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Abstract
According to an example aspect of the present invention, there is provided an apparatus comprising at least one processing core, at least one memory including computer program code, the at least one memory and the computer program code configured to cause the apparatus to receive an identifier of a function, encrypted input data, an encrypted computation result, encrypted random data and an encrypted output of the function, when nm with the random data, obtain a homomorphic polynomial factorization of the function, comprising obtaining a decomposed representation of the function, the representation comprising a sum of polynomials, and verify that the computation result is correct by checking, whether a difference between the encrypted output and the encrypted computation result equals a value of the decomposed representation, wherein the encrypted random data and the encrypted input data are used as parameter values in the sum of polynomials.
14 Citations
51 Claims
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1-31. -31. (canceled)
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32. An apparatus comprising at least one processor;
- and at least one memory including computer program code;
the at least one memory and the computer program code being configured to, with the at least one processor, cause the apparatus at least to;receive an identifier of a function, encrypted input data, an encrypted computation result, encrypted random data and an encrypted output of the function, when run with the encrypted random data; obtain a homomorphic polynomial factorization of the function, further comprising to obtain a decomposed representation of the function, the representation comprising a sum of polynomials, and verify that the encrypted computation result is correct by checking, whether a difference between the encrypted output and the encrypted computation result equals a value of the decomposed representation, wherein the encrypted random data and the encrypted input data are used as parameter values in the sum of the polynomials. - View Dependent Claims (33, 34, 35, 36, 37, 38, 39)
- and at least one memory including computer program code;
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40. An apparatus comprising at least one processor;
- and at least one memory including computer program code, the at least one memory and the computer program code being configured to, with the at least one processor, cause the apparatus at least to;
perform a homomorphic polynomial factorization of a function to obtain a decomposed representation of the function, the representation comprising a sum of polynomials; obtain random data, and generate an output of the function, when run with the random data, and provide to a verifier node the random data in an encrypted form, the output in an encrypted form, and an identifier of the function, the verifier node distinct from a cloud computing server, wherein the apparatus is configured to offload computation of the function to the cloud computing server. - View Dependent Claims (41, 42, 43, 44)
- and at least one memory including computer program code, the at least one memory and the computer program code being configured to, with the at least one processor, cause the apparatus at least to;
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45. A method comprising:
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receiving an identifier of a function, encrypted input data, an encrypted computation result, encrypted random data and an encrypted output of the function, when run with the encrypted random data; obtaining a homomorphic polynomial factorization of the function, further comprising obtaining a decomposed representation of the function, the representation comprising a sum of polynomials, and verifying that the encrypted computation result is correct by checking, whether a difference between the encrypted output and the encrypted computation result equals a value of the decomposed representation, wherein the encrypted random data and the encrypted input data are used as parameter values in the sum of the polynomials. - View Dependent Claims (46, 47, 48)
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49. A method comprising:
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performing a homomorphic polynomial factorization of a function to obtain a decomposed representation of the function, the representation comprising a sum of polynomials; obtaining random data, and generating an output of the function, when run with the random data, and providing to a verifier node the random data in an encrypted form, the output in an encrypted form, and an identifier of the function, the verifier node distinct from a cloud computing server, wherein an apparatus performing the method is configured to offload computation of the function to the cloud computing server. - View Dependent Claims (50, 51)
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Specification