基于格(Lattice)的公钥密码体制是继RSA、ECC之后提出的新型公钥密码体制之一,它包括NTRU体制、Ajtai-Dwork体制、GGH体制等。这些体制的安全性基于求最短格向量困难问题(SVP)、求最近格向量困难问题(CVP)等,并且已经证明,这些体制能够抗量子计算攻击。研讨了对格困难问题及格公钥的相互关系,并展望了格困难问题及格公钥的研究方向。 Lattice-based public key cryptosystem is one of the new public-key cryptosystems proposed after RSA and ECC. It includes NTRU system, Ajtai-Dwork system and GGH system. The security of these regimes is based on finding the shortest gridvector problem (SVP) and finding the nearest gridvector problem (CVP), etc., and these systems have been shown to be resistant to quantum computing attacks. This paper discusses the interrelationship between the pass-hard public key and the pass-hard problem and looks forward to the research direction of the pass-hard public key.