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Rényi divergence on learning with errors
Science China Information Sciences ( IF 8.8 ) Pub Date : 2020-08-10 , DOI: 10.1007/s11432-018-9788-1
Yang Tao , Han Wang , Rui Zhang

Many lattice-based schemes are built from the hardness of the learning with errors problem, which naturally comes in two flavors: the decision LWE and search LWE. In this paper, we investigate the decision LWE and search LWE by Rényi divergence respectively and obtain the following results: For decision LWE, we apply RD on LWE variants with different error distributions (i.e., center binomial distribution and uniform distribution, which are frequently used in the NIST PQC submissions) and prove the pseudorandomness in theory. As a by-product, we extend the so-called public sampleability property and present an adaptively public sampling property to the application of Rényi divergence on more decision problems. As for search LWE, we improve the classical reduction proof from GapSVP to LWE. Besides, as an independent interest, we also explore the intrinsic relation between the decision problem and search problem.



中文翻译:

Rényi在错误学习方面的分歧

许多基于格的方案都是基于有错误的学习的难点而构建的,它自然地具有两种形式:决策LWE和搜索LWE。在本文中,我们分别研究了决策LWE和通过Rényi散度搜索LWE,并获得以下结果:对于决策LWE,我们将RD应用于具有不同误差分布(即中心二项分布和均匀分布,这是经常使用的)的LWE变体。在NIST PQC提交中),并从理论上证明了伪随机性。作为副产品,我们扩展了所谓的公共抽样属性,并提出了适应性公共抽样属性,以将Rényi散度应用于更多决策问题。对于搜索LWE,我们将经典归约证明从GapSVP改进为LWE。此外,作为独立利益,

更新日期:2020-08-17
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