Cryptographic machines with N-state lab-transformed switching devices
N-state switching tables are transformed by a Lab-transform into a Lab-transformed n-state switching table. Memory devices, processors and combinational circuits with inputs and an output are characterized by the Lab-transformed n-state switching table and perform switching operations between physical states in accordance with a Lab-transformed n-state switching table. The devices characterized by Lab-transformed n-state switching tables are applied in cryptographic devices. The cryptographic devices perform standard cryptographic operations that are modified in accordance with a Lab-transform.
1. A cryptographic apparatus to modify one or more signals into one or more cryptographic signals in a message transmitted to a receiving device, comprising:
an input of the cryptographic apparatus to receive the one or more signals;
an n-state Lab-transformed switching circuit with n>2 containing an n-state switching circuit with a first n-state reversible inverter at a first and at a second input and with at an output a second n-state inverter, wherein the first and second n-state reversible inverters in combination establish identity wherein an n-state signal is modified by the first n-state inverter into a modified n-state signal and the second n-state inverter has a structure that modifies the modified n-state signal into the n-state-signal and wherein the first n-state inverter is one of n! (factorial n) n-state inverters, the n-state Lab-transformed switching circuit being characterized by a modification of an n-state switching table that characterizes the n-state switching circuit and the n-state Lab-transformed switching circuit is enabled to process signals related to the one or more signals; and
an output of the cryptographic apparatus to provide on a communication channel to the receiving device the one or more cryptographic signals that are based on one or more signals processed by the n-state Lab-transformed switching circuit, wherein cryptographic signals generated from a first set of n-state input signals by the cryptographic apparatus with the n-state switching circuit without applying the first and second inverters are different from cryptographic signals generated from the first set of n-state input signals by the cryptographic apparatus applying the n-state Lab-transformed switching circuit; and
wherein the n-state switching circuit is characterized by one of: an addition over a finite field GF(n), a multiplication over a finite field GF(n), and a multiplication modulo-n and the n-state Lab-transformed switching circuit is part of the cryptographic apparatus to perform one of: an Advanced Encryption Standard encryption or decryption, a Rivest-Shamir-Adleman (RSA) based encryption or decryption, a Diffie-Hellman based key generation, an Elliptic Curve Cryptography (ECC) operation, a message digest generation as defined in a Federal Information Processing Standards Secure Hash Standard (SHS).
2. The cryptographic apparatus of claim 1 , wherein the n-state switching device is characterized by a modulo-n multiplication.
3. The cryptographic apparatus of claim 1 , wherein the n-state switching device is characterized by a multiplication over a finite field GF(n).
4. The cryptographic apparatus of claim 1 , wherein the n-state switching device is characterized by an addition over a finite field GF(n).
5. The cryptographic apparatus of claim 1 , wherein the n-state switching device is characterized by a modulo-n addition.
6. The cryptographic apparatus of claim 1 , wherein the n-state switching device is characterized by a two input operation characterized by an expression mod((i1+i2−1),n)+(((i1+i2−1)>=n)*1), wherein mod means modulo, i1 indicates a state of a first input and i2 indicates a state of a second input.
7. The cryptographic apparatus of claim 1 , wherein the n-state switching device is characterized by a two input operation characterized by an expression (e-i1-i2)mod-n, wherein mod means modulo, i1 indicates a state of a first input and i2 indicates a state of a second input and e is an offset.
8. The cryptographic apparatus of claim 1 , wherein the cryptographic apparatus performs a symmetric encryption or a symmetric decryption operation.
9. The cryptographic apparatus of claim 8 , wherein the cryptographic apparatus performs substantially a Lab-transformed Advanced Encryption Standard (AES) operation.
10. The cryptographic apparatus of claim 1 , wherein the cryptographic apparatus performs a public-key cryptography operation.
11. The cryptographic apparatus of claim 1 , wherein the cryptographic apparatus performs a hashing or message digest operation.
12. The cryptographic apparatus of claim 1 , wherein the cryptographic apparatus performs an elliptic curve cryptography operation.
