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Cryptanalysis of Reduced Round SPEEDY

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Progress in Cryptology - AFRICACRYPT 2022 (AFRICACRYPT 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13503))

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Abstract

SPEEDY is a family of ultra low latency block ciphers proposed by Leander, Moos, Moradi and Rasoolzadeh at TCHES 2021. Although the designers gave some differential/linear distinguishers for reduced rounds, a concrete cryptanalysis considering key recovery attacks on SPEEDY was completely missing. The latter is crucial to understand the security margin of designs like SPEEDY which typically use low number of rounds to have low latency. In this work, we present the first third-party cryptanalysis of SPEEDY-r-192, where \(r \in \{5, 6, 7\}\) is the number of rounds and 192 is block and key size in bits. We identify cube distinguishers for 2 rounds with data complexities \(2^{14}\) and \(2^{13}\), while the differential/linear distinguishers provided by designers has a complexity of \(2^{39}\). Notably, we show that there are several such cube distinguishers, and thus, we then provide a generic description of them. We also investigate the structural properties of 13-dimensional cubes and give experimental evidence that the partial algebraic normal form of certain state bits after two rounds is always the same. Next, we utilize the 2 rounds distinguishers to mount a key recovery attack on 3 rounds SPEEDY. Our attack require \(2^{17.6}\) data, \(2^{25.5}\) bits of memory and \(2^{52.5}\) time. Our results show that the practical variant of SPEEDY, i.e., SPEEDY-5-192 has a security margin of only 2 rounds. We believe our work will bring new insights in understanding the security of SPEEDY.

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Notes

  1. 1.

    XOR-ing the evaluation of a state bit at all possible \(2^{14}\) values of cube variables.

  2. 2.

    From point of cryptanalysis.

  3. 3.

    Test vectors are provided along with the codes.

  4. 4.

    This is one of the example of a pattern.

  5. 5.

    Column numbers taken modulo 32.

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Acknowledgements

The authors would like to thank the reviewers of Africacrypt 2022 for providing us with insightful comments to improve the quality of the paper.

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Authors and Affiliations

  1. Cryptography Research Centre, Technology Innovation Institute, Abu Dhabi, UAE

    Raghvendra Rohit

  2. Indian Institute of Technology Madras, Chennai, India

    Santanu Sarkar

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  1. Raghvendra Rohit
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Correspondence to Raghvendra Rohit .

Editor information

Editors and Affiliations

  1. Radboud University, Nijmegen, The Netherlands

    Lejla Batina

  2. Radboud University, Nijmegen, Gelderland, The Netherlands

    Joan Daemen

A SPEEDY Round Constants

A SPEEDY Round Constants

In Table 3, we list the first 6 round constants of SPEEDY.

Table 3. Round constants of SPEEDY
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Rohit, R., Sarkar, S. (2022). Cryptanalysis of Reduced Round SPEEDY. In: Batina, L., Daemen, J. (eds) Progress in Cryptology - AFRICACRYPT 2022. AFRICACRYPT 2022. Lecture Notes in Computer Science, vol 13503. Springer, Cham. https://doi.org/10.1007/978-3-031-17433-9_6

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  • DOI: https://doi.org/10.1007/978-3-031-17433-9_6

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