基于理想格的近似平滑投射Hash函数

近似平滑投射Hash（ASPH）函数是基于格（Lattice）的密码学中的一个重要组件，被Katz等用来构造抗量子攻击的口令认证密钥交换（PAKE）协议。已有的ASPH函数均是基于欧氏格上的困难性问题设计的，存在密钥长度过长、实现效率过低等问题。文章基于理想格上的错误学习（R．LWE）问题，设计了能适用于PAKE协议设计的新的公钥加密体制和ASPH函数，并对其安全性进行了证明。与已有方案相比，新体制具有密钥长度短、运算速度快、实现效率高等优点。

Approximate Smooth Projective Hash Functions from Ideal Lattices

An approximate smooth projective hash function is an important primitive of the lattice based cryptography, and it is used to construct password based authenticated key exchange protocol which is resistant to quantum attacks by Katz et al. The available ASPH function based on the hardness of the standard lattice problem has a large key size and impractical implementations. Based on learning with error problem from ideal lattices , this paper designs a new public key encryption scheme and an associated ASPH function that can apply to PAKE protocol, and gives a proof of its security. Compared with the existing system, the new system has a small key size, fast computing speed and high efficiency.