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Unifying Freedom and Separation for Tight Probing-Secure Composition

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Advances in Cryptology – CRYPTO 2023 (CRYPTO 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14083))

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Abstract

The masking countermeasure is often analyzed in the probing model. Proving the probing security of large circuits at high masking orders is achieved by composing gadgets that satisfy security definitions such as non-interference (NI), strong non-interference (SNI) or free SNI. The region probing model is a variant of the probing model, where the probing capabilities of the adversary scale with the number of regions in a masked circuit. This model is of interest as it allows better reductions to the more realistic noisy leakage model. The efficiency of composable region probing secure masking has been recently improved with the introduction of the input-output separation (IOS) definition.

In this paper, we first establish equivalences between the non-interference framework and the IOS formalism. We also generalize the security definitions to multiple-input gadgets and systematically show implications and separations between these notions. Then, we study which gadgets from the literature satisfy these. We give new security proofs for some well-known arbitrary-order gadgets, and also some automated proofs for fixed-order, special-case gadgets. To this end, we introduce a new automated formal verification algorithm that solves the open problem of verifying free SNI, which is not a purely simulation-based definition. Using the relationships between the security notions, we adapt this algorithm to further verify IOS. Finally, we look at composition theorems. In the probing model, we use the link between free SNI and the IOS formalism to generalize and improve the efficiency of the tight private circuit (Asiacrypt 2018) construction, also fixing a flaw in the original proof. In the region probing model, we relax the assumptions for IOS composition (TCHES 2021), which allows to save many refresh gadgets, hence improving the efficiency.

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Notes

  1. 1.

    We note that, while the composition proof is flawed, the TPC construction considered in [12] which relies on ISW multiplication and refresh gadgets is still secure since these gadgets achieve the necessary free SNI notion as we further show in the present paper.

  2. 2.

    This augmented version of IronMask is available at https://github.com/CryptoExperts/IronMask.

  3. 3.

    In this paper, we restrict ourselves to additive encodings as recalled in Definition 1.

  4. 4.

    This notion of admissible pair can be trivially extended to the notion of admissible tuple for any number of inputs.

  5. 5.

    The definition for \(\ell \)-input gadgets is given in the full version of the paper.

  6. 6.

    The definition for \(\ell \)-input gadgets is given in the full version of the paper.

  7. 7.

    When we implemented the parallel multiplication gadgets from [6, SNI gadgets from Table 4], we detected a correctness flaw for the case \(n \mod 4 =2\). That is why we could not test such a gadget with six shares.

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Acknowledgements

This work is partly supported by SGS and the French FUI-AAP25 VeriSiCC project. The authors would also like to thank Benjamin Grégoire for his insightful comments and constructive discussions.

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Authors and Affiliations

  1. CryptoExperts, Paris, France

    Sonia Belaïd, Matthieu Rivain & Abdul Rahman Taleb

  2. Sorbonne Université, CNRS, LIP6, 75005, Paris, France

    Abdul Rahman Taleb

  3. TU Graz, Graz, Austria

    Gaëtan Cassiers

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  1. Sonia Belaïd
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Correspondence to Sonia Belaïd .

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  1. Rambus Inc., San Jose, CA, USA

    Helena Handschuh

  2. Brown University, Providence, RI, USA

    Anna Lysyanskaya

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Belaïd, S., Cassiers, G., Rivain, M., Taleb, A.R. (2023). Unifying Freedom and Separation for Tight Probing-Secure Composition. In: Handschuh, H., Lysyanskaya, A. (eds) Advances in Cryptology – CRYPTO 2023. CRYPTO 2023. Lecture Notes in Computer Science, vol 14083. Springer, Cham. https://doi.org/10.1007/978-3-031-38548-3_15

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