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中文摘要：
代理重签名是简化密钥管理的重要工具，能够提供路径证明和简化证书管理等。目前的代理重签名方案都是基于整数分解与离散对数的，其在量子环境下都不安全。针对这个问题，该文利用原像抽样技术与固定维数的格基委派技术，基于格上的小整数解问题（Small Integer Solution, SIS）的困难性，构造了格上基于身份的代理重签名方案。该方案具有单向性，多次使用性等性质。与其它具有相同性质的基于身份的代理重签名相比，该方案具有验证开销小，渐近复杂度低等优点。
英文摘要：
Proxy re-signature is an important tool for simplifying key management, and can be used to prove a proof for a path, manage group signatures, simplify certificate management and so on. Currently, proxy re-signature schemes are based on large integer factorization and discrete logarithm which are not security in quantum setting. For this problem, the first identity-based proxy re-signature scheme over lattices is constructed in this paper, which uses preimage sampleable technology and lattice basis delegation in fixed dimension technology. Its security is based on the hardness of Small Integer Solution （SIS） problem. This scheme possesses the properties of unidirectional, multi-use and so on. Compared with the previous schemes which have the same properties, the proposed scheme has the advantage of low verification cost and low asymptotic computational complexity.
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