Outline
In the public key algebraic encryption system the ciphered message is produced as two or three matrix functions of the plaintext message and a random error. In the matrix functions, only non-invertable matrices are used as coefficients. The public key is formed by the coefficient matrices. The coefficients matrices are defined as the product of two matrices, one of which is invertable and the other one is non-invertable. The matrices of the private key are produced from the matrix factors of the coefficient matrices of the public key through linear algebraic operations. For determining the matrices of the private key, factorization of the matrices of the public key is necessary. To solve this mathematical problem, there is no known method that could be performed within polinomial time by using a future quantum computer if substantially large matrices with substantially large matrix entries are used. So the encryption method can be regarded a candidate post-quantum cryptographic method.