Cryptographic machines characterized by a Finite Lab-Transform (FLT)

A device to provide cryptographic data on a communication channel, comprising:

• a processor and a memory coupled to the processor, wherein the processor is capable of executing programmed instructions stored in the memory to perform the steps:
• processing a message in an n-state symbol format with n greater than 4 in accordance with a modification of an n-state computer operation in a cryptographic method, the cryptographic method being selected from the group consisting of an encryption, a decryption, a Diffie-Hellman key exchange, a message digest generation, an elliptic curve cryptographic operation, a digital signature generation, a message authentication code (MAC) generation, the modification is a Finite Lab Transform (FLT) of the n-state computer operation into a Finite Lab Transformed (FLTed) n-state computer operation, the n-state computer operation is selected from the group consisting of a modulo-n addition, a modulo-n multiplication, an addition over finite field GF(n), a multiplication over finite field GF(n) and an n-state multiplication all with n greater than 4, wherein the FLT includes a reversible n-state inverter on a first input and a same reversible n-state inverter on a second input to the n-state computer operation and a reversing n-state inverter on an output of the n-state computer operation, a combination of the reversible n-state inverter and the reversing n-state inverter establishing identity;
• and wherein
• the FLTed n-state computer operation is different from the n-state computer operation and the FLTed n-state computer operation is not in the group consisting of:
• a modulo-n addition, a modulo-n multiplication, an addition over finite field GF(n=qp) with q a prime number and p greater than 2 and determined by an irreducible polynomial of degree p over GF(q), a multiplication over finite field GF(n=qp) determined by an irreducible polynomial of degree p over GF(q), p bitwise XOR operations with p being greater than 2;
• and
• providing the cryptographic data, generated in accordance with the modification of the cryptographic method, on the communication channel.