Systems and methods for providing a quantum-proof key exchange
A system and method are disclosed for providing a quantum proof key exchange. The method includes generating at a first computing device a random bit a i , encrypting a i using quantum-proof homomorphic encryption ξ to yield ξ A (a i ), transmitting ξ A (a i ) to a second computing device, generating at the second computing device a random bit b i , encrypting b i using the quantum-proof homomorphic encryption ξ to yield ξ B (b i ), transmitting ξ B (b i ) to the first computing device and generating a common key between the first computing device and the second computing device based on ξ A (a i ) and ξ B (b i ).
1. A method comprising:
generating at a first computing device a random bit a i ;
encrypting a i using quantum-proof homomorphic encryption ξ to yield ξ A (a i );
transmitting ξ A (a i ) to a second computing device;
generating at the second computing device a random bit b i ;
encrypting b i using the quantum-proof homomorphic encryption ξ to yield ξ B (b i );
transmitting ξ B (b i ) to the first computing device; and
generating a common key between the first computing device and the second computing device based on ξ A (a i ) and ξ B (b i ).
2. The method of claim 1 , wherein multiple random bits are generated at the first computing device and the second computing device.
3. The method of claim 1 , wherein generating the common key between the first computing device and the second computing device based on ξ A (a i ) and ξ B (b i ) further comprises:
computing, at the first computing device, ξ B (b i +a i ); and
transmitting ξ B (b i +a i ) from the first computing device to the second computing device.
4. The method of claim 3 , further comprising:
computing, at the second computing device, ξ A (a i +b i ); and
transmitting ξ A (a i +b i ) from the second computing device to the first computing device.
5. The method of claim 3 , wherein computing, at the first computing device, ξ B (b i +a i ), is performed using homomorphic features of the quantum-proof homomorphic encryption ξ.
6. The method of claim 4 , further comprising:
decrypting, at the first computing device, ξ A (a i +b i ) to yield a i +b i ; and
setting k i =a i +b i .
7. The method of claim 4 , wherein computing, at the second computing device, ξ A (a i +b i ), is performed using homomorphic features of the quantum-proof homomorphic encryption ξ.
8. The method of claim 6 , further comprising:
decrypting, at the second computing device, ξ B (a i +b i ) to yield a i +b i ; and
setting k i =a i +b i .
9. The method of claim 8 , further comprising:
setting a common key at the first computing device and the second computing device as k 1 +2k 2 + . . . +2 n k n .
10. The method of claim 9 , further comprising:
using the common key for secure communication between the first computing device and the second computing device.
11. A computing device comprising:
a processor; and
a computer-readable storage device storing instructions which, when executed by the processor, cause the processor to perform operations comprising:
generating a random bit a i ;
encrypting a i using quantum-proof homomorphic encryption ξ to yield ξ A (a i );
transmitting ξ A (a i ) to a second computing device, wherein the second computing device generates a random bit b i and encrypts b i using the quantum-proof homomorphic encryption ξ to yield ξ B (b i );
receiving ξ B (b i ) from the second computing device; and
generating a common key between the computing device and the second computing device based on ξ A (a i ) and ξ B (b i ).
12. The computing device of claim 11 , wherein multiple random bits are generated at the computing device and the second computing device.
13. The computing device of claim 11 , wherein generating the common key between the computing device and the second computing device based on ξ A (a i ) and ξ B (b i ) further comprises:
computing ξ B (b i +a i ); and
transmitting ξ B (b i +a i ) to the second computing device.
14. The computing device of claim 13 , wherein the second computing device computes ξ A (a i +b i ) and wherein the computer-readable storage device stores further instructions which, when executed by the processor, cause the processor to perform operations comprising:
receiving ξ A (a i +b i ) from the second computing device.
15. The computing device of claim 13 , wherein computing ξ B (b i +a i ) is performed using homomorphic features of the quantum-proof homomorphic encryption ξ.
16. The computing device of claim 14 , wherein the computer-readable storage device stores further instructions which, when executed by the processor, cause the processor to perform operations comprising:
decrypting ξ A (a i +b i ) to yield a i +b i ; and
setting k i =a i +b i .
17. The computing device of claim 14 , wherein computing, at the second computing device, ξ A (a i +b i ), is performed using homomorphic features of the quantum-proof homomorphic encryption ξ.
18. The computing device of claim 16 , wherein the second computing device decrypts ξ B (a i +b i ) to yield a i +b i and sets k i =a i +b i .
19. The computing device of claim 18 , wherein the computer-readable storage device stores further instructions which, when executed by the processor, cause the processor to perform operations comprising:
setting a common key at the computing device and the second computing device as k 1 +2k 2 + . . . +2 n k n .
20. The computing device of claim 19 , wherein the computing device and the second computing device use the common key for secure communication between the computing device and the second computing device.