格上的代理重签名方案

针对量子环境下基于大整数分解与离散对数困难问题代理重签名的不安全性，提出一种能够抵抗量子攻击的代理重签名方案．借助Xagawa的代理重加密技术和格上的无陷门签名技术，构造了第一个基于格的代理重签名方案，并运用格上的小整数解问题(Small Integer Solution，SIS)的困难性对其进行了安全性证明．证明和效率分析结果表明，该方案具有双向性、多次使用性、密钥最优性以及透明性，与基于其他困难问题的代理重签名方案相比，具有渐近计算复杂度低的优点．最后，把该方案扩展为基于身份的代理重签名方案．

Proxy re-signature scheme over the lattice

For the proxy insecurity of the re-signature schemes based on large integer factorization and the discrete logarithm problem in quantum environment, we present a proxy re-signature scheme that can resist the quantum attack. Using Xagawa's proxy re-encryption technology and lattice signatures without trapdoors technology, we construct the first lattice-based proxy re-signature scheme. The security of this scheme is based on the hardness of the Small Integer Solution(SIS) problem. The results of the proof and efficiency analysis show that this scheme has the properties of bidirection, multi-use, optimal key and transparency. Compared with previous schemes relying on other hardness assumptions, it has the advantage of low asymptotic computational complexity. Finally, we extend the scheme to the identity-based proxy re-signature scheme.