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Using Freivalds' Algorithm to Accelerate Lattice-Based Signature Verifications

机译：使用Freivalds算法加速基于格子的签名验证

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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.
机译：我们提出了一种新颖的计算技术来检查矩阵矢量产品是否正确，具有相对高的概率。虽然这个想法可能与可验证的委派计算有关，但是这项工作行中的大多数文献都侧重于可透明的安全功能方面，并且不提供明确的计算技术来验证产品XA = Y是否正确，其中x，a和y是正确的未通过缔约方给予或计算，这需要有效检查：这通常是一些基于加密格子的签名方案的情况。本文侧重于计算方面和在实现这种验证者时对速度和内存的改进，并使用实际示例：对角线减少签名（DRS）方案，因为它是近期国家标准研究所的候选人之一技术后量子加密标准化要求提案竞争。我们表明，在DRS的情况下，我们可以在验证速度下获得20倍。

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