In the Forward Secure Ordered Aggregation (FssAgg) signature system, the signer gradually and orderly aggregates the signatures under different keys in different periods into one signature in a hierarchical “onion-like” manner. Among them, the innermost signature is the first signature. In addition, compared with ordinarily ordered aggregate signatures, forward secure requested aggregate signatures are the aggregation of different signatures of the same signer rather than the signatures of additional signers so that the signature verifier can use public key complete verification of all aggregation processes. The forward-safe ordered aggregate signature has the advantages of both forward-secure signature and aggregate signature. It has been widely used in many application scenarios, such as log systems and blockchains. Several existing forward-safe ordered aggregate signatures are based on traditional number theory problems, which will no longer be problematic in the post-quantum era. Therefore, finding a forward-safe requested aggregate signature in the quantum computing environment is imminent. Based on the small integer solution problem on the lattice, a forward-secure lattice-based rated aggregate signature scheme under the standard model is constructed. To achieve high efficiency, the system uses fixed-dimensional lattice-based delegation technology to realize critical updates and achieve forward security; then, the message to be signed and the difficulty problem on the lattice are respectively embedded into the signature using message addition technology and preimage sampling algorithm, making the signature unforgeable under the standard model.
In the Forward Secure Ordered Aggregation (FssAgg) signature system, the signer gradually and orderly aggregates the signatures under different keys in different periods into one signature in a hierarchical “onion-like” manner. Among them, the innermost signature is the first signature. In addition, compared with ordinarily ordered aggregate signatures, forward secure requested aggregate signatures are the aggregation of different signatures of the same signer rather than the signatures of additional signers so that the signature verifier can use public key complete verification of all aggregation processes. The forward-safe ordered aggregate signature has the advantages of both forward-secure signature and aggregate signature. It has been widely used in many application scenarios, such as log systems and blockchains. Several existing forward-safe ordered aggregate signatures are based on traditional number theory problems, which will no longer be problematic in the post-quantum era. Therefore, finding a forward-safe requested aggregate signature in the quantum computing environment is imminent. Based on the small integer solution problem on the lattice, a forward-secure lattice-based rated aggregate signature scheme under the standard model is constructed. To achieve high efficiency, the system uses fixed-dimensional lattice-based delegation technology to realize critical updates and achieve forward security; then, the message to be signed and the difficulty problem on the lattice are respectively embedded into the signature using message addition technology and preimage sampling algorithm, making the signature unforgeable under the standard model.
In the forward secure sequential aggregate (FssAgg) signature scheme, the signer combines signatures generated in different intervals under different secret keys incrementally and sequentially in a layered “onion-like” fashion with the first signature innermost in the aggregate. In contrast with general (not forward-secure) aggregate signature schemes which aggregate signatures from multiple signers, a FssAgg signature scheme aggregates signatures of a single signer not the signatures of different signers, so the verifier uses a single public key to verify the entire aggregate. With the advantages of forward secure signature and the aggregate signature at the same time, the FssAgg signature scheme has been widely applied in logging systems and blockchain since it was proposed in 2007. Although there have been several FssAgg signature schemes, all of them are based on the classic number theory problem, which are no longer secure in the quantum era. So looking for the quantum-immune FssAgg signature is much urgent. Based on the small integer solution over lattice, a FssAgg signature in the standard model is proposed. In order to improve the efficiency, this paper uses the fixed-dimensional lattice basis delegation technique to update the keys, and the forward security is achieved. This paper uses the message addition technique and the pre-image sampling technique to embed the message and the small integer solution into the signature process, and the existentially unforgeability of the scheme is also guranteed in the standard model.
The forward secure sequential aggregate (Fss-Agg) signature has the advantages of forward secure signature and the sequential aggregate signature at the same time. Since its proposal in 2007, it has been widely applied in many application scenarios, such as logging systems, e-business, e-government, blockchain, etc. Although there have been several Fss-Agg signature schemes, all of them are based on the classic number theory problem, which are no longer secure in the quantum era when the general quantum computers become reality. So looking for the quantum-immune Fss-Agg signature is much urgent. In this paper, the definition of Fss-Agg signature scheme is described, and the forward security and the existential unforgeability under the chosen message attack are combined to define the existential unforgeability of Fss-Agg signature aganist chosen message attack. Based on the small integer solution assumption on lattice, using the pre-image sampling and the lattice basis delegation techniques, the quantum-immune Fss-Agg signature is proposed, which is the first lattice-based Fss-Agg signature scheme. It is proven to be correct, forward secure and existentially unforgeable in the random oracle model.
An aggregate signature turns multi-message multi-authentication into multi-message single-authentication, reducing the required storage space, transmission cost, and number of verification calculations, and is suitable for fast message authentication in the big data era, particularly in wireless sensor networks and secure email systems. Many aggregate signature schemes have been proposed, including lattice-based ones, which have good resistance to quantum machine attacks. However, the existing lattice-based aggregate signature schemes, which either have strict requirements on the signing order or encounter security risks, are not suitable for the unordered polymerization environment. In this paper, we accordingly propose a lattice-based unordered aggregate signature scheme. The proposed scheme makes use of the intersection method and solves the unordered aggregate problem of lattice signatures with different public keys. Therefore, it avoids both the signing order limitation and the risk of single signature forgery. Furthermore, the scheme follows the improved security model; hence, it is robust against collusion attacks. In addition, the scheme's security depends on the small integer solution problem, which enables the scheme to resist quantum algorithm attacks.
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.
Ring signatures, a novel cryptographic primitive, were introduced by Rivest, Shamir, and Tauman at ASIACRYPT 2001. It allows a member of a group to sign a message on behalf of an ad-hoc group of users, known as a ring, without revealing its identity. Ring signatures, initially introduced for applications such as whistle-blowing and confidential disclosures, have since gained significant relevance and widespread adoption across various domains, including blockchain technologies, ad-hoc networks, anonymous transactions, location-based services, cloud computing platforms, and outsourced computation. However, traditional ring signatures are vulnerable if the signers’ keys are compromised. To resolve this vulnerability, Liu and Wong introduced the notion of forward-secure ring signatures at IJNS 2008. Forward-security ensures that even if a signer’s secret key is compromised, signatures generated in prior time periods remain secure. It significantly reduces the damage caused by secret key exposure, making it crucial for long-term security in applications such as whistle-blowing or anonymous authentication. However, most existing forward-secure ring signature schemes are based on number-theoretic assumptions, making them vulnerable to quantum adversaries. Yu and Wang proposed a quantum-safe forward-secure ring signature scheme at ICICS 2023, and Yu et al. further extended this work in Computer Networks (2025), retaining the same ring signature scheme with forward security. But the scheme suffers from large signatures that grow linearly with the ring size. In this paper, we propose a lattice-based forward-secure ring signature scheme in the quantum random oracle model ( QROM ) that simultaneously achieves security against quantum adversaries and compact signature size. Notably, the signature size is logarithmic in the number of members in the ring, enabling significantly better scalability compared to prior constructions.
The provably secure public-key cryptosystems in the standard model are more practical,but the provably secure lattice-based proxy signature schemes in the standard model have not been constructed up to now. A new lattice-based proxy signature scheme was constructed by using the Boyen's preimage sampling algorithm. The proposed proxy signature scheme was proved to satisfy the existential unforgeability against adaptive chosen-message attacks based on the hardness of the small integer solution( SIS) problem in the standard model. Finally,the computational performance of the proposed proxy signature scheme was compared with that of the existing lattice-based proxy signature schemes. The comparative results showed that the proposed proxy signature scheme has higher efficiency.