ABSTRACT Transitive signatures are a special type of homomorphic signature proposed by Turing Award winners Micali and Rivest, which are highly suitable for authenticating dynamically growing graph‐based data systems. In such a signature scheme, anyone with the signer's public key is allowed to generate a signature for a composed edge , from two signatures on adjacent edges and . To prevent the problem of malicious dissemination of signatures by verifiers leading to data privacy leakage, researchers have proposed a series of universal designated verifier transitive signature (UDVTS) schemes. However, existing work requires that the designated verifier create its own secret‐public key pair using the public key parameters provided by the signer. Besides, these schemes suffer from significant performance defects due to expensive pairing or exponentiation operations. In this work, we design a pairing‐free and exponentiation‐free UDVTS proof scheme based on the SM2 digital signature algorithm and a zero‐knowledge proof scheme. We prove the security of our construction based on rigorous cryptographic assumptions. The performance comparison with related work shows that our UDVTS proof scheme has an optimal computational cost and desirable communication cost. For example, compared to the state‐of‐the‐art work, we reduce the signing cost by and the designated verification cost by .

Cloud auditing enables remote data integrity verification without downloading the entire dataset, significantly advancing cloud storage services. In long-term usage scenarios, key exposure poses a critical challenge, as a compromised private key enables the cloud service provider (CSP) to forge tags for incorrect data. Although key updatable auditing protocols have been proposed to mitigate key exposure risks, most do not support tag updates triggered by key changes, allowing the CSP to still exploit the leaked historical key for tag forgery. In this article, we propose a block tag updatable certificate-based integrity auditing protocol for long-term cloud storage. By leveraging certificate-based cryptography, our protocol eliminates the need for costly secure channels. It supports simultaneous key and tag updates, ensuring that even with previous private key leaks, the CSP cannot forge valid tags under newly updated key-pairs. The protocol achieves high efficiency through: 1) 2-D data partitioning that reduces computational and storage overhead; 2) optimized tag generation requiring only one map-to-point hash function operation for multiple data blocks; 3) strategic delegation of computationally intensive tag update operations to the CSP; and 4) constant-time proof verification regardless of the number of challenged blocks. Security proofs and performance evaluations demonstrate that the protocol offers desirable security and efficiency, making it well-suited for long-term cloud storage.

Abstract Redactable signatures allow the signature holder to remove admissible data blocks in the signed data while generating valid signatures about different redacted data without communicating with the primary signer. Now, this sort of signature has attracted widespread attention due to its many application scenarios such as electronic medical records, smart grids and XML files. However, there are rarely redactable signature schemes that can resist quantum attacks so far. In the wake of quantum calculation era, it is essential to blossom more quantum-resistant redactable signatures for different data structures. Moreover, it is popular to use accumulators to design redactable signature schemes. Unfortunately, the existing accumulators do not support tree data structures. Therefore, this paper first gives the definition of accumulator schemes for trees, and designs a lattice-based accumulator scheme for trees. Our accumulator scheme features shorter accumulator values and a faster witness generation algorithm than existing lattice trapdoor accumulators. Second, this paper resorts to approximate trapdoors and the preimage sampleable technique, and presents a lattice-based redactable signature scheme for trees using our accumulator scheme. Meanwhile, this scheme fulfills unforgeability, transparency and privacy under adaptive chosen-message attacks. Furthermore, the experiment results show that the redactable signature scheme meets actual revision requirements well.

Abstract Linearly homomorphic signatures (LHSs) allow any entity to linearly combine a set of signatures and to provide authentication service for the corresponding (combined) data. The public key of the current known LHSs from lattices in the standard model requires $O(l)$ matrices and $O(k)$ vectors, where $l$ is the length of file identifier and $k$ is the maximum data set size that linear functions support. In this paper, we construct two lattice-based LHS schemes with provable security in the standard model and both schemes can authenticate vectors defined over finite field. First, we present a basic LHS scheme satisfying selective security, based on the full-rank difference hash functions. Second, we modify the chameleon hash function constructed by (Cash, D., Hofheinz, D., Kiltz, E. and Peikert, C. (2010) Bonsai Trees, or How to Delegate a Lattice Basis. In Proc. EUROCRYPT 10, Monaco/French Riviera, May 30 to June 3, pp. 523–552. Springer, Berlin) to construct a linearly homomorphic chameleon hash function (LHCHF), which can be applied to all transformations from selectively secure LHS scheme that authenticates vectors defined over finite field $\mathbb{F}_{p}$ ($p=poly(n)$) to fully secure one, except for a new one that authenticates vectors defined over a small field. Starting from LHCFH and the basic scheme as above, we obtain a fully secure LHS scheme. Both schemes can be used to sign multiple files and have relatively short public keys consisting of $O(1)$ matrices and $O(k)$ vectors.

Abstract The functional encryption scheme designed using the lattice can realize fine-grained encryption and it can resist quantum attacks. Unfortunately, the sizes of the keys and ciphertexts in cryptographic applications based on learning with errors are large, which makes the algorithm inefficient. Therefore, we construct a functional encryption for inner product predicates scheme by improving the learning with errors scheme of Agrawal et al. [Asiacrypt 2011], and its security relies on the difficulty assumption of ring learning with errors. Our construction can reduce the sizes of the keys and ciphertexts compared with the learning with errors scheme.

In this paper, some results of the fuzzy relation inequalities with addition-min composition are given. First, the uniqueness of minimal solutions of this system is discussed. Then, the relation between this system and the corresponding equations' system is introduced. The definition of the critical set is presented, and an algorithm of the critical system is obtained. Finally, an algorithm for the fuzzy relation inequalities is presented.