© Springer Nature Switzerland AG, 2019. We present a novel computational technique to check whether a matrix-vector product is correct with a relatively high probability. While the idea could be related to verifiable delegated computations, most of the literature in this line of work focuses on provably secure functional aspects and do not provide clear computational techniques to verify whether a product $$xA = y$$ is correct where x, A and y are not given nor computed by the party which requires validity checking: this is typically the case for some cryptographic lattice-based signature schemes. This paper focuses on the computational aspects and the improvement on both speed and memory when implementing such a verifier, and use a practical example: the Diagonal Reduction Signature (DRS) scheme as it was one of the candidates in the recent National Institute of Standards and Technology Post-Quantum Cryptography Standardization Calls for Proposals competition. We show that in the case of DRS, we can gain a factor of 20 in verification speed.

At PKC 2008, Plantard et al. published a theoretical framework for a lattice-based signature scheme. Recently, after ten years, a new signature scheme dubbed as the Diagonal Reduction Signature (DRS) scheme was presented in the NIST PQC Standardization as a concrete instantiation of the initial work. Unfortunately, the initial submission was challenged by Yu and Ducas using the structure that is present on the secret key noise. In this paper, we are proposing a new method to generate random noise in the DRS scheme to elimite the aforementioned attack, and all subsequent potential variants.

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