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IEEE Access

A New Post-Quantum Blind Signature From Lattice Assumptions

Pingyuan Zhang, Han Jiang, Zhihua Zheng, Pei-Chu Hu, Qiuliang Xu

Published Jan 1, 2018• 37 citations
Publisher

Abstract

At present, several post-quantum cryptosystems have been proposed, and lattice-based cryptography is the main candidate. Especially in the direction of digital signatures, there are now many practical lattice-based signature schemes. However, there exist few lattice-based signatures with special property such as blind signature. Blind signature was introduced by Chaum for creating untraceable payment system. Then, it is widely used in e-cash and voting, especially in the revolutionary digital cash system based on blockchain. In our paper, we present a method to construct a post-quantum blind signature based on lattice assumptions, and we proved that any existential forger against the security of the resulting scheme can solve the${\text {SIS}}_{q, n, m, \beta }$problem for$\beta = \widetilde {O}(dn)$. Our main technique is the rejection sampling theory. The expected number of times needed to output a blind signature is at most$e^{2}$under aborting, and our new scheme has much smaller signature size than those of all the previously proposed blind signature schemes over lattices.

DOI
10.1109/access.2018.2833103

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At present, several post-quantum cryptosystems have been proposed, and lattice-based cryptography is the main candidate. Especially in the direction of digital signatures, there are now many practical lattice-based signature schemes. However, there exist few lattice-based signatures with special property such as blind signature. Blind signature was introduced by Chaum for creating untraceable payment system. Then, it is widely used in e-cash and voting, especially in the revolutionary digital cash system based on blockchain. In our paper, we present a method to construct a post-quantum blind signature based on lattice assumptions, and we proved that any existential forger against the security of the resulting scheme can solve theSISq,n,m,β{\text {SIS}}_{q, n, m, \beta }SISq,n,m,β​problem forβ=O~(dn)\beta = \widetilde {O}(dn)β=O(dn). Our main technique is the rejection sampling theory. The expected number of times needed to output a blind signature is at moste2e^{2}e2under aborting, and our new scheme has much smaller signature size than those of all the previously proposed blind signature schemes over lattices.
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.
Digital signatures are used to ensure authentication. Blind signature schemes are a special form of digital signatures and important in scenarios which depend on anonymous and secure authentication. (e.g. e-voting) The common digital blind signature schemes are based on asymmetric cryptography with underlying hard problems like integer factorization or discrete logarithm. These hard problems will become weak with the development of quantum computers. To avoid the uselessness of classic cryptography in the post quantum era, it will be important to find alternative methods based on other hard problems. This book deals with the attempt of developing a new blind signature scheme based on lattice signature schemes.
Blind signatures were first introduced by David Chaum. They allow a user to have a message signed by a signer without revealing the message itself. This property is particularly useful in applications such as electronic voting and digital cash, where user anonymity is important. In a blind signature scheme, the user blinds their message before sending it to the signer, who signs the blinded message. The user then unblinds the signed message to obtain a valid signature that can be verified publicly, ensuring that the signer cannot trace the signed message back to the original unblinded version. A good analogy is placing the message inside an envelope and having the envelope signed. Once the envelope is opened, the signature remains valid for the enclosed message, ensuring that the content remains confidential. Such constructions provide anonymity and privacy to the user but given a practical quantum computer, the security of traditional crypto-systems providing such features will be broken. To address this, the development of quantum-resistant cryptographic protocols is essential for maintaining the security of digital transactions and data. Aligning with the same goal, this work aims to thoroughly review the background of lattice-based blind signatures. We start with the foundations of digital signatures in the classical settings and then move on to lattice-based constructions.
This paper proposes an efficient lattice-based blind signature scheme built upon the BLISS framework. By incor porating bimodal Gaussian distributions and rejection sampling techniques, the scheme ensures secure output distributions and prevents information leakage during the signing process. It achieves blindness and one-more unforgeability with only two rounds of interaction, significantly improving efficiency compared to earlier multi-round lattice-based blind signature schemes. Performance analysis demonstrates that the scheme maintains relatively compact parameters, with a public key size of about 20KB, a private key size of 99KB, and a signature size of 120KB. These characteristics make it practical for post-quantum secure environments. Overall, the proposed scheme combines provable security, anonymity, and efficiency, and is well-suited for privacy preserving applications such as blockchain systems, electronic voting, and anonymous payments.
Blind signatures are a central tool for privacy-preserving protocols. They allow users to obtain signatures from a signer without the signer seeing the signed message. For instance, it enables electronic cash: signatures correspond to coins which can be issued by the bank in a privacy-preserving manner via blind signing. To mitigate the risk of key compromise, threshold blind signatures allow the distribution of the signing key amongst N parties. While recent works have focused on improving the security of this primitive in the classical setting, no construction is known to date in the post-quantum setting. We present the first construction of a threshold blind signature secure in the post-quantum setting, based on lattices. We prove its security under an interactive variant of the SIS assumption introduced in [Agrawal et al., CCS’22]. Our construction has a reasonable overhead of a factor of roughly 1.4 X to 2.5 X in signature size over comparable non-threshold blind signatures over lattices under heuristic but natural assumptions.
In the 4th industrial revolution, the blockchain that distributes and manages data through a P2P network is used as a new decentralized networking paradigm in various fields such as manufacturing, culture, and public service. However, with the advent of quantum computers, quantum algorithms that are able to break existing cryptosystems such as hash function, symmetric key, and public key cryptography have been introduced. Currently, because most major blockchain systems use an elliptic curve cryptography to generate signatures for transactions, they are insecure against the quantum adversary. For this reason, the research on the quantum-resistant blockchain that utilizes lattice-based cryptography for transaction signatures is needed. Therefore, in this paper, we propose a blind signature scheme for the blockchain in which the contents of the signature can be verified later, as well as signing by hiding the contents to be signed using lattice-based cryptography with the property of quantum resistance. In addition, we prove the security of the proposed scheme using a random oracle model.