Cryptographic machines characterized by a Finite Lab-Transform (FLT)
Digital n-state switching devices are characterized by n-state switching tables with n greater than 4. N-state switching tables are transformed by a Finite Lab-transform (FLT) into an FLTed n-state switching table. Memory devices, processors and combinational circuits with inputs and an output are characterized by an FLTed n-state switching table and perform switching operations between physical states in accordance with an FLTed n-state switching table. The devices characterized by FLTed n-state switching tables are applied in cryptographic devices. The cryptographic devices perform standard cryptographic operations or methods that are modified in accordance with an FLT. One or more standard cryptographic methods are specified in Federal Information Processing Standard (FIPS) Publications. Security is improved by at least a factor n 2 .
1. 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=q p ) 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=q p ) 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.
2. The device of claim 1 , wherein the FLTed n-state computer operation has a one element that is not interpreted as 1 and/or has a zero element that is not interpreted as 0.
3. The device of claim 1 , wherein the FLTed n-state computer operation represents a modified modulo-n multiplication.
4. The device of claim 1 , wherein the FLTed n-state computer operation represents a modified multiplication over a Finite Field GF(n=2 p ) with GF being a galois field and p an integer greater than 2.
5. The device of claim 1 , wherein the device performs an Advanced Encryption Standard (AES) encryption or decryption as described in a Federal Information Processing Standard (FIPS) Publication that is modified in accordance with the FLT.
6. The device of claim 1 , wherein the device performs a message digest generation as described in a Federal Information Processing Standard (FIPS) Publication that is modified in accordance with the FLT.
7. The device of claim 1 , wherein the device performs a digital signature generation as described in a Federal Information Processing Standard (FIPS) Publication that is modified in accordance with the FLT.
8. The device of claim 1 , wherein the device performs a Rivest-Shamir-Adleman (RSA) operation that is modified in accordance with the FLT.
9. The device of claim 1 , wherein the device performs an elliptic curve cryptography (ECC) operation that is modified in accordance with the FLT.
10. The device of claim 1 , wherein the device is a networked computer.
11. The device of claim 1 , wherein the device is a smartphone.
12. The device of claim 1 , wherein the device is a chipcard.
13. The device of claim 1 , wherein the device is a door opener.
14. The device of claim 1 , wherein the device is configured in accordance with a Transport Layer Security (TLS) protocol.
15. The device of claim 1 , wherein n is greater than two to the power hundred.
16. A method for generating cryptographic data, comprising:
processing a message in an n-state format with n greater than 4 by a processor 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 part of the group consisting of: a modulo-n addition, a modulo-n multiplication, an addition over finite field GF(n=q p ) 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=q p ) determined by an irreducible polynomial of degree p over GF(q), p bitwise XOR operations with p being greater than 2; and
providing by the processor of the cryptographic data generated in accordance with the modification of the cryptographic method on the communication channel.
17. The method of claim 16 , wherein the FLTed n-state computer operation has a zero element that is not 0 in origin-0.
18. The method of claim 16 , wherein the processor is included in a device selected from the group consisting of: a computer, a smartphone, a chipcard, an ATM-machine, a device connected to the Internet, a Near Field Communication (NFC) device.