Since its birth by Chaum, blind signatures have become one of the fundamental components in the so-called e-cash or e-voting. The scheme ensures a message to be blinded before being signed. Among all lattice-based signatures submitted to NIST post-quantum cryptographic standardization, Dilithium is a very promising candidate. The scheme has some advantages such as simple to implement securely, conservative with parameters and minimal in total size of public key and signature. In this paper, we propose a blind signature scheme based on the framework of Dilithium in order to take advantages of Dilithium. The proposed scheme is blind and one-more unforgeable secure in the random oracle model under the hardness of the module Learning with Errors problem MLWE and the module short integer solution problem MSIS.
Since its birth by Chaum, blind signatures have become one of the fundamental components in the so-called e-cash or e-voting. The scheme ensures a message to be blinded before being signed. Among all lattice-based signatures submitted to NIST post-quantum cryptographic standardization, Dilithium is a very promising candidate. The scheme has some advantages such as simple to implement securely, conservative with parameters and minimal in total size of public key and signature. In this paper, we propose a blind signature scheme based on the framework of Dilithium in order to take advantages of Dilithium. The proposed scheme is blind and one-more unforgeable secure in the random oracle model under the hardness of the module Learning with Errors problem MLWE and the module short integer solution problem MSIS.
To overcome the issue of traditional blind signature schemes being vulnerable to quantum computing attacks during interactions over the consumer electronic Internet of Things (CIoT), a new blind signature scheme called CDBS has been developed. The post quantum digital signature technique CRYSTALS-Dilithium, which was standardized by NIST, serves as the foundation for the quantum-resistant blind signature scheme, CDBS, presented in this study. This system is appropriate for a variety of internet application scenarios, including e-ticketing, anonymous payments, and privacy protection, because it integrates the idea of blind signatures, which is not included in typical digital signature schemes. This scheme is designed to resist quantum computing attacks and is based on the post-quantum digital signature algorithm CRYSTALS-Dilithium, which NIST has selected. The whole technique utilizes the Fiat-Shamir signature structure, which consists of five stages: key creation, blinding, signing, unblinding, and verification. The security of the proposed scheme is dependent on the resolution of the Module Learning with Errors (MLWE) problem and the Short Integer Solution (SIS) problem. Additionally, the scheme must satisfy the criteria of correctness, blindness, and unforgeability. According to the test results, the CRYSTALS-Dilithium scheme requires an average of 401.89 μ s for a single round of verification and signing. The CDBS technique takes an average of 657.65 ls for one round of signing and verification since the blinding and unblinding modules are added on top of the original algorithm, increasing the algorithm’s complexity. The software testing results indicate that the average time required to complete a single full blind signature and verification operation is 657.65 microseconds. The suggested system offers a framework for expanding the CRYSTALS-Dilithium digital signature algorithm.
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.
The development of quantum computers is a threat to current cryptographic algorithms, such as the RSA algorithm. Due to this, the development of post quantum cryptography is a topic of research. One digital signature algorithm that is proposed as a quantum proof solution is the Dilithium digital signature system. Dilithium is based on a learning with errors problem (LWE) in which the value of generated signatures includes an error term. The security of Dilithium is based on previous re- search on topics such as the Module LWE problem, the Fiat Shamir transformation with aborts and the Module Short integer solution problem (MSIS ). The reference implementation includes optimization in the signature generation process. By using the number theoretic transform the multiplication of the ring elements is point-wise or in other words in linear time. This thesis presents the mathematical foundations on which the systems security is based on. In addition, the security of digital signatures, identification schemes and the LWE problem are discussed. In the final chapter these topics are brought together to present the Dilithium scheme.
We propose a new lattice-based digital signature scheme MLWRSign by modifying Dilithium, which is one of the second-round candidates of NIST's call for post-quantum cryptographic standards. To the best of our knowledge, our scheme MLWRSign is the first signature scheme whose security is based on the (module) learning with rounding (LWR) problem. Due to the simplicity of the LWR, the secret key size is reduced by approximately 30% in our scheme compared to Dilithium, while achieving the same level of security. Moreover, we implemented MLWRSign and observed that the running time of our scheme is comparable to that of Dilithium.
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 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.