Cryptographic computer machines with novel switching devices

A cryptographic method, comprising:

• performing by a first computer of a modified n-state operation characterized by an n-state operation wherein input n-state data provided on two inputs of the n-state operation is modified by a first n-state reversible inverter and n-state data being generated by the n-state operation is modified by a second n-state reversible inverter with n being an integer greater than 2, wherein
• the n-state operation is selected from the group consisting of modulo-n addition, modulo-n multiplication, known addition over a Finite Field GF(n) and known multiplication over a Finite Field GF(n) and the modified n-state operation is not selected from the group consisting of modulo-n addition, modulo-n multiplication, known addition over GF(n) and known multiplication over GF(n);
• generating by the first computer of data in a cryptographic operation selected from the group consisting of encryption, public key cryptography, message digest generation, and elliptic curve cryptography wherein the modified n-state operation is used;
• and
• exchanging data generated in the cryptographic operation by the first computer with a second computer.

A cryptographic computer device, comprising:

• a processor connected to a memory, the processor enabled to execute instructions retrieved from the memory;
• the processor being configured to perform the steps of a modified n-state operation which is characterized by a modification of an n-state operation the modification including a first n-state reversible inverter applied to n-state data being inputted to the n-state operation and a second n-state reversible inverter being applied to n-state data being outputted by the n-state operation with n being greater than 2, wherein:
• the n-state operation being selected from the group consisting of modulo-n addition, modulo-n multiplication, known addition over a Finite Field (GF(n)) and known multiplication over GF(n) and the modified n-state operation is not selected from the group consisting of modulo-n addition, modulo-n multiplication, known addition over GF(n) and known multiplication over GF(n);
• communication circuitry to transmit n-state data generated by the n-state processing circuit in a cryptographic operation selected from the group consisting of encryption, public key cryptography, message digest generation, and elliptic curve cryptography wherein the modified n-state operation is applied.