IEICE TRANSACTIONS on Fundamentals
Open Access
The Lower Bound of Second-Order Nonlinearity of a Class of Boolean Functions
-
Full Text Views
44
- Cite this
- Free PDF (774KB)
Summary :
The r-th nonlinearity of Boolean functions is an important cryptographic criterion associated with higher order linearity attacks on stream and block ciphers. In this paper, we tighten the lower bound of the second-order nonlinearity of a class of Boolean function over finite field F2n, fλ(x)=Tr(λxd), where λ∈F*2r, d=22r+2r+1 and n=7r. This bound is much better than the lower bound of Iwata-Kurosawa.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E105-A No.9 pp.1317-1321
- Publication Date
- 2022/09/01
- Publicized
- 2022/03/10
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.2021EAP1146
- Type of Manuscript
- PAPER
- Category
- Cryptography and Information Security
Authors
Luozhong GONG
Changsha Nomal University
Shangzhao LI
Changshu Institute of Technology
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
Luozhong GONG, Shangzhao LI, "The Lower Bound of Second-Order Nonlinearity of a Class of Boolean Functions" in IEICE TRANSACTIONS on Fundamentals,
vol. E105-A, no. 9, pp. 1317-1321, September 2022, doi: 10.1587/transfun.2021EAP1146.
Abstract: The r-th nonlinearity of Boolean functions is an important cryptographic criterion associated with higher order linearity attacks on stream and block ciphers. In this paper, we tighten the lower bound of the second-order nonlinearity of a class of Boolean function over finite field F2n, fλ(x)=Tr(λxd), where λ∈F*2r, d=22r+2r+1 and n=7r. This bound is much better than the lower bound of Iwata-Kurosawa.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2021EAP1146/_p
Copy
@ARTICLE{e105-a_9_1317,
author={Luozhong GONG, Shangzhao LI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={The Lower Bound of Second-Order Nonlinearity of a Class of Boolean Functions},
year={2022},
volume={E105-A},
number={9},
pages={1317-1321},
abstract={The r-th nonlinearity of Boolean functions is an important cryptographic criterion associated with higher order linearity attacks on stream and block ciphers. In this paper, we tighten the lower bound of the second-order nonlinearity of a class of Boolean function over finite field F2n, fλ(x)=Tr(λxd), where λ∈F*2r, d=22r+2r+1 and n=7r. This bound is much better than the lower bound of Iwata-Kurosawa.},
keywords={},
doi={10.1587/transfun.2021EAP1146},
ISSN={1745-1337},
month={September},}
Copy
TY - JOUR
TI - The Lower Bound of Second-Order Nonlinearity of a Class of Boolean Functions
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1317
EP - 1321
AU - Luozhong GONG
AU - Shangzhao LI
PY - 2022
DO - 10.1587/transfun.2021EAP1146
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E105-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2022
AB - The r-th nonlinearity of Boolean functions is an important cryptographic criterion associated with higher order linearity attacks on stream and block ciphers. In this paper, we tighten the lower bound of the second-order nonlinearity of a class of Boolean function over finite field F2n, fλ(x)=Tr(λxd), where λ∈F*2r, d=22r+2r+1 and n=7r. This bound is much better than the lower bound of Iwata-Kurosawa.
ER -
English
