Cryptographic computer machines with novel switching devices
Operational n-state digital gates execute Finite Lab-transformed (FLT) n-state switching functions or n-state switching function tables to process n-state signals provided on at least 2 inputs to generate an n-state signal on an output, with n>2, n>3 and n>64. The FLT is an enhancement of a computer architecture. Cryptographic apparatus and methods apply circuits that are characterized by FLT-ed addition and multiplication over finite field GF(n) or by addition and multiplication modulo-n that are modified in accordance with reversible n-state inverters, and are no longer characterized by known operations. Known cryptographic methods executed with novel n-state digital gates include encryption/decryption, public key generation, message digest and Elliptic Curve Cryptography wherein one n-state switching function is replaced by an FLT'ed n-state switching function.
1. A cryptographic computer system, comprising:
a first and a second computer, each having a processor and each processor configured to execute instructions to perform a modified n-state operation, the modified n-state operation being characterized by an n-state operation that is modified by a first n-state reversible inverter applied to n-state data being inputted on two inputs of the n-state operation and a second n-state reversible inverter being applied to n-state data being outputted by an output of the n-state operation, with n an integer greater than 2 and an n-state being one of n states, wherein:
the n-state operation characterizes an n-state switching function operating on n-state data elements to generate n-state data elements, 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);
the first computer and second computer enabled to exchange n-state data generated by a cryptographic operation selected from the group consisting of encryption, public key cryptography, signature generation, message digest generation, and elliptic curve cryptography wherein the modified n-state operation is applied.
2. The cryptographic computer system of claim 1 , wherein the cryptographic operation is performed in accordance with an Advanced Encryption Standard (AES) wherein at least one n-state operation is replaced by the modified n-state operation.
3. The cryptographic computer system of claim 1 , wherein the cryptographic operation is a public key exchange operation in accordance with Diffie-Hellman key exchange wherein at least one n-state operation is replaced by the modified n-state operation.
4. The cryptographic computer system of claim 1 , wherein the cryptographic operation is a public key exchange operation in accordance with Rivest-Shamir-Adleman (RSA) cryptography wherein at least one n-state operation is replaced by the modified n-state operation.
5. The cryptographic computer system of claim 1 , wherein the cryptographic operation is a public key exchange operation in accordance with Learning-with-Errors (LWE) cryptography wherein at least one n-state operation is replaced by modified n-state operation.
6. The cryptographic computer system of claim 1 , wherein the cryptographic operation is a message digest generation.
7. The cryptographic computer system of claim 1 , wherein the message digest generation is selected from the group consisting of Secure Hash Algorithm (SHA) family of standards wherein at least one n-state operation is replaced by the modified n-state operation.
8. The cryptographic computer system of claim 1 , wherein the modified n-state operation is characterized by n-state inverter modification of the addition modulo-n or addition over GF(n) and the modified n-state operation has a zero-element that is not 0.
9. The cryptographic computer system of claim 1 , wherein the modified n-state operation is characterized by n-state inverter modification of the multiplication modulo-n or multiplication over GF(n) and the modified n-state operation has a zero-element that is not 0.
10. The cryptographic computer system of claim 1 , wherein a combination of the first and second reversible inverters establishes identity.
11. 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.
12. The cryptographic method of claim 11 , wherein the cryptographic operation is a public key exchange operation in accordance with Diffie-Hellman key exchange wherein at least one n-state operation is replaced by the modified n-state operation.
13. The cryptographic method of claim 11 , wherein the cryptographic operation is a public key exchange operation in accordance with Rivest-Shamir-Adleman (RSA) cryptography wherein at least one n-state operation is replaced by the modified n-state operation.
14. The cryptographic method of claim 11 , wherein the cryptographic operation is a public key exchange operation in accordance with Learning-with-Errors (LWE) cryptography wherein at least one n-state operation is replaced by the modified n-state operation.
15. The cryptographic method of claim 11 , wherein the cryptographic operation is message digest generation selected from the group consisting of Secure Hash Algorithm (SHA) family of standards wherein at least one n-state operation is replaced by the modified n-state operation.
16. The cryptographic method of claim 11 , wherein the modified n-state operation is characterized by modification of the multiplication modulo-n or multiplication over GF(n) and the modified n-state operation has a zero-element that is not 0.
17. The cryptographic method of claim 11 , wherein a combination of the first and second reversible inverters establishes identity.
18. 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.
19. The cryptographic computer device of claim 18 , wherein a combination of the second reversible n-state inverter and the first reversible n-state inverter establishes identity.