Abstract: Embodiments of the invention provide random number generators and methods that are able to generate numbers with infinite possible outcomes while being able to estimate efficiently the probability of random number generation failure due to hardware constraint(s).

Abstract: Embodiments of the invention relate to symmetric encryption that converts plain text to Diophantine equations, i.e. cipher text, and communication of the Diophantine equations by electromagnetic, mechanical and/or matter waves or signals. More particularly, at least one wave characteristic of electromagnetic, mechanical and/or matter waves or signals are utilised to define the Diophantine equations.

Abstract: Embodiments of the invention relate to symmetric encryption that converts plain text to Diophantine equations, i.e. cipher text, and creates a symmetric key which is held by a sender (or encryption apparatus) and a recipient (or decryption apparatus). The key is used by the decryption apparatus to decrypt the Diophantine equations, and convert them to original plain text. Particularly, undecidable encryption and artificial intelligence (AI) are employed in combination. More particularly, the AI would exclude any class of Diophantine equations which has been solved or deciphered without key, or known to be solvable. In the event certain classes of Diophantine equations are solved in the future, the AI will exclude the use of these solved or solvable classes of Diophantine equation in encryption.