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.
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 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
Among post-quantum alternatives, latticebased cryptography is the most promising one, due to its simple operations, reduction from aver-age-case to worstcase hardness, and supporting of rich functionalities. Ring signature enables a user to sign anonymously on behalf of an adaptively chosen group, and has multiple applications in anonymous e-voting, anonymous authentication, whistle blowing etc. However, most lattice-based ring signature schemes were constructed in the random oracle model from lattice basis delegation and they suffer large verification key sizes as a common disadvantage. This work proposes an efficient ring signature scheme from lattice basis delegation without random oracle based on the extended split-SIS problem, whose security is approximately as hard as the worst-case SIVP problem. Our scheme is proved to be anonymous and existentially unforgeable under latticebased assumptions. Finally, the verification key size is significantly reduced to a small constant, instead of increasing linearly with the number of ring members.
A group signature allows a group member who signs the message on behalf of the other group members. Any recipient also verifies the signature without knowing the signer. However, it is possible to reveal the signer’s identity since the group signatures have the tracing mechanism. In general, the group signature size increases the number of group members. However, the schemes are also proposed with the constant signature size. On the other hand, the security of some schemes are based on the discrete logarithm and factorization problems while some schemes which are secure against quantum attacks are proposed. To the best of our knowledge, the signature scheme in the group concept has not been proposed on lattices in quantum oracles. In this paper, we propose a new constant-size and partially-dynamic group signature scheme on lattice assumptions. We combine the Dilithium signature scheme, a Stern-like zero-knowledge scheme and Regev’s encryption scheme. We give a zero-knowledge argument system for our proposed scheme and security analysis in the quantum random oracle model. According to the comparison results, the proposed scheme has better size complexity in asymptotic concept.
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.
Abstract A forward-secure group signature (FSGS) ensures the unforgeability of signatures in the past time period despite signing secret key is leaked in the current time period. As we know, traditional FSGS schemes are mostly relying on number-theoretic assumptions unable to resist quantum attacks. Therefore, we present an efficient lattice-based fully dynamic (i.e. users can flexibly join or quit the group) forward-secure group signature (DFSGS) by combining an improved version of FSGS scheme proposed by Ling. Based on an efficient zero-knowledge argument, we construct argument of knowledge of the committed value and the plaintext that help with privacy protection. Our DFSGS scheme is proved to be anonymous and forward-secure traceable relying on short integer solution and learning with errors assumptions in random oracle model. Moreover, the lengths of group public key and signature of our DFSGS scheme have been improved, and the length of user secret key has no connection with the quantity of group members.
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.