13. The cryptographic apparatus of claim 1 , wherein the cryptographic apparatus performs an authentication operation.
14. The cryptographic apparatus of claim 1 , wherein the n-state switching device is characterized by an addition or a multiplication over a Finite Field GF(n=p k ) with p a prime number greater than 1 and k an integer greater than 1 and the n-state Lab-transformed circuit is characterized by an n-state switching table that has a zero-element that is different from the n-state switching table that characterizes the n-state switching circuit.
15. The cryptographic apparatus of claim 1 , wherein the n-state switching device is characterized by a multiplication over a Finite Field GF(n=p k ) with p a prime number greater than 1 and k an integer greater than 1 and the n-state Lab-transformed circuit is characterized by an n-state switching table that has a different one-element than the n-state switching table that characterizes the n-state switching circuit.
16. The cryptographic apparatus of claim 1 , wherein the cryptographic apparatus is part of the group consisting of a desktop computer, a server computer, a blade computer, a processor, a controller, a laptop computer, a tablet computer, a smartphone, a chip card, a smart card, an RFID, a FPGA, a phone, an opening device, a FOB, a TV set, and a media player.
17. A method for cryptographic communications of one or more cryptographic signals based on one or more signals between a first computer device and a second computer device over a communication channel, comprising:
receiving on an input of the first computer device the one or more signals;
generating signals based on the one or more signals by an n-state Lab-transformed switching circuit with n>2, the n-state Lab-transformed switching circuit containing an n-state switching circuit with a first n-state reversible inverter at a first and a second input and with at an output a second n-state inverter that in combination with the first n-state reversible inverter establish identity wherein an n-state signal is modified by the first n-state inverter into a modified n-state signal and the second n-state inverter has a structure that modifies the modified n-state signal into the n-state-signal and wherein the first n-state inverter is one of n! (factorial n) n-state inverters, the n-state Lab-transformed switching circuit being characterized by a modification of an n-state switching table that characterizes the n-state switching function; and
providing by the first computer device to the second computing device over the communication channel the one or more cryptographic signals that are based on the signals generated by the n-state Lab-transformed circuit, wherein cryptographic signals generated from a first set of signals by the first computer with the n-state switching device without the first and second inverters are different from cryptographic signals generated from the first set of signals by the first computer with the n-state Lab-transformed circuit; and
wherein the n-state switching circuit is characterized by one of: an addition over a finite field GF(n), a multiplication over a finite field GF(n), and a multiplication modulo-n and the n-state Lab-transformed switching circuit is part of the cryptographic apparatus to perform one of: an Advanced Encryption Standard encryption or decryption, a Rivest-Shamir-Adleman (RSA) based encryption or decryption, a Diffie-Hellman based key generation, an Elliptic Curve Cryptography (ECC) operation, a message digest generation as defined in a Federal Information Processing Standards Secure Hash Standard (SHS).
18. The method of claim 17 , wherein the n-state Lab-transformed circuit is characterized by an operation selected from the group consisting of: an n-state zero Lab-transformed switching device, an n-state one Lab-transformed switching device, an n-state zero-one Lab-transformed switching device and an n-state k-row Lab-transformed switching device.
19. The method of claim 17 , wherein the n-state switching circuit is characterized by an n-state operation from the group of n-state operations consisting of: a modulo-n multiplication, a modulo-n addition, an addition over a finite field GF(n), an addition over a finite field GF(n=2 p and p>1), a multiplication over a finite field GF(n), a multiplication over a finite field GF(n=2 p and p>1), an operation defined by an expression mod((i1+i2−1),n)+(((i1+i2−1)>=n)*1), wherein mod means modulo, i1 indicates a state of a first input and i2 indicates a state of a second input; an operation defined by an expression (e-i1-i2)mod-n, wherein mod means modulo, i1 indicates a state of a first input and i2 indicates a state of a second input and e is an offset, and an operation characterized by k bitwise XOR operations.
20. The method of claim 17 , wherein the method is part of a cryptographic operation selected from the group consisting of: an encryption, a decryption, a hashing or message digest operation, a public-key cryptographic operation, an elliptic curve cryptography operation, an authentication operation and a digital signature operation.