With the ever-increasing volume of transactions on e-commerce platforms, the protection of consumer privacy becomes a paramount concern. In this context, group signatures have proven to be an effective tool for the privacy-preserving of consumers. However, conventional group signature schemes are unable to effectively and flexibly control the number of user signatures. Moreover, with the advent of the post-quantum era, the existing cryptographic systems for electronic consumer systems, which rely on traditional number theory, will be undermined by quantum computation. This paper presents an event-oriented linkable group signature scheme from lattice that introduces a higher degree of flexibility in terms of signature control. Then, we prove its security in the random oracle model and based on the hardness of module short integer solution and module learning with errors. The security analysis shows that the scheme respectively achieves quantum security levels of 93-bit and 207-bit for two selected parameter sets. We have also evaluated the storage and time cost of the scheme, which indicates that our scheme is quite practical and could have a promising future in the consumer electronics sector.

Federal learning and privacy protection are inseparable. The participants in federated learning need to be the targets of privacy protection. On the other hand, federated learning can also be used as a tool for privacy attacks. Group signature is regarded as an effective tool for preserving user privacy. Additionally, message recovery is a useful cryptographic primitive that ensures message recovery during the verification phase. In federated learning, message recovery can reduce the transmission of parameters and help protect parameter privacy. In this paper, we propose a lattice-based group signature with message recovery (GS-MR). We then prove that the GS-MR scheme has full anonymity and traceability under the random oracle model, and we reduce anonymity and traceability to the hardness assumptions of ring learning with errors (RLWE) and ring short integer solution (RSIS), respectively. Furthermore, we conduct some experiments to evaluate the sizes of key and signature, and make a performance comparison between three lattice-based group signature schemes and the GS-MR scheme. The results show that the message–signature size of GS-MR is reduced by an average of 39.17% for less than 2000 members.

With the rapid growth of online users, protecting user privacy in access control scenarios has become a critical challenge in the field of information security. Group signatures serve as a fundamental cryptographic primitive that enables users to sign on behalf of a group, providing anonymity while supporting traceability of signers. However, traditional group signature schemes, which rely on number-theoretic assumptions vulnerable to quantum algorithms, face significant security threats in the advent of quantum computing. In this paper, we propose a module lattice-based group signature scheme (ML-GS). ML-GS leverages FIPS 204 standard, a recently standardized signature scheme by the National Institute of Standards Technology (NIST), and integrates a dualrejection-sampling signature mechanism with the K-PKE encryption scheme from FIPS 203 standard, forming a “sign-hybrid-encrypt” hybrid structure to ensure both efficiency and traceability. In the key generation phase, we introduce a module Gaussian preimage sampling algorithm that reduces public key size and supports dynamic user enrollment. The security of ML-GS is formally proven in the random oracle model under the Module Learning with Error (MLWE) and Module Short Integer Solution (MSIS) assumptions. Experimental results demonstrate that, compared to existing scheme with equivalent security level, the ML-GS scheme achieves significant improvements in both time and storage overhead.