Public key, linear multivariate encryption system

The computer-implemented method for encrypting a plaintext message represented by an n x n rational matrix M is disclosed, wherein a ciphertext message (Y) represented by three n x n rational code matrices Y1, Y2, Y3 is produced. The method comprises the steps of providing (100) an arbitrary n x n rational random error matrix E, where E≠0; from the matrix M computing (110) the code matrices Y1, Y2, Y3 according to the following algorithm: X1·K1 + K3·X2 = Y1; X1·K1 + K4·X2 = Y2; X1·K2 + ϕ(M) + K5·X2 = Y3, where K1 = Q·A, K2 = Q·B, K3 = C·R, K4 = D·R and K5 = G·R and ϕ is an invertable matrix function, and wherein the matrices Ki and the matrix function φ are used as a public key, and the matrices A, B, C, D and G, as well as the random error matrix E are kept in secret; and finally outputting (120) the code matrices Y1, Y2, Y3 representing the ciphertext message (Y).