Abstract:Multivariate public key cryptosystem is an important method to guarantee the security of communication after quantum computer appears. There are lots of practical multivariate signature schemes, but only a few multivariate encryption schemes show up. The simple matrix encryption scheme proposed by Tao, et al. is an efficient and secure multivariate encryption scheme in PQCrypto2013. However, the ratio of length of cipher text to plain text is always 2. Cubic AB encryption scheme is a way to fix it. It uses a very wide matrix to replace square matrixes (B and C), and the elements of matrix A are random quadratic polynomials. With this method, the ratio of length of cipher text to plain text could be changed easily. Besides, rank attack cannot be used to attack this scheme. At the same time, the length of cipher text and plain text will be shorter, which could make the process of decryption faster.