Efficient Lattice-Based Ring Signature Scheme without Trapdoors for Machine Learning

Machine learning (ML) and privacy protection are inseparable. On the one hand, ML can be the target of privacy protection; on the other hand, it can also be used as an attack tool for privacy protection. Ring signature (RS) is an effective way for privacy protection in cryptography. In particular, lattice-based RS can still protect the privacy of users even in the presence of quantum computers. However, most current lattice-based RS schemes are based on a strong trapdoor like hash-and-sign, and in such constructions, there is a hidden algebraic structure, that is, added to lattice so that the trapdoor shape is not leaked, which greatly affects the computational efficiency of RS. In this study, utilizing Lyubashevsky collision-resistant hash function over lattice, we construct an RS scheme without trapdoors based on ideal lattice via Fiat‒Shamir with aborts (FSwA) protocol. Regarding security, the proposed scheme satisfies unconditional anonymity against chosen setting attacks (UA-CSA), which is stronger than anonymity against full key exposure (anonymity-FKE), and moreover, our scheme satisfies unforgeability with respect to insider corruption (EU-IC). Regarding computational overhead, compared with other RS schemes that satisfy the same degree of security, our scheme has the highest computational efficiency, the signing and verification time costs of the proposed scheme are obviously better than those of other lattice-based RS schemes without trapdoors, which is more suitable for ML scenarios.