balanced Boolean functions is deduced, the new nonlinearity improves the previously known nonlinearity.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E98.A.1313/_p
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@ARTICLE{e98-a_6_1313,
author={Yu ZHOU, Lin WANG, Weiqiong WANG, Xiaoni DU, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Balanced Boolean Functions of σƒ>22n+2n+3(n≥4)},
year={2015},
volume={E98-A},
number={6},
pages={1313-1319},
abstract={The global avalanche characteristics measure the overall avalanche properties of Boolean functions, an n-variable balanced Boolean function of the sum-of-square indicator reaching σƒ=22n+2n+3 is an open problem. In this paper, we prove that there does not exist a balanced Boolean function with σƒ=22n+2n+3 for n≥4, if the hamming weight of one decomposition function belongs to the interval Q*. Some upper bounds on the order of propagation criterion of balanced Boolean functions with n (3≤n≤100) variables are given, if the number of vectors of propagation criterion is equal and less than 7·2n-3-1. Two lower bounds on the sum-of-square indicator for balanced Boolean functions with optimal autocorrelation distribution are obtained. Furthermore, the relationship between the sum-of-squares indicator and nonlinearity of balanced Boolean functions is deduced, the new nonlinearity improves the previously known nonlinearity.},
keywords={},
doi={10.1587/transfun.E98.A.1313},
ISSN={1745-1337},
month={June},}
Copy
TY - JOUR
TI - Balanced Boolean Functions of σƒ>22n+2n+3(n≥4)
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1313
EP - 1319
AU - Yu ZHOU
AU - Lin WANG
AU - Weiqiong WANG
AU - Xiaoni DU
PY - 2015
DO - 10.1587/transfun.E98.A.1313
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E98-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 2015
AB - The global avalanche characteristics measure the overall avalanche properties of Boolean functions, an n-variable balanced Boolean function of the sum-of-square indicator reaching σƒ=22n+2n+3 is an open problem. In this paper, we prove that there does not exist a balanced Boolean function with σƒ=22n+2n+3 for n≥4, if the hamming weight of one decomposition function belongs to the interval Q*. Some upper bounds on the order of propagation criterion of balanced Boolean functions with n (3≤n≤100) variables are given, if the number of vectors of propagation criterion is equal and less than 7·2n-3-1. Two lower bounds on the sum-of-square indicator for balanced Boolean functions with optimal autocorrelation distribution are obtained. Furthermore, the relationship between the sum-of-squares indicator and nonlinearity of balanced Boolean functions is deduced, the new nonlinearity improves the previously known nonlinearity.
ER -
English
