理想格上基于身份的环签名方案

Identity based ring signature scheme in ideal lattice

现有的签名方案大多是基于双线性对,但在量子计算环境下此类方案被证明是不安全的。格具有运算简单、困难问题难以破解等特点,为了抵抗量子攻击,基于格中标准的小整数解(SIS)困难假设,利用Ducas等提出的理想格技术(DUCAS L,MICCIANCIO D.Improved short lattice signatures in the standard model.Proceedings of the 34th Annual Cryptology Conference on Advances in Cryptology.Berlin:Springer,2014:335-352),构造了一种能够在标准模型下给出安全性证明的基于身份的环签名方案。该方案主要分为4个步骤:主密钥生成算法、签名私钥生成算法、签名算法和验证算法。输出的签名为单个向量。相比同类型格上的签名方案,在一定程度上缩减了公钥、签名私钥及签名的长度,提高了运算效率,适用于轻量级认证,算法的安全性也间接保证了电子商务和云计算等领域的安全性。

The existing signature schemes based on bi-linear pairings were proved to be insecure in quantum computing environment. A lattice has the features of simple computational operations and difficult problems on which are hard to solve. In order to resist the quantum attack, an identity based ring signature scheme was presented based on the assumption of the hardness of lattice problem-Small Integer Solution（ SIS）, and it was provably secure in the standard model by using the Ducas＇ ideal lattice technology（ DUCAS L, MICCIANCIO D. Improved short lattice signatures in the standard model. Proceedings of the 34 th Annual Cryptology Conference on Advances in Cryptology. Berlin： Springer, 2014： 335- 352）. The scheme was mainly divided in to four steps： master key generation algorithm, the signature private key generation algorithm, signature algorithm and validation algorithm. The signature was output as a single vector. Compared to the same type signature schemes,to some extent, the proposed scheme shortens the length of private key, public key and the signature, improves the operation efficiency, in addition, it is also suitable for lightweight authentication, and the security of electronic commerce and cloud computing are indirectly ensured by the security of the signature algorithm.