Parameterized method for specifying vector finite fields of arbitrary dimensions

Finite fields defined in the form of finite algebras are of significant interest for constructing multivariate-cryptography algorithms with a relatively small size of public key. This application is associated with specifying vector finite fields of dimension m with large number of their modifications for various fixed values of m: A method for parameterized unified generation of multiplication tables of basis vectors is proposed, with the help of which the commutative and associative multiplication operation is specified. The method is represented by a mathematical formula that includes the dimension m and parameters for specifying the distribution of basis vectors and various independent structural constants.