Efficient random masking of values while maintaining their sign under fully homomorphic encryption (FHE)
A method, apparatus and computer program product for privacy-preserving homomorphic inferencing. In response to receipt of encrypted data, a ciphertext of real numbers is generated. Each real number has an associated sign that is desired to be maintained. A mask is then identified, preferably via an iterative algorithm that works on a trial and error basis to locate an appropriate solution. The mask comprises set of values randomly distributed over a given positive range and that remain positive after encoding under a fixed-point arithmetic and with a low scale value. Under homomorphic encryption, the ciphertext is then multiplied by the mask to generate a result comprising values corresponding to the real numbers in the ciphertext and that maintain their associated signs. The result is provided as a response to the encrypted data.
1. A method for privacy-preserving homomorphic inferencing, comprising:
receiving an encrypted data point;
in response to receipt of the encrypted data point, generating a ciphertext having one or more real numbers each having an associated sign;
identifying a mask comprising a set of values that are randomly distributed over a given positive range and that remain positive after encoding under a fixed-point arithmetic and with a scale value, wherein the fixed-point arithmetic is Cheon-Kim-Kim-Song (CKKS) scheme;
under homomorphic encryption, multiplying the ciphertext by the mask to generate a result, the result comprising one or more values corresponding to the one or more real numbers in the ciphertext, the one or more values in the result maintaining the associated signs of the one or more real numbers in the ciphertext to which the values correspond; and
providing the result as a response to the encrypted data point.
2. The method as described in claim 1 wherein the scale value is 1.
3. The method as described in claim 2 wherein the set of values in the mask are identified by an iterative algorithm that, for one or more increasing minimum values of a range from which random values are selected, each minimum value as adjusted by the scale value corresponding to an iteration, evaluates encodings of the random values under the fixed-point arithmetic until the set of values in the mask are identified.
4. The method as described in claim 1 wherein the ciphertext is multiplied by the set of values under fully homomorphic encryption.
5. The method as described in claim 4 wherein the fixed-point arithmetic is a homomorphic encryption scheme for approximate arithmetic.
6. The method as described in claim 1 wherein the one or more values in the result differ in magnitude from the one or more real numbers in the ciphertext.
7. An apparatus, comprising:
a processor;
computer memory holding computer program instructions executed by the processor to provide privacy-preserving homomorphic inferencing, the computer program instructions comprising program code configured to:
receive an encrypted data point;
in response to receipt of the encrypted data point, generate a ciphertext having one or more real numbers each having an associated sign;
identify a mask comprising a set of values that are randomly distributed over a given positive range and that remain positive after encoding under a fixed-point arithmetic and with a scale value, wherein the fixed-point arithmetic is Cheon-Kim-Kim-Song (CKKS) scheme;
under homomorphic encryption, multiply the ciphertext by the mask to generate a result, the result comprising one or more values corresponding to the one or more real numbers in the ciphertext, the one or more values in the result maintaining the associated signs of the one or more real numbers in the ciphertext to which the values correspond; and
provide the result as a response to the encrypted data point.
8. The apparatus as described in claim 7 wherein the scale value is 1.
9. The apparatus as described in claim 8 wherein the program code configured to identify the set of values in the mask comprises an iterative algorithm that, for one or more increasing minimum values of a range from which random values are selected, each minimum value as adjusted by the scale value corresponding to an iteration, evaluates encodings of the random values under the fixed-point arithmetic until the set of values in the mask are identified.
10. The apparatus as described in claim 7 wherein the ciphertext is multiplied by the set of values under fully homomorphic encryption.
11. The apparatus as described in claim 10 wherein the fixed-point arithmetic is a homomorphic encryption scheme for approximate arithmetic.
12. The apparatus as described in claim 7 wherein the one or more values in the result differ in magnitude from the one or more real numbers in the ciphertext.
13. A computer program product comprising: a non-transitory computer readable medium, the computer program product holding computer program instructions executed by a processor in a host processing system to provide privacy-preserving homomorphic inferencing, the computer program instructions comprising program code configured to:
receive an encrypted data point;
in response to receipt of the encrypted data point, generate a ciphertext having one or more real numbers each having an associated sign;
identify a mask comprising a set of values that are randomly distributed over a given positive range and that remain positive after encoding under a fixed-point arithmetic and with a scale value, wherein the fixed-point arithmetic is Cheon-Kim-Kim-Song (CKKS) scheme;
under homomorphic encryption, multiply the ciphertext by the mask to generate a result, the result comprising one or more values corresponding to the one or more real numbers in the ciphertext, the one or more values in the result maintaining the associated signs of the one or more real numbers in the ciphertext to which the values correspond; and
provide the result as a response to the encrypted data point.
14. The computer program product as described in claim 13 wherein the scale value is 1.
15. The computer program product as described in claim 14 wherein the program code configured to identify the set of values in the mask comprises an iterative algorithm that, for one or more increasing minimum values of a range from which random values are selected, each minimum value as adjusted by the scale value corresponding to an iteration, evaluates encodings of the random values under the fixed-point arithmetic until the set of values in the mask are identified.
16. The computer program product as described in claim 13 wherein the ciphertext is multiplied by the set of values under fully homomorphic encryption.
17. The computer program product as described in claim 16 wherein the fixed-point arithmetic is a homomorphic encryption scheme for approximate arithmetic.
18. The computer program product as described in claim 13 wherein the one or more values in the result differ in magnitude from the one or more real numbers in the ciphertext.