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Revisiting Lattice-based Non-interactive Blind Signature

Anindya Ganguly, Angshuman Karmakar, Suparna Kundu, Debranjan Pal, Sumanta Sarkar

Published Oct 8, 2025• 0 citations

Abstract

Blind signatures (BS) allow a signer to produce a valid signature on a message without learning the message itself.They have niche applications in privacy-preserving protocols such as digital cash and electronic voting.Non-interactive blind signatures (NIBS) remove the need for interaction between the signer and the user.In the post-quantum era, lattice-based NIBS schemes are studied as candidates for long-term security.In Asiacrypt 2024, Baldimtsi et al. proposed the first lattice-based NIBS construction, whose security relies on the random one-more inhomogeneous short integer solution (rOM-ISIS) assumption.This rOM-ISIS is considered to be a non-standard assumption.Later, Zhang et al. introduced another lattice-based construction in ProvSec 2024, and proved its security under the standard module short integer solution (MSIS) assumption.We analyse the security of the latter scheme.In the random oracle model, we show that it fails to achieve both nonce blindness and receiver blindness.We present explicit attacks where an adversary breaks both properties with probability 1.Our attack is based on a crucial observation that uncovers a flaw in the design.Specifically, this flaw allows an attacker to link a message-signature pair with its presignature-nonce pair.In addition, we also identify a flaw in the unforgeability proof.Finally, we suggest a modification to address the issue, which is similar to Baldimtsi et al. construction, and its security relies again on the non-standard rOM-ISIS assumption.This work again raises the question of the feasibility of achieving NIBS from standard assumptions.

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Blind signatures (BS) allow a signer to produce a valid signature on a message without learning the message itself.They have niche applications in privacy-preserving protocols such as digital cash and electronic voting.Non-interactive blind signatures (NIBS) remove the need for interaction between the signer and the user.In the post-quantum era, lattice-based NIBS schemes are studied as candidates for long-term security.In Asiacrypt 2024, Baldimtsi et al. proposed the first lattice-based NIBS construction, whose security relies on the random one-more inhomogeneous short integer solution (rOM-ISIS) assumption.This rOM-ISIS is considered to be a non-standard assumption.Later, Zhang et al. introduced another lattice-based construction in ProvSec 2024, and proved its security under the standard module short integer solution (MSIS) assumption.We analyse the security of the latter scheme.In the random oracle model, we show that it fails to achieve both nonce blindness and receiver blindness.We present explicit attacks where an adversary breaks both properties with probability 1.Our attack is based on a crucial observation that uncovers a flaw in the design.Specifically, this flaw allows an attacker to link a message-signature pair with its presignature-nonce pair.In addition, we also identify a flaw in the unforgeability proof.Finally, we suggest a modification to address the issue, which is similar to Baldimtsi et al. construction, and its security relies again on the non-standard rOM-ISIS assumption.This work again raises the question of the feasibility of achieving NIBS from standard assumptions.

Blind multisignature (BMS), first introduced by Horster et al, constitutes a crucial primitive that allows a user to generate a signature of a message from multiple signers, while the signers cannot obtain any information about the message. With these useful properties, blind multisignature is suitable for electronic payments and electronic voting. However, most of the current BMS schemes may be attacked by quantum computers in the future because they are based on traditional number theories, such as discrete logarithm assumption and large integer factor assumption. In this work, we first formalize the notion and the sound security models of the identity-based blind multisignature scheme (IDBMS). Then we present an instantiation based on lattices, along with rigorous proofs of the blindness and unforgeability under the lattice hard assumption (short integer solution, SIS), which is considered to remain secure under quantum computer attacks. To the best of our knowledge, it is the first identity-based quantum-resistant scheme that has the advantages of blind signature and multisignature.

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.

Blind signature allows a user to get a signature of a signer on an arbitrary message, and the verifier can convince that the signature is indeed signed by the signer without leaking any information about the message. This property is necessary when the user’s privacy needs protection, such as a bank bill, a trade secret, etc. As an alternative of public key infrastructure, the identity-based system can simplify the key management procedures in certificate-based public key systems. Inspired by the requirement of identity-based blind signature in the post quantum world, we research on identity-based blind signature based on hard lattice problems under the random Oracle model. We propose a construction built upon the blind signature by Rückert, and it is proved to be one-more unforgeable against selective identity and chosen message attacks (sID-CMA) and unconditionally blind. The proposed scheme has 2 moves, and its security can be reduced to the small integer solution (SIS) problem.

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 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.

A proxy blind signature scheme is a special form of blind signature which allowed a designated person called proxy signer to sign on behalf of original signers without knowing the content of the message. It combines the advantages of proxy signature and blind signature. Up to date, most proxy blind signature schemes rely on hard number theory problems, discrete logarithm, and bilinear pairings. Unfortunately, the above underlying number theory problems will be solvable in the postquantum era. Lattice‐based cryptography is enjoying great interest these days, due to implementation simplicity and provable security reductions. Moreover, lattice‐based cryptography is believed to be hard even for quantum computers. In this paper, we present a new identity‐based proxy blind signature scheme from lattices without random oracles. The new scheme is proven to be strongly unforgeable under the standard hardness assumption of the short integer solution problem (SIS) and the inhomogeneous small integer solution problem (ISIS). Furthermore, the secret key size and the signature length of our scheme are invariant and much shorter than those of the previous lattice‐based proxy blind signature schemes. To the best of our knowledge, our construction is the first short lattice‐based identity‐based proxy blind signature scheme in the standard model.