Method for verifying information

1. A method for verifying information in a cloud computing system, the method comprising:

by one or more computation devices:

generating an evaluation key and a verification key in a memory available to at least one of the one or more computation devices based on a security parameter and a function to be evaluated;

computing an output of the function to be evaluated in a memory available to at least one of the one or more computation devices using an input;

computing a proof for an outcome using the evaluation key in a memory available to at least one of the computation devices; and

verifying if the proof is valid based on the verification key in a memory available to at least one of the one or more computation devices,

wherein the function is defined as a mapping between matrix groups over a finite field and encoded into a polynomial in a memory available to at least one of the one or more computation devices,

wherein the polynomial is described and implemented as an arithmetic circuit, and

wherein the function to be evaluated is encoded such that the polynomial is a trace of a difference between the product of left and right input matrix polynomials of all gates of the arithmetic circuit and the output matrix polynomial of all gates of the arithmetic circuit.

2. The method according to claim 1 , wherein the function to be evaluated is encoded such that a target polynomial is generated belonging to the finite field over the input which always divides the polynomial.

3. The method according to claim 2 , wherein the input and output matrix polynomials are randomly shifted by adding a product of the target polynomial with a random number to the input and output matrix polynomials.

4. The method according to claim 3 , wherein, when computing the outcome, a second polynomial is used with the input and the random number which is used for generating the evaluation key and the verification key.

5. The method according to claim 3 , wherein the proof is computed using the randomly shifted input and output matrix polynomials dependent from the random number.

6. The method according to claim 1 , wherein for verifying the validity of the proof, a correct structure of the arithmetic circuit is checked.

7. The method according to claim 3 , wherein for verifying the validity of the proof, it is checked whether the target polynomial divides the randomly shifted input and output matrix polynomials.

8. The method according to claim 3 , wherein for verifying the validity of the proof, linear combinations computed over the randomly shifted input and output matrix polynomials are checked if they are in their corresponding spans.

9. The method according to claim 1 , wherein the input is private.

10. A computing system in a cloud computing system comprising one or more computation devices communicating with each other and being operable and configured to:

generate an evaluation key and a verification key in a memory available to at least one of the one or more computation devices based on a security parameter and a function to be evaluated by a key generator,

compute an output of the function to be evaluated using an input in a memory available to at least one of the one or more computation devices,

compute a proof for an outcome using the evaluation key in a memory available to at least one of the one or more computation devices, and

verify if the proof is valid based on the verification key in a memory available to at least one of the one or more computation devices,

wherein the function is defined as a mapping between matrix groups over a finite field and encoded into a polynomial in a memory available to at least one of the one or more computation devices,

wherein the polynomial is described and implemented as an arithmetic circuit, and

wherein the function to be evaluated is encoded such that the polynomial is a trace of a difference between the product of left and right input matrix polynomials of all gates of the arithmetic circuit and the output matrix polynomial of all gates of the arithmetic circuit.

11. The system according to claim 10 , wherein the function to be evaluated is encoded such that a target polynomial is generated belonging to the finite field over the input which always divides the polynomial.

12. The system according to claim 11 , wherein the input and output matrix polynomials are randomly shifted by adding a product of the target polynomial with a random number to the input and output matrix polynomials.

13. The system according to claim 12 , wherein, when computing the outcome, a second polynomial is used with the input and the random number which is used for generating the evaluation key and the verification key.

14. The system according to claim 12 , wherein the proof is computed using the randomly shifted input and output matrix polynomials dependent from the random number.

15. The system according to claim 10 , wherein for verifying the validity of the proof, a correct structure of the arithmetic circuit is checked.

16. The system according to claim 12 , wherein for verifying the validity of the proof, it is checked whether the target polynomial divides the randomly shifted input and output matrix polynomials.

17. The system according to claim 12 , wherein for verifying the validity of the proof, linear combinations computed over the randomly shifted input and output matrix polynomials are checked if they are in their corresponding spans.

18. The system according to claim 10 , wherein the input is private.