Improvement of the Matrix for Simple Matrix Encryption Scheme.

Multivariable public key cryptography is a scheme that can meet the anti-quantum characteristics. The Simple Matrix scheme is constructed using the operations between three matrices. An improved version of the Simple Matrix scheme is proposed in this paper. The public key mapping of the new scheme includes two matrices made up of random cubic polynomials as elements, so that the rank attack is infeasible for the new scheme, and the algebraic attack breaks the system is at least as hard as solving a set of random quadratic equations. One of the private key matrices is improved so that the ratio of the ciphertext to the plaintext of the new scheme is greater than or equal to 2 times, which breaks the fixed ciphertext and plaintext ratio of the Simple Matrix scheme. The new scheme not only has a flexible ratio of the ciphertext to the plaintext to meet different needs, but also increases the redundancy of the ciphertext and further strengthens the security.