In [15], Leonardi and Ruiz-Lopez propose an additively homomorphic public key encryption scheme whose security is expected to depend on the hardness of the learning homomorphism with noise problem (LHN). Choosing parameters for their primitive requires choosing three groups $G$, $H$, and $K$. In their paper, Leonardi and Ruiz-Lopez claim that, when $G$, $H$, and $K$ are abelian, then their public key cryptosystem is not quantum secure. In this paper, we study security for finite abelian groups $G$, $H$, and $K$ in the classical case. Moreover, we study quantum attacks on instantiations with solvable groups.
翻译:在[15]中,Leonardi和Ruiz-Lopez提出一个添加式同质公用钥匙加密方案,其安全性预计将取决于学习的同质性与噪音问题(LHN)的坚硬性。 选择原始参数需要选择三个组(G$、H美元和K美元 ) 。 莱昂纳迪和Ruiz-Lopez在他们的论文中声称,当G$和K美元是贝利人时,他们的公用钥匙加密系统就不是量子安全。 在本文中,我们研究有限的阿贝利人组的安全性(G$、H$和经典案例的K美元 ) 。 此外,我们还研究与可溶性组一起对即时袭击的数量。</s>