Blind signature (BS) plays one of key ingredients in electronic cash or electronic voting system. However, the key exposures bring out very serious problems in insecure mobile devices. Forward-secure blind signatures preserve the validity of past signatures and prevent a forger from forging past signatures even if current secret key has been compromised. In this paper, we propose the first forward-secure identity-based shorter blind signature scheme from lattices which can resist quantum attack, and prove that our scheme satisfies the security requirements of blindness, unforgeability, and forward secrecy in the random oracle model. Furthermore, we also extend our construction to a forward-secure identity-based shorter blind signature in the standard model.
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.
The security of digital signatures depends significantly on the signature key. Therefore, to reduce the impact of leaked keys upon existing signatures and subsequent ones, a digital signature scheme with strong forward security could be an effective solution. Most existing strong forward-secure digital signature schemes rely on traditional cryptosystems, which cannot effectively resist quantum attacks. By introducing lattice-based delegation technology into the key-iteration process, a two-direction and lattice-based key-iteration algorithm with strong forward security is proposed. In the proposed algorithm, a unique key pair is assigned to the signer in every period. Based on the proposed algorithm, a strong forward-secure signature scheme is further put forward, which achieves resistance to quantum attacks. Performance analysis shows that under the security assumption of the SIS problem on the lattice, the proposed strong forward-secure signature scheme is existentially unforgeable under the random oracle model. Ultimately, based on the proposed strong forward-secure signature scheme, a remote identity-authentication scheme that is resistant to quantum attacks is proposed, ensuring post-quantum security in the user-authentication process.
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,βproblem forβ=O(dn). Our main technique is the rejection sampling theory. The expected number of times needed to output a blind signature is at moste2under aborting, and our new scheme has much smaller signature size than those of all the previously proposed blind signature schemes over lattices.
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.
Group signatures allow users to sign messages on behalf of a group without revealing authority is capable of identifying the user who generated it. However, the exposure of the user's signing key will severely damage the group signature scheme. In order to reduce the loss caused by signing key leakage, Song proposed the first forward-secure group signature. If a group signing key is revealed at the current time period, the previous signing key will not be affected. This means that the attacker cannot forge group signatures regarding messages signed in the past. To resist quantum attacks, many lattice-based forward-secure group signatures have been proposed. However, their key-update algorithm is expensive since they require some costly computations such as the Hermite normal form (HNF) operations and conversion from a full-rank set of lattice vectors into a basis. In this paper, we propose the group signature with forward security from lattice. In comparison with previous works, we have several advantages: Firstly, our scheme is more effective since we only need to sample some vectors independently from a discrete Gaussian during the key-update algorithm. Secondly, the derived secret key size is linear instead of quadratic with the lattice dimensions, which is more friendly towards lightweight applications. Anonymous authentication plays an increasingly critical role in protecting privacy and security in the environment where private information could be collected for intelligent analysis. Our work contributes to the anonymous authentication in the post-quantum setting, which has wide potential applications in the IoT environment.