On the Hardness of the Asymmetric Learning With Errors Problem
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摘要: 由于基于最坏情况困难假设等优点，基于格的密码被认为是最具前景的抗量子密码研究方向。作为格密码的常用的两个主要困难问题之一，含错学习(LWE)问题被广泛用于密码算法的设计。为了提高格密码算法的性能，Zhang等人(2019)提出了非对称含错学习问题，该文将从理论上详细研究非对称含错学习问题和标准含错学习问题关系，并证明在特定错误分布下非对称含错学习问题和含错学习问题是多项式时间等价的，从而为基于非对称含错学习问题设计安全的格密码算法奠定了理论基础。Abstract: Due to the advantages such as the worst-case hardness assumption, lattice-based cryptography is believed to the most promising research direction in post-quantum cryptography. As one of the two main hard problems commonly used in lattice-based cryptography, Learning With Errors (LWE) problem is widely used in constructing numerous cryptosystems. In order to improve the efficiency of lattice-based cryptosystems, Zhang et al. (2019) introduced the Asymmetric LWE (ALWE) problem. In this paper, the relation between the ALWE problem and the standard LWE problem is studied, and it shows that for certain error distributions the two problems are polynomially equivent, which paves the way for constructing secure lattice-based cryptosystems from the ALWE problem.
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