Apparatus and method with homomorphic encryption
An apparatus and method with homomorphic encryption are provided. A method for performing a homomorphic encryption operation may include generating a second ciphertext, having a second total number of dimensions, by performing a key switching operation using a key-switching key to generate the second ciphertext, encrypted by a second secret key, based on a homomorphic encrypted first ciphertext on a first modulus encrypted by a first secret key, where the first ciphertext has a first total number of dimensions, and generating a ciphertext on a second modulus by performing a blind rotation operation based on the second ciphertext and an operation key.
1. A processor-implemented method for performing a homomorphic encryption operation, the method comprising:
generating a second ciphertext, having a second total number of dimensions, by performing a key switching operation using a key-switching key to generate the second ciphertext, encrypted by a second secret key, based on a homomorphic encrypted first ciphertext on a first modulus encrypted by a first secret key, where the first ciphertext has a first total number of dimensions; and
generating a ciphertext on a second modulus by performing a blind rotation operation based on the second ciphertext and an operation key.
2. The method of claim 1 , wherein the second total number of dimensions is less than the first total number of dimensions, and the second modulus is greater than the first modulus.
3. The method of claim 1 , wherein the key-switching key is based on a scaled up version of the first secret key.
4. The method of claim 3 , wherein the performing of the blind rotation operation comprises:
generating a result of a summation of respective products of each element of the second ciphertext and the operation key; and
generating a result of a product of the result of the summation and an initial function that is determined based on the key-switching key.
5. The method of claim 1 , wherein the key switching key is based on a scaled up error corresponding to the key switching operation.
6. The method of claim 1 , wherein the second secret key is a sub-vector of the first secret key.
7. The method of claim 1 , further comprising receiving the key-switching key, the operation key which is dependent on the second secret key, and a ring learning with errors (RLWE) ciphertext as the first ciphertext,
wherein the RLWE ciphertext corresponds to the RLWE ciphertext having been generated from data set for performing a homomorphic encryption operation.
8. The method of claim 7 ,
wherein the second ciphertext is a second learning with errors (LWE) ciphertext,
wherein the method further comprises:
performing a homomorphic rounding operation on the RLWE ciphertext; and
generating a first LWE ciphertext having the first total number of dimensions based on a result of the homomorphic rounding operation, and
wherein the generating of the second ciphertext comprises generating the second ciphertext by performing the key switching operation on the first LWE ciphertext.
9. The method of claim 8 ,
wherein the ciphertext on the second modulus is a RLWE ciphertext, and
wherein the second modulus is greater than the first modulus.
10. A non-transitory computer-readable storage medium storing instructions that, when executed by a processor, configure the processor to perform the method of claim 1 .
11. A processor-implemented method for homomorphic encryption, the method comprising:
receiving a first secret key of a first ciphertext having a first total number of dimensions and a second secret key for a second ciphertext having a second total number of dimensions less than the first total number of dimensions;
generating a key-switching key configured to generate the second ciphertext based on the first ciphertext and the first secret key;
generating an operation key, based on the second secret key, configured to generate bootstrapping blind rotation results with respect to a homomorphic encryption operation that is dependent on the key-switching key; and
outputting the key-switching key and the operation key.
12. The method of claim 11 , wherein the generating of the key-switching key comprises:
scaling up the first secret key; and
generating the key-switching key based on the scaled up first secret key.
13. The method of claim 11 , wherein the generating of the key-switching key comprises:
scaling up an error used corresponding to a use of the key-switching key to perform a key-switching operation; and
generating the key-switching key based on the scaled up error.
14. An apparatus, the apparatus comprising:
a processor configured to:
generate a second ciphertext, having a second total number of dimensions, through performance of a key switching operation that uses a key-switching key to generate the second ciphertext, encrypted by a second secret key, based on a homomorphic encrypted first ciphertext on a first modulus encrypted by a first secret key, where the first ciphertext has a first total number of dimensions; and
generate a ciphertext on a second modulus by performing a blind rotation operation based on the second ciphertext and an operation key.
15. The apparatus of claim 14 , wherein the second total number of dimensions is less than the first total number of dimensions, and the second modulus is greater than the first modulus.
16. The apparatus of claim 14 , wherein the key-switching key is based on a scaled up version of the first secret key.
17. The apparatus of claim 16 , wherein, for the performing of the blind rotation operation, the processor is further configured to:
generate a result of a summation of respective products of each element of the second ciphertext and the operation key; and
generate a result of a product of the result of the summation and an initial function that is determined based on the key-switching key.
18. The apparatus of claim 14 , wherein the key switching key is based on a scaled up error corresponding to the key switching operation.
19. The apparatus of claim 14 , wherein the second secret key is a sub-vector of the first secret key.
20. The apparatus of claim 14 , further comprising a receiver to receive the key-switching key, the operation key which is dependent on the second secret key, and a ring learning with errors (RLWE) ciphertext on the first modulus as the first ciphertext,
wherein the second ciphertext is a second learning with errors (LWE) ciphertext,
wherein the processor is further configured to:
perform a homomorphic rounding operation on the RLWE ciphertext; and
generate a first LWE ciphertext having the first total number of dimensions based on a result of the homomorphic rounding operation, and
wherein, for the generation of the second ciphertext, the processor is configured to generate the second ciphertext through performance of the key switching operation on the first LWE ciphertext.