A secure and efficient group signature scheme based on multivariate public key cryptography

Group signatures are significant primitive for anonymity, which allow group members to sign messages while hiding in the group, however, the signers remain accountable. Most of the existing schemes on group signature are relying on traditional cryptographic primitives, whereas rapid advancements in quantum computing suggest an originating threat to usual cryptographic primitives. This makes the necessity of quantum computer resistant cryptographic primitives. Multivariate public key cryptography (MPKC) is one of the promising options that may withstand quantum attacks. Its constructions are potential candidates for post-quantum (PQ) cryptography as they are very fast and require only modest computational resources. There are many existing secure and practical multivariate digital signatures. However, there is a deficiency of more advanced multivariate group signature scheme. The existing multivariate group signature has weaknesses in terms of security and efficiency. This paper introduces a new multivariate group signature scheme employing a 5-pass identification protocol and multivariate signature scheme as its building blocks. The proposed signature scheme possesses unforgeability, user's anonymity, unlinkability, exculpability and traceability property. Unlike most of the existing post-quantum group signatures, the sizes of the signatures and the public parameters are not dependent on the number of group users in our construction. It depends only on the security parameters. In particular, our construction is the first MPKC based group signature, where signature size and public parameter size are independent of the number of group users.

Automated summary

Group signatures allow group members to sign messages while hiding their identities, but most existing schemes rely on traditional cryptographic primitives, which may be vulnerable to quantum attacks. Multivariate public key cryptography (MPKC) is a promising option that can withstand quantum attacks and is considered a potential candidate for post-quantum cryptography due to its speed and efficiency. Existing multivariate group signatures have weaknesses in terms of security and efficiency, while the proposed MPKC-based group signature in this paper overcomes these limitations by providing unforgeability, user anonymity, unlinkability, exculpability, and traceability properties.