Abstract: As an important tool of key management, the proxy re-signature scheme can not only simplify the secret key management and certificate management, but also can be used to provide certificate path and so on. Currently, for the difficulty of integer factorizating and logarithm discretization and the insecurity of proxy re-signature schemes in the quantum environments, a proxy re-signature scheme that can resist the attack of quantum has been presented in the literature. The first identity-based proxy re-signature scheme over ideal lattice is constructed in this paper, by using ideal lattice and based on the difficulty of the Small Integer Solution（SIS） problem. Compared with other proxy re-signature scheme that has the same properties, this has a shorter signature, and public key, and the advantage of decreasing the computational complexity.

Key words: proxy re-signature, ideal lattice, Small Integer Solution （SIS） problem

摘要： 代理重签名作为密钥管理的一个重要工具，它不仅能够简化密钥管理、简化证书管理，还能够提供路径证明等功能。目前，针对基于大整数分解与离散对数的困难问题，在量子环境下代理重签名方案的不安全性，有人提出了一种能够抵抗量子攻击的代理重签名。利用理想格，以及基于理想格上的小整数解的困难性，构造了理想格上基于身份的代理重签名方案，该方案与其他的具有相同性质的基于身份的代理重签名方案相比，具有较短的签名和公钥、运算复杂度降低的优点。

关键词: 代理重签名, 理想格, 小整数解问题