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Investigation for 8-bit SKINNY-like S-boxes, analysis and applications

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Abstract

Nowadays, ciphers have been widely used in high-end platforms, resource-constrained, and side-channel attacks vulnerable environments. This motivates various S-boxes aimed at providing a good trade-off between security and efficiency. For small S-boxes, the most natural approach of constructing such S-boxes is a comprehensive search in the space of permutations, which inevitably becomes more challenging when the size grows. For large S-boxes (e.g., 8-bit), previous works concentrated on creations from finite fields or smaller ones (e.g., 4-bit). This paper proposes a new algorithm with a layered structure to search for 8-bit SKINNY-like S-boxes. We compare our new S-box with the original 8-bit SKINNY S-box by analyzing its security properties. Besides, due to our searching algorithm’s rules and constraints, SKINNY-like S-boxes have other features of lightweight implementation, low multiplicative complexity, low AND depth, and an effective inverse. Eventually, the searching algorithm outputs 224000 8-bit SKINNY-like S-boxes. The cipher designers can use these new S-boxes to construct lightweight block ciphers with easy-to-mask property and efficient implementation performance.

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Notes

  1. For instance, there exits 256! ≈ 21684 possible permutations in \(\mathbb {F}_{2}^{8} \rightarrow \mathbb {F}_{2}^{8}\).

  2. \({x_{i}^{j}}\) is the j-th state bit in the i-th layer, where j ∈{0, 1,…,n − 1} and i ∈{0, 1,…,ℓ − 1}.

  3. In the rest of this paper, unless otherwise stated, the SKINNY-like S-box refers to an 8-bit S-box.

  4. f0 is derived from the special invertible instructions (a ∧ b) ⊕ c → c [21].

  5. ℓ ∈{1, 2, 3}. The 0-th layer denotes the Input layer.

  6. In the rest of this paper, unless otherwise stated, SKINNY refers to its 128-bit block version.

  7. According to AVX implementation of SKINNY cipher given at https://github.com/kste/skinny_avx/tree/master/skinny128/avx2, we modify partial program about S-box to obtain parallel bit-sliced implementations.

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Acknowledgements

This work has been supported by the National Natural Science Foundation of China (Grant No. 62032014), the National Key Research and Development Program of China (Grant No. 2018YFA0704702), the Major Basic Research Project of Natural Science Foundation of Shandong Province, China (Grant No. ZR202010220025), the National Natural Science Foundation of China (Grant No. 61902100), and the Program of Qilu Young Scholars of Shandong University (Grant No. 61580082063088).

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Authors and Affiliations

  1. School of Cyber Science and Technology, Shandong University, Qingdao, Shandong, 266237, China

    Yanhong Fan, Weijia Wang, Yongqing Li & Meiqin Wang

  2. Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University, Qingdao, Shandong, 266237, China

    Yanhong Fan, Weijia Wang, Yongqing Li & Meiqin Wang

  3. Department of Mathematics, University of Paris VIII, F-93526 Saint-Denis, Laboratory Geometry, Analysis and Applications, LAGA, University Sorbonne Paris Nord, CNRS, UMR, 7539, F-93430, Villetaneuse, France

    Sihem Mesnager

  4. Telecom Paris, 91120, Palaiseau, France

    Sihem Mesnager

  5. School of Cyberspace, Hangzhou Dianzi University, Hangzhou, Zhejiang, 310018, China

    Tingting Cui

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  1. Yanhong Fan
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Appendix A: Hardware implementation of some SKINNY-like S-Boxes

Appendix A: Hardware implementation of some SKINNY-like S-Boxes

In Table 5, (X7,X6,X5,X4,X3,X2,X1,X0) and (Y7,Y6,Y5,Y4,Y3,Y2,Y1,Y0) are defined as inputs and outputs of the S-boxes, and X7 and Y7 are the most significant bits (MSB).

Table 5 Hardware implementation of 7 new S-boxes mentioned in Table 2 and 3
Full size table

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Fan, Y., Mesnager, S., Wang, W. et al. Investigation for 8-bit SKINNY-like S-boxes, analysis and applications. Cryptogr. Commun. 13, 617–636 (2021). https://doi.org/10.1007/s12095-021-00486-y

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