Having the advantages of certificateless signature and the aggregate signature at the same time, certificateless aggregate signature has been widely applied in e-business, e-government and software security since it was proposed in 2007. Although a number of certificateless aggregate signature schemes have been proposed, all of them are based on the classic number theory problem, which are no longer secure in the quantum era. In this paper, a certificateless sequential aggregate signature over number theory research unit lattice is proposed, which is proven to be secure in random oracle model. Moreover, we extend the new scheme into an efficient certificatebased sequential aggregate signature which is also secure in quantum era.
Having the advantages of certificateless signature and the aggregate signature at the same time, certificateless aggregate signature has been widely applied in e-business, e-government and software security since it was proposed in 2007. Although a number of certificateless aggregate signature schemes have been proposed, all of them are based on the classic number theory problem, which are no longer secure in the quantum era. In this paper, a certificateless sequential aggregate signature over number theory research unit lattice is proposed, which is proven to be secure in random oracle model. Moreover, we extend the new scheme into an efficient certificatebased sequential aggregate signature which is also secure in quantum era.
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.
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.
Certificateless cryptography solves the certificate management problem in public-key cryptography and the key-escrow problem in identity-based cryptography. Xie et al. proposed a certificateless signature scheme using NTRU lattices. They proved that their scheme was existential unforgeable for Type I and Type II adversaries under the intractability of the Small Integer Solution (SIS) problem on NTRU lattices in the random oracle model. Subsequently, Hung et al. proposed a revocable certificateless signature scheme on NTRU lattices that gave a revocation method via public channels to revoke illegal or compromised users. They also proved that their scheme was existential unforgeable for Type I, Type II and Type III adversaries under the intractability of the SIS problem. Recently, Wang et al. proposed a certificateless aggregate signature scheme from bilinear pairings and Rezaeibagha et al. proposed a new lightweight certificateless scheme for Industrial Internet of Things from bilinear pairings. The security of their schemes was proven for Type I and Type II adversaries under the intractability of some mathematical problems. In this paper, we show that the two schemes on NTRU lattices are insecure against Type I or Type II adversaries. We also point out invalidity of Wang et al.'s scheme and vulnerability of Rezaeibagha et al.'s scheme against Type I attacks. We then suggest some improvements to prevent our attacks.
Proxy signature plays an important role in distributed systems, mobile agent applications, distributed shared object systems, global distribution networks and mobile communications etc., since it allows the original signer to delegate another proxy signer to sign the message instead of himself. However, the proxy signature schemes constructed on the number theory cannot resist quantum computers attack and depend on the public key infrastructure. To mitigate these problems, the alternative schemes are Identity-based proxy signature constructed on lattice. In this paper, an identity-based proxy signature scheme based on Number theorem research unit (NTRU) lattice is proposed and proven secure in the random oracle. Compared with the other existing identity-based proxy signature schemes, the proposed scheme outperforms them in terms of original signer's signature size and signing key size and proxy signer's signing key size.
A ring signature (RS) scheme enables a group member to sign messages on behalf of its group without revealing the definite signer identify, but this also leads to the abuse of anonymity by malicious signers, which can be prevented by traceable ring signatures (TRS). Up until that point, traceable ring signatures have been secure based on the difficult problem of number-theoretic (discrete logarithms or RSA), but since the advent of quantum computers, traditional traceable ring signatures may no longer be secure. Thus Feng proposed a lattice based TRS, which are resistant to attacks by quantum computers. However, that works did not tackle the certificate management problem. To close this gap, a quantum-resistant certificateless TRS scheme was proposed in the study. To the best of our knowledge, this is the first lattice based certificateless TRS. In detail, a specific TRS scheme was combined with the lattice-based certificateless signature technology to solve the certificate management problem while avoid key escrow problem. Additionally, a better zero-knowledge protocol is used to improve the computational efficiency of the scheme, and by reducing the soundness error of the zero-knowledge protocol, the number of runs of the zero-knowledge protocol is reduced, so that the communication overhead of the scheme is reduced. Under random oracle model, the proposed scheme satisfies tag-linkability, anonymity, exculpability and is secure based on the SIS problem and the DLWE problem. In conclusion, the proposed scheme is more practical and promising in e-voting.
Certificateless signcryption can simultaneously provide certificateless signature and encryption. In recent years, many certificateless signcryption schemes have been proposed. However, these schemes are based on traditional mathematical theory and not have the ability of resisting the quantum computing attacks. Up to now, lattice-based certificateless signature or encryption schemes have been proposed; however, these schemes only have one function and cannot fulfill two functions of certificateless signature and encryption at the same time. In consideration of this reason, in this article, a certificateless signcryption scheme from lattice (L-CLSS) is constructed. L-CLSS has three advantages. First, in the random oracle model, it is provably indistinguishable against adaptive ciphertext-chosen attacks under the intractability of the learning with errors (LWE) problem and unforgeable against adaptive message-chosen attacks under the hardness of small integer solution (SIS) problem. Second, comparison with the cryptographic algorithms under the difficulty of large integer decomposition, L-CLSS can resist the quantum computing attacks. Third, L-CLSS has higher computation efficiency and a lower communication cost than the existing schemes.