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International Conference on Cyber Security and Information Engineering (ICCSIE)

Fine-grained Privately Puncturable Signatures with Adaptive Security from Lattices

Junshuai Zhang, Zhenhua Liu, Dongdong Yao

Published Jul 23, 2025• 1 citation
Publisher

Abstract

Puncturable digital signatures, enable fine-grained revocation of signing authority but typically offer security only against static adversaries. To address this limitation, this paper construct a lattice-based signature scheme that supports private puncturing and achieves adaptive security in the random oracle model. This paper design integrates a private puncturable pseudorandom function (Private PRF), which allows secure secret key updates without revealing any information about the punctured messages or their corresponding signatures. This ensures existential unforgeability under adaptive chosen message attacks. The results demonstrate the feasibility of achieving adaptively secure, privacy-preserving puncturable signatures under post-quantum assumptions.

DOI
10.1145/3759179.3760358

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Puncturable digital signatures, enable fine-grained revocation of signing authority but typically offer security only against static adversaries. To address this limitation, this paper construct a lattice-based signature scheme that supports private puncturing and achieves adaptive security in the random oracle model. This paper design integrates a private puncturable pseudorandom function (Private PRF), which allows secure secret key updates without revealing any information about the punctured messages or their corresponding signatures. This ensures existential unforgeability under adaptive chosen message attacks. The results demonstrate the feasibility of achieving adaptively secure, privacy-preserving puncturable signatures under post-quantum assumptions.
The security of traditional identity-based signatures wholly depends on the security of secret keys.Exposure of secret keys requires reissuing all previously assigned signatures.Based on this,to revoke private key leaks or malicious users in the signature scheme,an adaptive secure revocable identity-based signature over lattices is proposed,which provides an efficient revocation mechanism to revoke misbehaving or compromised users from the systems.The scheme is proved to be strongly Unforgeable against adaptive Chosen-message Attacks(sUFCMA)under Small Integer Solution(SIS)assumption.Security analysis results show that the proposed scheme not only can meet the security of revocable identity-based signature,but also can resist the quantum attack.
Strongly unforgeable signature schemes provide a more stringent security guarantee than the standard existential unforgeability. It requires that not only forging a signature on a new message is hard, it is infeasible as well to produce a new signature on a message for which the adversary has seen valid signatures before. Strongly unforgeable signatures are useful both in practice and as a building block in many cryptographic constructions. This work investigates a generic transformation that compiles any existential-unforgeable scheme into a strongly unforgeable one, which was proposed by Teranishi et al. and was proven in the classical random-oracle model. Our main contribution is showing that the transformation also works against quantum adversaries in the quantum random-oracle model. We develop proof techniques such as adaptively programming a quantum random-oracle in a new setting, which could be of independent interest. Applying the transformation to an existential-unforgeable signature scheme due to Cash et al., which can be shown to be quantum-secure assuming certain lattice problems are hard for quantum computers, we get an efficient quantum-secure strongly unforgeable signature scheme in the quantum random-oracle model.
With the rapid development of electronic information technology, digital signature has become an indispensable part of our lives. Traditional public key certificate cryptosystems cannot overcome the limitations of certificate management. Identity-based cryptosystems can avoid the certificate management issues. The development of quantum computers has brought serious challenges to traditional cryptography. Post-quantum cryptography research is imperative. At present, almost all post-quantum identity-based signature (IBS) schemes are constructed using Gaussian sampling or trapdoor technologies. However, these two technologies have a great impact on computational efficiency. To overcome this problem, we construct an IBS scheme on lattices by employing Lyubashevsky’s signature scheme. Based on the shortest vector problem on lattices, our scheme does not use Gaussian sampling or trapdoor technologies. In the random oracle model, it is proved that our scheme is strongly unforgeable against adaptive chosen messages and identity attacks. The security level of our scheme is strongly unforgeable, which is a higher level than the existential unforgeability of other schemes. Compared with other efficient schemes, our scheme has advantages in computation complexity and security.
Blind signature schemes (BSS) play a pivotal role in privacy-oriented cryptography. However, with BSS, the signed message remains unintelligible to the signer, giving them no guarantee that the blinded message he signed actually contained valid information. Partially BSS (PBSS) were introduced to address precisely this problem. In this study, the authors present the first leakage-resilient, lattice-based PBSS in the literature. The proposed construction is provably secure in the random oracle model and offers quasi-linear complexity w.r.t. key/signature sizes and signing speed. In addition, it offers statistical partial blindness and its unforgeability is based on the computational hardness of worst-case ideal lattice problems for approximation factors in O ~ ( n 4 ) in dimension n. The proposed scheme benefits from the subexponential hardness of ideal lattice problems and remains secure even if a ( 1 − o ( 1 ) ) fraction of the signer's secret key leaks to an adversary via arbitrary side-channels. Several extensions of the security model, such as honest-user unforgeability and selective failure blindness, are also considered and concrete parameters for instantiation are proposed.
Certificateless signatures (CLS) are noticeable because they may resolve the key escrow problem in ID-based signatures and break away the management problem regarding certificate in conventional signatures. However, the security of the mostly previous CLS schemes relies on the difficulty of solving discrete logarithm or large integer factorization problems. These two problems would be solved by quantum computers in the future so that the signature schemes based on them will also become insecure. For post-quantum cryptography, lattice-based cryptography is significant due to its efficiency and security. However, no study on addressing the revocation problem in the existing lattice-based CLS schemes is presented. In this paper, we focus on the revocation issue and present the first revocable CLS (RCLS) scheme over lattices. Based on the short integer solution (SIS) assumption over lattices, the proposed lattice-based RCLS scheme is shown to be existential unforgeability against adaptive chosen message attacks. By performance analysis and comparisons, the proposed lattice-based RCLS scheme is better than the previously proposed lattice-based CLS scheme, in terms of private key size, signature length and the revocation mechanism.
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.