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Journal of Information and Intelligence

A new lattice-based partially blind signature with more complete proof

Peiyu Li, Juntao Gao, Xuelian Li

Published Mar 11, 2024• 2 citations
Publisher

Abstract

Partially blind signatures are introduced on the basis of blind signatures, which not only retain the advantages of blind signatures, but also solve the contradiction between anonymity and controllability in blind signatures. With the development of quantum computing technology, it becomes more urgent to construct secure partially blind signature schemes in quantum environments. In this paper, we present a new partially blind signature scheme and prove the security under the Ring-SIS assumption in the random oracle model. To avoid the restart problem of signature schemes caused by rejection sampling, a large number of random numbers are sampled in advance, so that they only need to be re-selected at the current stage without terminating the whole signature process when the conditions are not met. In addition, the hash tree technology is used to reduce communication costs and improve interactive performance. In order to avoid the errors in the security proof of the previous scheme, our proof builds upon and extends the modular framework for blind signatures of Hauck et al., and the correctness, partial blindness, and one-more unforgeability of the scheme are proved in detail according to the properties of the linear hash function.

DOI
10.1016/j.jiixd.2024.03.001

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Partially blind signatures are introduced on the basis of blind signatures, which not only retain the advantages of blind signatures, but also solve the contradiction between anonymity and controllability in blind signatures. With the development of quantum computing technology, it becomes more urgent to construct secure partially blind signature schemes in quantum environments. In this paper, we present a new partially blind signature scheme and prove the security under the Ring-SIS assumption in the random oracle model. To avoid the restart problem of signature schemes caused by rejection sampling, a large number of random numbers are sampled in advance, so that they only need to be re-selected at the current stage without terminating the whole signature process when the conditions are not met. In addition, the hash tree technology is used to reduce communication costs and improve interactive performance. In order to avoid the errors in the security proof of the previous scheme, our proof builds upon and extends the modular framework for blind signatures of Hauck et al., and the correctness, partial blindness, and one-more unforgeability of the scheme are proved in detail according to the properties of the linear hash function.
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On the basis of the signatures scheme without trapdoors from lattice, which was proposed by Vadim Lyubashevsky in 2012, we present a new ring signature scheme from lattice. The proposed ring signature scheme is an extension of the signatures scheme without trapdoors. We prove that our scheme is strongly unforgeable against adaptive chosen message in the random oracle model, and prove that the security of our scheme can be reduced to the hardness of the small integer solution (SIS) problem by rejection samplings. Compared with the existing lattice-based ring signature schemes, our new scheme is more efficient and with shorter signature length.
On the basis of the signatures scheme without trapdoors from lattice, which was proposed by Vadim Lyubashevsky in 2012, we present a new ring signature scheme from lattice. The proposed ring signature scheme is an extension of the signatures scheme without trapdoors. We prove that our scheme is strongly unforgeable against adaptive chosen message in the random oracle model, and prove that the security of our scheme can be reduced to the hardness of the small integer solution (SIS) problem by rejection samplings. Compared with the existing lattice-based ring signature schemes, our new scheme is more efficient and with shorter signature length.
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.
This paper proposes a lattice based multi-mode blind signature framework that uniformly supports three operating modes: full blindness, partial blindness, and non-blindness. The design employs public matrices with trapdoors, combined with hash functions mapping into ℤ𝑞𝑛, short preimage sampling mechanisms, and an identity encryption component to ensure fairness and enable traceability in case of misuse. Based on this construction, the user generates a blinded request, the signer produces a short response bound to the encrypted identity, and the user performs an unblinding step to obtain the final signature. The paper also presents the system model, research methodology, security claims, and parameter discussions in the post-quantum setting. The main properties analyzed include correctness, blindness, partial blindness, existential unforgeability, one more unforgeability, fairness, and traceability under the SIS and one more SIS assumptions. The results indicate that the proposed approach provides a flexible solution for applications requiring a balance between anonymity, accountability, and post-quantum security.
Blind signature offer the protection for sender's privacy and become an important primitive for electronic commerce. In this paper, we present a technique of matrix-vector-blinding for lattice-based blind signature. Building on this result, we propose two hierarchical ID-based blind signature schemes from lattice with and without random oracle, which are secure against quantum attacks. We apply the latest technique of "lattice basis delegation in fixed dimension" from ABB10's[1] scheme to our constructions which contribute to shorter public key and signature. Both of our blind signature schemes are proven to hold the properties of perfect blindness and one-more unforgeableability. Our hierarchical ID-based blind signature schemes are communicationally efficient and needs only one round data exchanges between the signer and the user, and with a shorter public key and signature in comparison with similar schemes[2, 3]. We prove that our scheme is secure assuming that the short integer solution (SIS) problem is hard.