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Practical MP-LWE-based encryption balancing security-risk versus efficiency

机译：基于MP-LWE的加密平衡安全风险与效率

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Middle-product learning with errors (MP-LWE is a variant of the LWE problem introduced at CRYPTO 2017 by Rosca et al. (Advances in cryptology-CRYPTO, Springer, Berlin, 2017). Asymptotically, the theoretical results of Rosca et al. (2017) suggest that MP-LWE gives lattice-based public-key cryptosystems offering a 'security-risk vs. efficiency' trade-off: higher performance than cryptosystems based on unstructured lattices and lower risk than cryptosystems based on structured lattices (Polynomial/Ring LWE. However, although promising in theory, Rosca et al. (2017) left the practical implications of MP-LWE for lattice-based cryptography unclear. In this paper, we show how to build practical public-key cryptosystems with strong security guarantees based on MP-LWE. On the implementation side, we present optimised fast algorithms for computing the middle-product operation over polynomial rings Zq[x], the dominant computation for MP-LWE. On the security side, we show how to obtain a nearly tight security proof for MP-LWE from the hardest Polynomial LWE problem over a large family of rings, improving on the loose reduction of Rosca et al. (2017). We also show and analyze an optimised cryptanalysis of MP-LWE that narrows the complexity gap between best known attacks on MP-LWE asand Polynomial LWE. To evaluate the practicality of P-LWE, we apply our results to construct, implement and optimise parameters for a practical MP-LWE-based public-key cryptosystem, Titanium, and compare its benchmarks to other lattice-based systems. Our results show that MP-LWE offers a new 'security-risk vs. efficiency' trade-off in lattice-based cryptography in practice, not only asymptotically in theory.
机译：用错误的中产权学习（MP-LWE是Rosca等人在Crypto 2017上引入的LWE问题的变体。（密码学 - 加密，斯普林克，柏林，2017）。渐近，Rosca等人的理论结果。 （2017）建议MP-LWE提供基于格子的公钥密码系统，提供“安全风险与效率”权衡：基于非结构化格子的密码系统高于基于结构化格子的密码系统（多项式/戒指。然而，虽然理论上有前途，但Rosca等人。（2017）留下了MP-LWE对基于格子的密码术的实际意义尚不清楚。在本文中，我们展示了如何构建具有强大安全保障的实用公钥密码系统基于MP-LWE。在实施方面，我们提出了优化的快速算法，用于计算多项式环ZQ [x]的中间产品操作，对MP-LWE的显性计算。在安全方面，我们展示了如何获得几乎是TI. GHT安全证明MP-LWE来自最艰难的多项式LWE在大家庭中的戒指中的问题，改善了Rosca等人的松散减少。 （2017）。我们还显示并分析了MP-LWE的优化密码分析，该分析缩小了MP-LWE ASAND多项式LWE的最佳已知攻击之间的复杂性差距。为了评估P-LWE的实用性，我们将结果应用于构建，实施和优化基于MP-LWE的公钥密码系统，钛的参数，并将其基于基于格子的系统的基准进行比较。我们的研究结果表明，MP-LWE在实践中，在莱迪思的加密中提供了新的“安全风险与效率”权衡，不仅渐近理论上。

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