Abstract
We describe a variation of the Schnorr-Lyubashevsky approach to devising signature schemes that is adapted to rank based cryptography. This new approach enables us to obtain a randomization of the signature, which previously seemed difficult to derive for code-based cryptography. We provide a detailed analysis of attacks and an EUF-CMA proof for our scheme. Our scheme relies on the security of the Ideal Rank Support Learning and the Ideal Rank Syndrome problems and a newly introduced problem: Product Spaces Subspaces Indistinguishability, for which we give a detailed analysis. Overall the parameters we propose are efficient and comparable in terms of signature size to the Dilithium lattice-based scheme, with a signature size of 4 kB for a public key of size less than 20 kB.
N. Aragon—This work was partially funded by French DGA.
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Acknowledgements
This work has been supported in part by the French ANR projects CBCRYPT (ANR-17-CE39-0007) and ID-FIX (ANR-16-CE39-0004). The authors would like to thank Alain Couvreur for his insightful comments.
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Aragon, N., Blazy, O., Gaborit, P., Hauteville, A., Zémor, G. (2019). Durandal: A Rank Metric Based Signature Scheme. In: Ishai, Y., Rijmen, V. (eds) Advances in Cryptology – EUROCRYPT 2019. EUROCRYPT 2019. Lecture Notes in Computer Science(), vol 11478. Springer, Cham. https://doi.org/10.1007/978-3-030-17659-4_25
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