Polynomial-based homomorphic encryption

1. A method, comprising:

identifying a field that includes a set of sequences;

generating a polynomial using the field, wherein the polynomial generated is based on a plurality of randomly selected sequences from the field;

generating a secret key for encryption and decoding data;

identifying a set of data stored in plaintext format;

converting, by a processing device, the set of data to ciphertext using a polynomial, a set of random noise, and the secret key, wherein the ciphertext is generated using the polynomial, the set of random noise and the secret key, wherein the secret key includes a random sequence from the set of sequences of the field with at least one distinct element;

sending the ciphertext to a remote device for data processing, wherein the remote device is to process the ciphertext without decoding the ciphertext;

receiving processed ciphertext from the remote device;

decoding, by the processing device, the processed ciphertext based on the secret key and the polynomial to yield processed plaintext; and

outputting the processed plaintext.

2. The method of claim 1 , wherein the generating the secret key comprises:

selecting the random sequence from the set of sequences of the field; and

setting the random sequence as the secret key.

3. The method of claim 1 , wherein the converting the set of data comprises

encrypting the set of data to create the ciphertext.

4. The method of claim 1 , wherein the set of data is encrypted with a degree of randomness.

5. The method of claim 1 , wherein the processed ciphertext is decoded using Reed-Solomon decoding techniques.

6. The method of claim 1 , wherein the decoding comprises:

retrieving the secret key from a data storage; and

reproducing the polynomial using the processed ciphertext and the secret key.

7. The method of claim 1 , wherein the outputting comprises displaying the processed plaintext on a display device.

8. A system, comprising;

a memory storing programmable code; and

a processor operatively coupled to the memory, the processor being configured to execute the programmable code to perform operations comprising:

identifying a field that includes a set of sequences;

generating a polynomial using the field, wherein the polynomial generated is based on a plurality of randomly selected sequences from the field;

generating a secret key for encryption and decoding data;

identifying a set of data stored in plaintext format;

converting the set of data to ciphertext using a polynomial, a set of random noise, and the secret key, wherein the ciphertext is generated using the polynomial, the set of random noise, and the secret key, wherein the secret key includes a random sequence from the set of sequences of the field with at least one distinct element;

sending the ciphertext to a remote device for data processing, wherein the remote device is to process the ciphertext without decoding the ciphertext;

receiving processed ciphertext from the remote device;

decoding the processed ciphertext based on the secret key and the polynomial to yield processed plaintext; and

outputting the processed plaintext.

9. The system of claim 8 , wherein the processor is further configured to, when generating the secret key, perform operations comprising:

selecting the random sequence from the set of sequences of the field; and

setting the random sequence as the secret key.

10. The system of claim 8 , wherein the processor is further configured to, when converting the set of data, perform operations comprising

encrypting the set of data to create the ciphertext.

11. The system of claim 8 , wherein the set of data is encrypted with a degree of randomness.

12. The system of claim 8 , further comprising decoding the processed ciphertext using Reed-Solomon decoding techniques.

13. The system of claim 8 , wherein the processor is further configured to, when decoding the processed ciphertext, perform operations comprising:

retrieving the secret key from a data storage; and

reproducing the polynomial using the processed ciphertext and the secret key.

14. The system of claim 8 , wherein the outputting comprises displaying the processed plaintext on a display device.

15. A non-transitory computer-readable medium having encoded therein programming code executable by a processor to perform or control performance of operations comprising:

identifying a field that includes a set of sequences;

generating a polynomial using the field, wherein the polynomial generated is based on a plurality of randomly selected sequences from the field;

generating a secret key for encryption and decoding data;

identifying a set of data stored in plaintext format;

converting the set of data to ciphertext using a polynomial, a set of random noise, and the secret key, wherein the ciphertext is generated using the polynomial, the set of random noise and the secret key, wherein the secret key includes a random sequence from the set of sequences of the field with at least one distinct element;

sending the ciphertext to a remote device for data processing, wherein the remote device is to process the ciphertext without decoding the ciphertext;

receiving processed ciphertext from the remote device;

decoding the processed ciphertext based on the secret key and the polynomial to yield processed plaintext; and

outputting the processed plaintext.

16. The non-transitory computer-readable medium of claim 15 , wherein the generating the secret key comprises:

selecting the random sequence from the set of sequences of the field; and

setting the random sequence as the secret key.

17. The non-transitory computer-readable medium of claim 15 , wherein the converting comprises

encrypting the set of data to create the ciphertext.

18. The non-transitory computer-readable medium of claim 15 , further comprising decoding the processed ciphertext using Reed-Solomon decoding techniques.

19. The non-transitory computer-readable medium of claim 15 , wherein the decoding comprises;

retrieving the secret key from a data storage; and

reproducing the polynomial using the processed ciphertext and the secret key.

20. The non-transitory computer-readable medium of claim 15 , wherein the outputting comprises displaying the processed plaintext on a display device.