Method and system for processing a GNSS signal using homomorphic encryption

1. A method for processing a global navigation satellite system (GNSS) signal, the GNSS comprising multiple satellites, wherein each satellite transmits a respective navigation signal containing a spreading code, the method comprising:

receiving an incoming signal at a receiver, wherein the incoming signal contains navigation signals from a satellite;

determining Doppler and code delay offsets for the satellite based on the incoming signal;

generating a public-private key pair comprising a public key to encrypt data and a private key to decrypt the data encrypted by the public key, using an asymmetric homomorphic encryption scheme;

generating a normalized signal based on the incoming signal and the Doppler and code delay offsets;

encrypting the normalized signal using the public key to form an encrypted signal;

transmitting the encrypted signal and the public key to a remote server;

receiving, from the remote server, one or more encrypted correlation values, each encrypted correlation value representing a dot product between the encrypted signal and a spreading code of the GNSS, wherein the spreading code is encrypted using the public key prior to performing the correlation;

decrypting the one or more encrypted correlation values using the private key; and

using the decrypted correlation values to determine the location of the receiver.

2. The method of claim 1 , wherein receiving the incoming signal comprises recording a set of samples of the incoming signal representing a given duration of time, and wherein encrypting the incoming signal comprises encrypting the set of samples to form the encrypted signal.

3. The method of claim 1 , wherein the homomorphic encryption scheme is partly homomorphic.

4. The method of claim 3 , wherein the homomorphic encryption scheme is multiplicatively homomorphic, and wherein the incoming signal is exponentiated prior to encryption.

5. The method of claim 3 , wherein the homomorphic encryption scheme is ElGamal.

6. The method of claim 1 , wherein the spreading code is securely maintained at the remote server and is not disclosed to the receiver.

7. A method for processing a global navigation satellite system (GNSS) signal at a server, the GNSS comprising multiple satellites, wherein each satellite transmits a respective navigation signal containing a spreading code, the method comprising:

at the server, receiving, from a receiver, an encrypted signal formed by encrypting a normalized GNSS signal using a public key created using an asymmetric homomorphic encryption scheme and the public key, the normalized signal generated based on Doppler and code delay offsets for a satellite;

encrypting a spreading code for the normalized GNSS using the public key to generate an encrypted spreading code;

performing correlations between the received encrypted signal and the encrypted spreading code to produce encrypted correlation values representing a dot product between the encrypted signal and the encrypted spreading code; and

transmitting the encrypted correlation values to the receiver.

8. The method of claim 7 , wherein the encrypted signal is quantised to one-bit such that the correlations can be performed just by addition.

9. The method of claim 7 , further comprising adding random noise to the encrypted correlation values to obfuscate the spreading code used to form the encrypted correlation values.

10. An apparatus configured to process a global navigation satellite system (GLASS) signal, the GNSS comprising multiple satellites, Wherein each satellite is configured to transmit a respective navigation signal containing a spreading code, the apparatus comprising:

memory; and

a processor coupled to the memory, the processor being configured to:

receive an incoming signal at a receiver, wherein the incoming signal contains navigation signals from a satellite;

determine Doppler and code delay offsets for the satellite based on the incoming signal;

generate a public-private key pair comprising a public key to encrypt data and a private key to decrypt the data encrypted by the public key, using an asymmetric homomorphic encryption scheme;

generate a normalized signal based on the incoming signal and the Doppler and code delay offsets;

encrypt the normalized signal using the public key to form an encrypted signal;

transmit the encrypted signal and the public key to a remote server;

receive, from the remote server, one or more encrypted correlation values, each encrypted correlation value representing a dot product between the encrypted signal and a spreading code of the GNSS, wherein the spreading code is encrypted using the public key prior to performing the correlation;

decrypt the one or more encrypted correlation values using the private key; and

use the decrypted correlation values to determine the location of the receiver.