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A CP-Based Automatic Tool for Instantiating Truncated Differential Characteristics

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Progress in Cryptology – INDOCRYPT 2023 (INDOCRYPT 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14459))

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Abstract

An important criteria to assert the security of a cryptographic primitive is its resistance against differential cryptanalysis. For word-oriented primitives, a common technique to determine the number of rounds required to ensure the immunity against differential distinguishers is to consider truncated differential characteristics and to count the number of active S-boxes. Doing so allows one to provide an upper bound on the probability of the best differential characteristic with a reduced computational cost. However, in order to design very efficient primitives, it might be needed to evaluate the probability more accurately. This is usually done in a second step, during which one tries to instantiate truncated differential characteristics with actual values and computes its corresponding probability. This step is usually done either with ad-hoc algorithms or with CP, SAT or MILP models that are solved by generic solvers. In this paper, we present a generic tool for automatically generating these models to handle all word-oriented ciphers. Furthermore the running times to solve these models are very competitive with all the previous dedicated approaches.

The work presented in this article was funded by the French National Research Agency as part of the DeCrypt project (ANR-18-CE39-0007).

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Acknowledgements

The authors would like to express their very great appreciation to Charles Prud’homme, Ph.D. from IMT for his valuable and constructive expertise of Choco during the development of this research work.

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Authors and Affiliations

  1. Université Clermont-Auvergne, CNRS, Mines de Saint-Étienne, LIMOS, Clermont-Ferrand, France

    François Delobel

  2. Univ Rennes, CNRS, IRISA, Rennes, France

    Patrick Derbez & Arthur Gontier

  3. EPITA Research Laboratory (LRE), 14/16 rue Voltaire, 94270, Le Kremlin-Bicêtre, France

    Loïc Rouquette

  4. LORIA, Université de Lorraine, 54000, Nancy, France

    Loïc Rouquette

  5. INSA Lyon, CITI, INRIA CHROMA, 69621, Villeurbanne, France

    Christine Solnon

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  1. François Delobel
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  4. Loïc Rouquette
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  5. Christine Solnon
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Corresponding author

Correspondence to Loïc Rouquette .

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Editors and Affiliations

  1. Nanyang Technological University, Singapore, Singapore

    Anupam Chattopadhyay

  2. Nanyang Technological University, Singapore, Singapore

    Shivam Bhasin

  3. Radboud University, Nijmegen, The Netherlands

    Stjepan Picek

  4. Indian Institute of Technology Madras, Chennai, India

    Chester Rebeiro

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Delobel, F., Derbez, P., Gontier, A., Rouquette, L., Solnon, C. (2024). A CP-Based Automatic Tool for Instantiating Truncated Differential Characteristics. In: Chattopadhyay, A., Bhasin, S., Picek, S., Rebeiro, C. (eds) Progress in Cryptology – INDOCRYPT 2023. INDOCRYPT 2023. Lecture Notes in Computer Science, vol 14459. Springer, Cham. https://doi.org/10.1007/978-3-031-56232-7_12

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  • DOI: https://doi.org/10.1007/978-3-031-56232-7_12

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