Research on Linear Properties of Keccak-like S-box
-
摘要:
该文将Keccak的S盒一般化为n元Keccak类S盒，研究了Keccak类S盒的线性性质。证明了这类S盒的相关优势的取值都为0或
\begin{document}${2^{ - k}}$\end{document} ，其中
且
，并且对于此范围内的任意k，都存在输入输出掩码使得相关优势取到
；证明了当输出掩码确定时，其非平凡相关优势都相等；给出了非平凡相关优势为最大值
时的充要条件与计数，解决了这类S盒的Walsh谱分布规律问题。
Abstract:In this paper, the S-box of Keccak is generalized into n-variable Keccak-like S-box, and the linear properties of n-variable Keccak-like S-box is studied. It is proved that all the values of correlation advantages of this kind of S-box are 0 or
\begin{document}${2^{ - k}}$\end{document} , where
and
, and for any k in this range, there is an input mask and an output mask that make the correlation advantage be
. Furthermore, it is proved that when the output mask is fixed, the values of the nontrivial correlation advantages of the S-box are determined. Then, the necessary and sufficient condition are given when the count for the nontrivial correlation advantage is the maximum value
. Finally, the value distribution of the Walsh spectrum of Keccak-like S-box is presented.
-
Key words:
- Hash function /
- Keccak /
- S-box /
- Linear properties
-
BERTONI G, DAEMEN J, PEETERS M, et al. Keccak[C]. The 32nd Annual International Conference on the Theory and Applications of Cryptographic Techniques on Advances in Cryptology, Athens, Greece, 2013: 313–314. NIST. Announcing request for candidate algorithm nominations for a new cryptographic hash algorithm (SHA-3) family[EB/OL]. http://www.nist.gov/hash-competition, 2007. 王永娟, 王涛, 袁庆军, 等. 密码算法旁路立方攻击改进与应用[J]. 电子与信息学报, 2020, 42(5): 1087–1093. doi: 10.11999/JEIT181075WANG Yongjuan, WANG Tao, YUAN Qingjun, et al. Side channel cube attack improvement and application on cryptographic algorithm[J]. Journal of Electronics &Information Technology, 2020, 42(5): 1087–1093. doi: 10.11999/JEIT181075 赵军, 曾学文, 郭志川. 支持国产密码算法的高速PCIe密码卡的设计与实现[J]. 电子与信息学报, 2019, 41(10): 2402–2408. doi: 10.11999/JEIT190003ZHAO Jun, ZENG Xuewen, and GUO Zhichuan. Design and implementation of high speed PCIe cipher card supporting GM algorithms[J]. Journal of Electronics &Information Technology, 2019, 41(10): 2402–2408. doi: 10.11999/JEIT190003 DAEMEN J. Cipher and hash function design strategies based on linear and differential cryptanalysis[D]. [Ph.D. dissertation], Katholieke Universiteit Leuven, 1995: 23–58. BERTONI G M, DAEMEN J, PEETERS M, et al. RadioGatún, a belt-and-mill hash function[C]. The 2nd Cryptographic Hash Workshop, Santa Barbara, USA, 2006: 24–25. GUO Xu, SRIVASTAV M, HUANG Sinan, et al. ASIC implementations of five SHA-3 finalists[C]. 2012 Design, Automation & Test in Europe Conference & Exhibition, Dresden, Germany, 2012: 1006–1011. JOSHI P, MUKHOPADHYAY D, and ROYCHOWDHURY D. Design and analysis of a robust and efficient block cipher using cellular automata[C]. The 20th International Conference on Advanced Information Networking and Applications, Vienna, Austria, 2006: 67–71. MANZONI L and MARIOT L. Cellular automata pseudo-random number generators and their resistance to asynchrony[C]. The 13th International Conference on Cellular Automata for Research and Industry, Como, Italy, 2018: 428–437. PICEK S, MARIOT L, YANG Bohan, et al. Design of S-boxes defined with cellular automata rules[C]. The Computing Frontiers Conference, Siena, Italy, 2017: 409–414. MARIOT L, PICEK S, LEPORATI A, et al. Cellular automata based S-boxes[J]. Cryptography and Communications, 2019, 11(1): 41–62. doi: 10.1007/s12095-018-0311-8 BAO Zhenzhen, GUO Jian, LING San, et al. PEIGEN-a platform for evaluation, implementation, and generation of S-boxes[J]. IACR Transactions on Symmetric Cryptology, 2019(1): 330–394. doi: 10.13154/tosc.v2019.i1.330-394 GHOSHAL A, SADHUKHAN R, PATRANABIS S, et al. Lightweight and side-channel secure 4×4 S-boxes from cellular automata rules[J]. IACR Transactions on Symmetric Cryptology, 2018(3): 311–334. doi: 10.13154/tosc.v2018.i3.311-334 关杰, 黄俊君. 一类新的基于元胞自动机的S盒的密码学性质研究[J]. 通信学报, 2019, 40(5): 192–200.GUAN Jie and HUANG Junjun. Research on cryptographic properties of a new S-box based on cellular automaton[J]. Journal on Communications, 2019, 40(5): 192–200. 李倩男, 李云强, 蒋淑静, 等. Keccak类非线性变换的差分性质研究[J]. 通信学报, 2012, 33(9): 140–146.LI Qiannan, LI Yunqiang, JIANG Shujing, et al. Research on differential properties of Keccak-like nonlinear transform[J]. Journal on Communications, 2012, 33(9): 140–146. 李倩男. Keccak类杂凑函数研究[D]. [硕士论文], 信息工程大学, 2013: 30–36.LI Qiannan. Research on Keccak-like Hash function[D]. [Master Dissertation], The PLA Information Engineering University, 2013: 30–36. 金晨辉, 郑浩然, 张少武, 等. 密码学[M]. 北京: 高等教育出版社, 2009: 30–36.JIN Chenhui, ZHENG Haoran, ZHANG Shaowu, et al. Cryptography[M]. Beijing: Higher Education Press, 2009: 30–36. -
计量
- 文章访问数: 2450
- HTML全文浏览量: 991
- PDF下载量: 74
- 被引次数: 0
下载:
