Nowadays, blockchain has become one of the most cutting-edge technologies, which has been widely concerned and researched. However, the quantum computer attack seriously threatens the security of blockchain, and related research is still less. Targeting at this issue, in this paper, we present the definition of post-quantum blockchain (PQB) and propose a secure cryp-tocurrency scheme based on PQB, which can resist quantum computer attacks. Firstly, we propose a signature scheme based on lattice problem. We use lattice basis delegation algorithm to generate secret keys with selecting a random value, and sign message by preimage sampling algorithm. In addition, we design the first-signature and last-signature in our scheme which are defined as double-signature. It is used to reduce the correlation between the message and signature. Secondly, by combining the proposed signature scheme with blockchain, we construct the PQB and propose this cryptocurrency scheme. Its security can be reduced to the lattice short integer solution (SIS) problem. At last, through our analysis, the proposed cryptocurrency scheme is able to resist the quantum computer attack and its signature satisfies correctness and one-more unforgeability under the lattice SIS assumption. Furthermore, compared with previous signature schemes, the sizes of signature and secret keys are relatively shorter than that of others, which can decrease the computational complexity. These make our cryptocurrency scheme more secure and efficient.

Internet of Things (IoT) has been widely used in various fields of our daily life in the past years. Obviously, in the future, the significance of its security will be more evident and enormous. However, there are still many security issues in the IoT, which makes it vulnerable to be attacked easily by some potential factors. Targeting at these issue, in this paper, we propose a secure access management scheme in IoT based on blockchain. Firstly, in our work, by using the Decisional Learning with Error (DLWE) problem, we propose a secure Key-policy Attribute-based Encryption (KP-ABE) scheme, it can implement fine-grained access control in IoT. Secondly, we use blockchain to solve the authentication and access management challenges. In addition, the smart contract in blockchain can process transactions automatically, which greatly reduces the management cost and running time for this scheme. Last but not the least, we further analyze the security of our proposed scheme. The result shows that our scheme can resist some common attacks in IoT, and it is more secure and efficient.

Although the copyright protection schemes supported by blockchain have significantly changed traditional copyright data management, there are still some data security challenges that cannot be ignored, especially the secure access and controllable management of copyright data. Quantum computing attacks also pose a threat to its security. Targeting these issues, we design and propose a blockchain copyright protection scheme based on attribute-based encryption (ABE). In this scheme, the security advantages of blockchain technology are utilized to ensure the authenticity and integrity of copyright data. Based on lattice cryptography and the decision ring learning with errors (R-LWE) problem, a new ABE algorithm that supports searchable ciphertext and policy updates is designed. Then, we introduce it into the blockchain copyright protection scheme, which enables secure access to copyright data and fine-grained control. In addition, the lattice cryptography can strengthen this scheme against quantum attacks. Through security analysis, our scheme can prove to be secure against adaptive chosen keyword attacks, selective chosen plaintext attacks, and adaptive chosen policy attacks in the random oracle model. More importantly, the comparison analysis and experimental results show that our proposed approach has lower computation costs and storage costs. Therefore, our scheme has better security and performance in copyright protection.

Applying blockchain to copyright protection is currently a popular research trend. However, the characteristics of blockchain open data also lead to the threat of copyright privacy leakage. Targeting at this issue, we design a secure digital copyright protection scheme based on blockchain and ring signature algorithm, which can achieve privacy protection of copyright information and improve the efficiency of data authentication. In this paper, we design a new ring signature scheme based on lattice. In this scheme, by using the lattice basis delegation algorithm, user’s public-private key pair is generated without expanding the dimension of lattice. Subsequently, according to the rejection sampling, message is signed by signer’s secret keys and other ring participants’ public keys. It can reduce scheme’s computational complexity. Finally, by combining ring signatures with blockchain technology, a new copyright protection scheme is proposed. More importantly, this scheme is proven to be secure with its correctness and anonymity. Meanwhile, it has less communication costs and shorter key sizes than those in other similar schemes. The results show that the proposed new scheme has good performance and efficiency.

Quantum computing increases the security risks of data in intelligent Internet of Things (IoT) based on traditional cryptography. Multivariate public key cryptography has the security advantage of resisting quantum computing and Rainbow is an important research focus in it. However, the Rainbow algorithm’s secret keys are too large to suitable for resource-constrained IoT system. We propose an efficient Rainbow signature scheme based on circulant and Toeplitz matrices for intelligent IoT. In our scheme, the variable matrices of polynomials have special forms constructed from circulant and Toeplitz matrices. Every variable matrix of central maps and public key polynomials is divided into four submatrices. Three submatrices of variable matrices are generated using seeds randomly chosen. The fourth submatrix is generated by an affine map and three submatrices. Therefore, the public key consists of seeds and variables in the fourth submatrices, rather than all variables of polynomials. Then, the correctness of our scheme has been proved and we provide a security analysis. More specifically, it is proved that the scheme can resist five attacks against Rainbow, such as Direct attacks, Unbalanced oil vinegar attacks, MinRank attacks, HighRank attacks, and Rainbow-band-separation attacks. At last, according to the experimental results, our system’s public key sizes are 97.96% smaller and private key size are 92.12% than the key sizes of the standard Rainbow scheme. Additionally, compare with other Rainbow-like schemes, the comparison analysis and experimental results show that our scheme has less communication costs and small key size than those in the similar literatures for IoT.