With the rapid development of electronic information technology, digital signature has become an indispensable part of our lives. Traditional public key certificate cryptosystems cannot overcome the limitations of certificate management. Identity-based cryptosystems can avoid the certificate management issues. The development of quantum computers has brought serious challenges to traditional cryptography. Post-quantum cryptography research is imperative. At present, almost all post-quantum identity-based signature (IBS) schemes are constructed using Gaussian sampling or trapdoor technologies. However, these two technologies have a great impact on computational efficiency. To overcome this problem, we construct an IBS scheme on lattices by employing Lyubashevsky’s signature scheme. Based on the shortest vector problem on lattices, our scheme does not use Gaussian sampling or trapdoor technologies. In the random oracle model, it is proved that our scheme is strongly unforgeable against adaptive chosen messages and identity attacks. The security level of our scheme is strongly unforgeable, which is a higher level than the existential unforgeability of other schemes. Compared with other efficient schemes, our scheme has advantages in computation complexity and security.

随着电子信息技术的飞速发展，数字签名已成为我们生活中不可或缺的一部分。传统的公钥证书密码系统无法克服证书管理的局限性。基于身份的密码系统可以避免证书管理问题。量子计算机的发展给传统密码学带来了严峻的挑战。后量子密码学研究势在必行。目前，几乎所有基于量子身份的签名（IBS）方案都是使用高斯采样或活板门技术构建的。但是，这两种技术对计算效率有很大的影响。为了克服这个问题，我们通过使用Lyubashevsky的签名方案在格子上构造了IBS方案。根据晶格上的最短向量问题，我们的方案不使用高斯采样或活板门技术。在随机预言模型中，证明了我们的方案对于自适应选择的消息和身份攻击是不可伪造的。我们方案的安全级别是高度不可伪造的，它比其他方案的存在不可伪造性更高。与其他高效方案相比，我们的方案在计算复杂度和安全性方面具有优势。