Abstract: Operational n-state digital circuits and n-state switching operations with n and integer greater than 2 execute Finite Lab-transformed (FLT) n-state switching functions to process n-state signals provided on at least 2 inputs to generate an n-state signal on an output. The FLT is an enhancement of a computer architecture. Cryptographic apparatus and methods apply circuits that are characterized by FLT-ed addition and/or multiplication over finite field GF(n) or by addition and/or multiplication modulo-n that are modified in accordance with reversible n-state inverters, and are no longer known operations. Cryptographic methods processed on FLT modified machine instructions include encryption/decryption, public key generation, and digital signature methods including Post-Quantum methods. They include modification of isogeny based, NTRU based and McEliece based cryptographic machines.

Abstract: A system includes a first device to select and transmit a first code by a transmitter to a remote device controlling a mechanism or access to a database or a computing device. The remote device implements a switching device based on the first code; the transmitter in the first device generates a first sequence of signals based on the first code; the switching device in the remote device processes the first sequence of signals and activates the mechanism based on the processing of the first sequence of signals. The first device may be a smartphone, a fob, an access card, or any other computing device.