The present method is directed, in the computer data security field, to cryptographic sponge and hash function processes which are embodied in a computer system and are typically keyless, but highly secure. The processes are based on the type of randomness exhibited by manipulation of the well known three dimensional Rubik's cube puzzle. Computation of the hash or sponge value (digest) is the result of executing in a model (such as computer code or logic circuitry) an algorithm modeling such a puzzle using the message as an input to the cube puzzle algorithm, then executing the cube puzzle algorithm. A state of the modeled cube puzzle (the final cube puzzle arrangement) after execution gives the sponge or hash digest value of the message.