Systems and methods for data encryption, decryption, and authentication

A computer-implemented method for generating a pair of integer values as matrix dimensions for encrypting data, comprising:

• generating a first pair of integer values (m, n) at random, wherein m represents a number of rows in a matrix and n represents a number of columns in a matrix;
• evaluating at least one property of the first pair of integer values, wherein the at least one property comprises a measure of randomness;
• applying selection logic to the first pair of integer values, wherein the selection logic is configured to accept or reject a pair of integer values based on at least one predefined criterion that is satisfied when the pair of integer values meets a predefined threshold for randomness;
• determining whether the first pair of integer values is accepted or rejected based on the applied selection logic;
• assigning the first pair of integer values as dimensions of a matrix for encrypting data when the first pair of integer values is accepted based on the applied selection logic;
• selecting an ordered sequence of two or more transformation engines, wherein the two or more transformation engines comprise two or more of Transformation Engine P+1, Transformation Engine P−1, Transformation Engine P−153, Transformation Engine m(P+1), or Transformation Engine m(P−1);
• and
• executing a mixing scheme on the matrix for encrypting data.