Summary For the problems that ring signature needs key escrow, has some security risks, and cannot avoid malicious key generation center (KGC) in the post‐quantum era, we design a certificateless ring signature scheme based on lattice (L‐CRSS). In our scheme, the bimodal Gaussian distribution is used to improve the security and efficiency. Compared with the previous ring signature scheme based on lattice, our design does not need key escrow, does not disclose the signer's identity, can avoid malicious KGC, achieves the constant signature size, and has higher security and efficiency in the post‐quantum era. Finally, under random oracle model (ROM), we prove that our scheme is anonymous against the full‐key exposure, and existentially unforgeable against adaptive chosen message attacks (EUF‐CMA).
Summary For the problems that ring signature needs key escrow, has some security risks, and cannot avoid malicious key generation center (KGC) in the post‐quantum era, we design a certificateless ring signature scheme based on lattice (L‐CRSS). In our scheme, the bimodal Gaussian distribution is used to improve the security and efficiency. Compared with the previous ring signature scheme based on lattice, our design does not need key escrow, does not disclose the signer's identity, can avoid malicious KGC, achieves the constant signature size, and has higher security and efficiency in the post‐quantum era. Finally, under random oracle model (ROM), we prove that our scheme is anonymous against the full‐key exposure, and existentially unforgeable against adaptive chosen message attacks (EUF‐CMA).
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.
Among post-quantum alternatives, latticebased cryptography is the most promising one, due to its simple operations, reduction from aver-age-case to worstcase hardness, and supporting of rich functionalities. Ring signature enables a user to sign anonymously on behalf of an adaptively chosen group, and has multiple applications in anonymous e-voting, anonymous authentication, whistle blowing etc. However, most lattice-based ring signature schemes were constructed in the random oracle model from lattice basis delegation and they suffer large verification key sizes as a common disadvantage. This work proposes an efficient ring signature scheme from lattice basis delegation without random oracle based on the extended split-SIS problem, whose security is approximately as hard as the worst-case SIVP problem. Our scheme is proved to be anonymous and existentially unforgeable under latticebased assumptions. Finally, the verification key size is significantly reduced to a small constant, instead of increasing linearly with the number of ring members.
Although the current lattice-based ring signcryption scheme resists quantum attacks,it has large key storage and high encryption/decryption time.The linkable lattice ring signcryption scheme not only can protect signer anonymity,but also can determine whether two signatures are generated by the same signer.Thus,based on the compact Gaussian sampling algorithm and rejection sampling technique,the identity-based linkable ring signcryption scheme is constructed on the NTRU lattice.Firstly,the system master key is generated using the trapdoor generation algorithm on the NTRU lattice.Then private keys of ring members are obtained based on the compact Gaussian sampling algorithm.Finally,the user signature is generated using rejection sampling,and the key encapsulation mechanism encrypts the signature.Security proof in the random oracle model (ROM) that DRLWE and NTRU small integer solutions are difficult to solve ensures confidentiality,unforgeability,unconditional anonymity,and linkability.Performance analysis shows that compared to the lattice-based ring signcryption and linkable ring signature schemes on NTRU,the proposed scheme has a smaller public key and lower encryption/decryption cost,greatly improving efficiency.
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.
With the rapid development of quantum computers and quantum computing, Internet of Things (IoT) networks equipped with traditional cryptographic algorithms have become very weak against quantum attacks. This paper focuses on the privacy-preserving problem in IoT networks and proposes a certificateless ring signature (CLRS) scheme. This CLRS is constructed with lattice theories, which show promising advantages in resisting quantum attacks. Meanwhile, the certificateless mechanism reduces the key control ability of the key generation center (KGC) by adding personal secret keys to the private key generated by the system. Meanwhile, the ring signature mechanism protects users' privacy information through a non-central control mechanism. Next, the security proof in a random oracle model is given, which shows that this CLRS scheme can obtain unforgeability and ensure the signer's anonymity. Its security properties include non-repudiation, traceability, and post-quantum security. Then, the efficiency comparison and performance results show that this CLRS scheme is more efficient and practical than similar schemes. Moreover, this work presents an exploration of the post-quantum cryptographic algorithm and its application in IoT networks.
The certificateless cryptography solves the certificate management and key escrow problems in the Internet of Things. However, these schemes are no longer safe in the quantum environment. Lattice cryptography has become the main method to solve quantum security. At present, only a few lattice-based certificateless signature schemes have been proposed and the use of the trapdoor function limits the efficiency of the lattice cryptography, and the security of these schemes can only reach existential unforgeability. We construct a lattice-based certificateless signature scheme based on Lyubashevsky's signature scheme. The security of our scheme can reach strong unforgeability and the computational efficiency of our scheme is lower than the previous schemes.