理想格上高效公钥加密方案

目前现存的R—LWE公钥加密方案，普遍存在公钥尺寸大、密文扩展率高的缺陷。给出一种高效的理想格上公钥加密方案，在多用户环境中，借助一个基于广义背包难题的可抵抗碰撞的哈希函数构造用户的公私钥对，缩短了公钥长度；通过增加整个密文中携带消息密文的份额，有效降低了加密每比特明文的平均开销。在安全性方面，由公钥恢复私钥的困难性可以归约到理想格中SVP问题，对密文的攻击相当于求解判定性R—LWE问题。因此，方案能够达到CPA安全性。

An Efficient Public Cryptosystem Based on Ideal Lattices

Most of the present public cryptosystems based on R-LWE have the drawbacks of large public-key size and high encryption blowup factor. We propose an improved scheme which further reduces the length of public-key generated by a hash function from generalized compact knapsacks in multi-user environments. In additions, we increase the proportion of the ciphertext with message compared with overall ciphertext so as to reduce the average cost of encrypting one bit. The hardness of recovering private-key from public-key can be reduced to solve the Ideal-SVP problem, and the attack to the ciphertext is equivalent to solving the decisional R-LWE hard assumption. So the scheme proposed can realize the CPA security.