IEICE TRANSACTIONS on Fundamentals
On the Sum-of-Squares of Differential Distribution Table for (n, n)-Functions
Summary :
S-box is one of the core components of symmetric cryptographic algorithms, but differential distribution table (DDT) is an important tool to research some properties of S-boxes to resist differential attacks. In this paper, we give a relationship between the sum-of-squares of DDT and the sum-of-squares indicator of (n, m)-functions based on the autocorrelation coefficients. We also get some upper and lower bounds on the sum-of-squares of DDT of balanced (n, m)-functions, and prove that the sum-of-squares of DDT of (n, m)-functions is affine invariant under affine affine equivalent. Furthermore, we obtain a relationship between the sum-of-squares of DDT and the signal-to-noise ratio of (n, m)-functions. In addition, we calculate the distributions of the sum-of-squares of DDT for all 3-bit S-boxes, the 4-bit optimal S-boxes and all 302 balanced S-boxes (up to affine equivalence), data experiments verify our results.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E105-A No.9 pp.1322-1329
- Publication Date
- 2022/09/01
- Publicized
- 2022/03/10
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.2022EAP1010
- Type of Manuscript
- PAPER
- Category
- Cryptography and Information Security
Authors
Rong CHENG
the Science and Technology on Communication Security Laboratory
Yu ZHOU
the Science and Technology on Communication Security Laboratory
Xinfeng DONG
the Science and Technology on Communication Security Laboratory
Xiaoni DU
Northwest Normal University
Keyword
Latest Issue
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Rong CHENG, Yu ZHOU, Xinfeng DONG, Xiaoni DU, "On the Sum-of-Squares of Differential Distribution Table for (n, n)-Functions" in IEICE TRANSACTIONS on Fundamentals,
vol. E105-A, no. 9, pp. 1322-1329, September 2022, doi: 10.1587/transfun.2022EAP1010.
Abstract: S-box is one of the core components of symmetric cryptographic algorithms, but differential distribution table (DDT) is an important tool to research some properties of S-boxes to resist differential attacks. In this paper, we give a relationship between the sum-of-squares of DDT and the sum-of-squares indicator of (n, m)-functions based on the autocorrelation coefficients. We also get some upper and lower bounds on the sum-of-squares of DDT of balanced (n, m)-functions, and prove that the sum-of-squares of DDT of (n, m)-functions is affine invariant under affine affine equivalent. Furthermore, we obtain a relationship between the sum-of-squares of DDT and the signal-to-noise ratio of (n, m)-functions. In addition, we calculate the distributions of the sum-of-squares of DDT for all 3-bit S-boxes, the 4-bit optimal S-boxes and all 302 balanced S-boxes (up to affine equivalence), data experiments verify our results.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2022EAP1010/_p
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@ARTICLE{e105-a_9_1322,
author={Rong CHENG, Yu ZHOU, Xinfeng DONG, Xiaoni DU, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On the Sum-of-Squares of Differential Distribution Table for (n, n)-Functions},
year={2022},
volume={E105-A},
number={9},
pages={1322-1329},
abstract={S-box is one of the core components of symmetric cryptographic algorithms, but differential distribution table (DDT) is an important tool to research some properties of S-boxes to resist differential attacks. In this paper, we give a relationship between the sum-of-squares of DDT and the sum-of-squares indicator of (n, m)-functions based on the autocorrelation coefficients. We also get some upper and lower bounds on the sum-of-squares of DDT of balanced (n, m)-functions, and prove that the sum-of-squares of DDT of (n, m)-functions is affine invariant under affine affine equivalent. Furthermore, we obtain a relationship between the sum-of-squares of DDT and the signal-to-noise ratio of (n, m)-functions. In addition, we calculate the distributions of the sum-of-squares of DDT for all 3-bit S-boxes, the 4-bit optimal S-boxes and all 302 balanced S-boxes (up to affine equivalence), data experiments verify our results.},
keywords={},
doi={10.1587/transfun.2022EAP1010},
ISSN={1745-1337},
month={September},}
Copy
TY - JOUR
TI - On the Sum-of-Squares of Differential Distribution Table for (n, n)-Functions
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1322
EP - 1329
AU - Rong CHENG
AU - Yu ZHOU
AU - Xinfeng DONG
AU - Xiaoni DU
PY - 2022
DO - 10.1587/transfun.2022EAP1010
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E105-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2022
AB - S-box is one of the core components of symmetric cryptographic algorithms, but differential distribution table (DDT) is an important tool to research some properties of S-boxes to resist differential attacks. In this paper, we give a relationship between the sum-of-squares of DDT and the sum-of-squares indicator of (n, m)-functions based on the autocorrelation coefficients. We also get some upper and lower bounds on the sum-of-squares of DDT of balanced (n, m)-functions, and prove that the sum-of-squares of DDT of (n, m)-functions is affine invariant under affine affine equivalent. Furthermore, we obtain a relationship between the sum-of-squares of DDT and the signal-to-noise ratio of (n, m)-functions. In addition, we calculate the distributions of the sum-of-squares of DDT for all 3-bit S-boxes, the 4-bit optimal S-boxes and all 302 balanced S-boxes (up to affine equivalence), data experiments verify our results.
ER -
English
