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Observations on the branch number and differential analysis of SPEEDY

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Abstract

In this paper, we present some new observations on the branch number and study concrete differential analysis of SPEEDY. It is a new low-latency block cipher proposed at TCHES 2021. It employs SPS-type round function and consists of only 5/6/7 rounds. Since the iteration rounds are rather small so as to achieve ultra low-latency in encryption speed, it will be crucially important to analyze its security margin accurately. In this paper, we first propose a new notation of partition branch number which can describe the minimum number of active S-boxes for 2-round SPEEDY more accurately. An efficient algorithm to compute the value of partition branch number is also given. Then by extending the notation to higher-order partition branch number, we can obtain more accurate results of the minimum number of active S-boxes for 3–7 rounds. As a result, the maximum expected differential probabilities are significantly higher than the results estimated by designers. Based on this, we search for optimal differential characteristics of SPEEDY while considering the difference distribution table of S-box. We present examples of differential characteristics for 2–7 rounds. Furthermore, by utilizing the simple bit-permutation key schedule of SPEEDY, we can extend the differential trail search method and construct an efficient 6-round related-key differential trail with probability \(2^{-179.2}\). Based on it, we can present related-key differential attack on full round SPEEDY-7-192 with data complexity of \(2^{186.2}\) chosen-plaintexts and time complexity of \(2^{160.13}\) encryptions.

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Acknowledgements

This work is supported by the CAS Project for Young Scientists in Basic Research (Grant No. YSBR-035), and National Natural Science Foundation of China (No. 62072445). Moreover, the author is very grateful to the anonymous reviewers for their helpful comments and suggestions.

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Authors and Affiliations

  1. Institute of Software, Chinese Academy of Sciences, Beijing, 100190, China

    Lei Zhang

  2. State Key Laboratory of Cryptology, P.O. Box 5159, Beijing, 100878, China

    Lei Zhang

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  1. Lei Zhang
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Appendix A

Appendix A

See Tables 9 and 10

Table 9 Probabilities of 1-bit to 1-bit differential trails for 4–7 rounds SPEEDY
Full size table
Table 10 \(\texttt {PB}\) bit-permutation for SPEEDY-r -192
Full size table

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Zhang, L. Observations on the branch number and differential analysis of SPEEDY. Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01336-z

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