On the security of 4-bit involutive S-boxes for lightweight designs

Authors:
Bozhong Liu;Zheng Gong;Weidong Qiu;Dong Zheng
Affiliations:
School of Information Security Engineering, Shanghai Jiaotong University, Shanghai, China;School of Computer Science, South China Normal University, Guangzhou, China;School of Information Security Engineering, Shanghai Jiaotong University, Shanghai, China and National Laboratory of Communication System Controlling Technology, Zhejiang, China;School of Information Security Engineering, Shanghai Jiaotong University, Shanghai, China
Venue:
ISPEC'11 Proceedings of the 7th international conference on Information security practice and experience
Year:
2011

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Abstract

In this work we investigate all the 4-bit involutive S-boxes with linear, differential and almost resilient analysis. The results show that involutive S-boxes can be optimal against linear attack. We prove that for a 4-bit involutive S-box there always exists a pair of input and output differences such that the Hamming distance is 1, which does not satisfy the strict resistance on differential analysis. Moreover, we find that the almost resilient property is not effective to judge the security of 4-bit involutive S-boxes in practise. How to use the almost resilient property to set up a criterion for an optimal secure S-box needs investigations.