Traceable Signatures is an extension of group signatures that allow tracing of all signatures generated by a particular group member without violating the privacy of remaining members. It also allows members to claim the ownership of previously signed messages. Till date, all the existing traceable signatures are based on number-theoretic assumptions which are insecure in the presence of quantum computers. This work presents the first traceable signature scheme in lattices, which is secure even after the existence of quantum computers. Our scheme is proved to be secure in the random oracle model based on the hardness of Short Integer Solution and Learning with Errors
Traceable Signatures is an extension of group signatures that allow tracing of all signatures generated by a particular group member without violating the privacy of remaining members. It also allows members to claim the ownership of previously signed messages. Till date, all the existing traceable signatures are based on number-theoretic assumptions which are insecure in the presence of quantum computers. This work presents the first traceable signature scheme in lattices, which is secure even after the existence of quantum computers. Our scheme is proved to be secure in the random oracle model based on the hardness of Short Integer Solution and Learning with Errors
Group signature is a cryptographic primitive where any member can anonymously sign a message on behalf of the population they belong to. Several group signatures were proposed based on number-theoretic assumptions. All these schemes are insecure in the presence of quantum computers. Group signatures based on lattice assumptions are believed to be quantum-resistant. In the past few years, group signatures based on lattice assumptions have been proposed and most of them are proved to be secure in random-oracle model. This paper presents a lattice-based group signature scheme without using random-oracle. Our scheme is based on correlation-intractable function ensembles for all evasive relations which are constructed recently based on well-defined assumptions. Security of our scheme is proved based on correlation-intractable function ensembles and hardness of Short Integer Solution and Learning With Errors problem.
Traceable signatures (Kiayas et al., 2004) is an anonymous digital signature system that extends the tracing power of opening authority in group signatures. There are many known constructions of traceable signatures but all are based on number-theoretical/pairing assumptions. For such reason, they may not be secure in the presence of quantum computers. This work revisits the notion of traceable signatures and presents a lattice-based construction provably secure in the quantum random oracle model (QROM).
Abstract Verifiably encrypted signature (VES) schemes are extensively utilized in fair exchange which combine the features of encryption and signature, aiming to provide a solution that can not only verify the validity of signatures but also safeguard the privacy of signatures. With the development of quantum algorithms and quantum computing, it is necessary to construct a VES protocol that can resist attack of quantum computing. At the same time, some new security properties can also be added to the VES protocol to enhance its security. To reach this goal, we propose a state-of-the-art lattice-based verifiably encrypted group signature (VEGS) scheme. In the random oracle model, the VEGS scheme is provably secure under the assumptions of learning with error (LWE) and inhomogeneous small integer solution (ISIS). Our scheme provides five security properties, namely unforgeability, opacity, extractability, anonymity and traceability. The three properties unforgeability, opacity and extractability are the properties that the VES protocol needs to meet, and the anonymity and traceability properties are additional security properties brought by combining with the group signature.
A ring signature (RS) scheme enables a group member to sign messages on behalf of its group without revealing the definite signer identify, but this also leads to the abuse of anonymity by malicious signers, which can be prevented by traceable ring signatures (TRS). Up until that point, traceable ring signatures have been secure based on the difficult problem of number-theoretic (discrete logarithms or RSA), but since the advent of quantum computers, traditional traceable ring signatures may no longer be secure. Thus Feng proposed a lattice based TRS, which are resistant to attacks by quantum computers. However, that works did not tackle the certificate management problem. To close this gap, a quantum-resistant certificateless TRS scheme was proposed in the study. To the best of our knowledge, this is the first lattice based certificateless TRS. In detail, a specific TRS scheme was combined with the lattice-based certificateless signature technology to solve the certificate management problem while avoid key escrow problem. Additionally, a better zero-knowledge protocol is used to improve the computational efficiency of the scheme, and by reducing the soundness error of the zero-knowledge protocol, the number of runs of the zero-knowledge protocol is reduced, so that the communication overhead of the scheme is reduced. Under random oracle model, the proposed scheme satisfies tag-linkability, anonymity, exculpability and is secure based on the SIS problem and the DLWE problem. In conclusion, the proposed scheme is more practical and promising in e-voting.
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.
Identity-based signature is an important technique for light-weight authentication. Recently, many efforts have been made to construct identity-based signatures over lattice assumptions since they would remain secure in future quantum age. In this paper we present a new identity-based signature scheme from lattice problems. This scheme is more efficient than other lattice-based identity-based signature schemes in terms of both computation and communication complexities. We prove its security in the random oracle model under short integer solution assumption that is as hard as approximating several worst-case lattice problems. We also extend the scheme to an identity-based message recovery signature scheme that has better performance.