Method and apparatus with homomorphic encryption
A processor-implemented method with homomorphic encryption includes: receiving a first ciphertext corresponding to a first modulus; generating a second ciphertext corresponding to a second modulus by performing modulus raising on the first ciphertext; and performing bootstrapping by encoding the second ciphertext using a commutative property and an associative property of operations included in a rotation operation.
1. A processor-implemented method with homomorphic encryption, the method comprising:
receiving a first ciphertext corresponding to a first modulus;
generating a second ciphertext corresponding to a second modulus by performing modulus raising on the first ciphertext; and
performing bootstrapping by encoding the second ciphertext using a commutative property and an associative property of operations included in a rotation operation, including after adding a result of multiplications associated with the second ciphertext, performing a modulus down operation on a result of the adding, performing a decompose operation on a result of performing a rescaling operation on the second ciphertext, and performing a sum of multiplications on a result of the decompose operation.
2. The method of claim 1 , wherein the generating of the second ciphertext comprises generating the second ciphertext by performing modulus raising on the first ciphertext such that the value of the first modulus multiplied by a predetermined value is the second modulus.
3. The method of claim 1 , wherein the performing of the bootstrapping comprises:
performing a permutation operation on the second ciphertext; and
performing the bootstrapping by performing a key switching operation based on a result of the permutation operation.
4. The method of claim 3 , wherein the performing of the bootstrapping by performing the key switching operation based on the result of the permutation operation comprises:
performing a rescaling operation based on the permutation operation;
performing the decompose operation on a result of the rescaling operation.
5. The method of claim 4 , wherein the performing of the rescaling operation based on the permutation operation comprises:
performing a multiplication of the result of the permutation operation and a plaintext; and
rescaling a result of the multiplication.
6. The method of claim 5 , wherein the performing of the multiplication between the result of the permutation operation and the plaintext comprises performing a multiplication of the result of the permutation operation and a diagonal component of a matrix corresponding to the plaintext.
7. The method of claim 4 , wherein the performing of the bootstrapping by performing the key switching operation based on the result of the permutation operation further comprises:
generating an addition result by adding a result of the sum of multiplications; and
performing the modulus down operation on the addition result.
8. The method of claim 1 , wherein the performing of the bootstrapping comprises performing the bootstrapping by performing modulus reduction on a result of encoding the second ciphertext.
9. The method of claim 8 , wherein the performing of the bootstrapping by performing the modulus reduction on the result of encoding the second ciphertext comprises performing the bootstrapping by decoding a result of the modulus reduction.
10. A processor-implemented encryption method with homomorphic encryption, the method comprising:
generating a second ciphertext corresponding to a second modulus by performing modulus raising on a first ciphertext corresponding to a first modulus;
rescaling a result of a multiplication between a plaintext and a result of a permutation operation performed on the second ciphertext;
performing a sum of multiplications on a result of a decompose operation performed on a result of the rescaling; and
performing a modulus down operation based on a result of the sum of multiplications.
11. The method of claim 10 , wherein a key switching operation comprises the rescaling, the decompose operation, and the sum of multiplications.
12. The method of claim 11 , wherein a bootstrapping encoding the second ciphertext comprises the permutation operation and the key switching operation.
13. The method of claim 10 , wherein the modulus down operation comprises:
generating an addition result by adding a result of the sum of multiplications; and
performing the modulus down operation on the addition result.