Welcome to the resource topic for 2023/1412
Title:
Algebraic isomorphic spaces of ideal lattices, reduction of Ring-SIS problem, and new reduction of Ring-LWE problem
Authors: Zhuang Shan, Leyou Zhang, Qing Wu, Qiqi Lai
Abstract:The main focus of this article is on an open problem, namely the Ring-SIS reduction problem.We first utilize a spatial isomorphism approach to reduce the Ring-SIS problem to the classic SIS problem in lattices, indirectly reducing it to the classic SIVP in lattices. This provides theoretical assurance to some extent for the difficulty and resistance against quantum attacks of the Ring-SIS
problem.
Additionally, we reduce the Ring-LWE problem to the Ring-SIS problem, which guarantees the security of encryption schemes based on Ring-LWE to a certain degree. Finally, this article proves
that the difficulty of the Ring-SIS problem and the Ring-LWE problem is relatively average with respect to the spatial dimension or polynomial degree.
ePrint: https://eprint.iacr.org/2023/1412
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