Novel and Efficient Rainbow Signature Scheme Based on Circulant and Toeplitz Matrices for Intelligent IoT

Abstract

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.