Apparatus for processing approximately encrypted messages and methods thereof
A method for processing an encryption is provided. The method for processing an encryption includes the steps of linearly transforming a homomorphic encryption for an approximate message including an error, performing an approximate modulus operation for the linearly transformed homomorphic encryption by using a multi-degree polynomial set such that input values within a predetermined range are approximate to an integer point, and linearly transforming the homomorphic encryption which was approximately modulus operated into a form of encryption.
1. A method for processing a homomorphic encryption comprising:
linearly transforming a homomorphic encryption for an approximate message including an error;
performing an approximate modulus operation for the linearly transformed homomorphic encryption by using a multi-degree polynomial set such that input values within a predetermined range are approximate to an integer point; and
linearly transforming the homomorphic encryption which was approximately modulus operated; and
encrypting the linearly transformed homomorphic encryption which was approximately modulus operated into a form of encryption,
wherein the multi-degree polynomial is an interpolation polynomial for a sine function or a cosine function that approximates the integer point from multiple input values within the predetermined range.
2. The method for processing a homomorphic encryption of claim 1 ,
wherein the multi-degree polynomial is a polynomial having a degree among any one of a 7th degree to an 80th degree, and the predetermined range is from −12 to 12.
3. The method for processing a homomorphic encryption of claim 1 ,
wherein the performing an approximate modulus operation comprises:
setting a double-angle number of times and a multi-degree polynomial corresponding to the double-angle number of times, and performing an approximate modulus operation by operating the linearly transformed homomorphic encryption as many times as the set double-angle number of times by using the set multi-degree polynomial.
4. The method for processing a homomorphic encryption of claim 1 ,
wherein the linearly transforming a homomorphic encryption comprises:
converting the homomorphic encryption into a form of polynomial; and
applying the converted homomorphic encryption to a predefined matrix.
5. The method for processing a homomorphic encryption of claim 4 ,
wherein the applying comprises:
decomposing the predefined matrix into a plurality of block diagonal matrices wherein there is a value in a diagonal component and the other values are 0, and applying the homomorphic encryption sequentially to the plurality of block diagonal matrices.
6. The method for processing a homomorphic encryption of claim 5 ,
wherein the applying comprises:
applying the homomorphic encryption to the plurality of block diagonal matrices in units of two continuous matrices.
7. An operation apparatus comprising:
a memory storing a homomorphic encryption for an approximate message including an error; and
a processor performing an operation for the homomorphic encryption, wherein the processor is configured to:
linearly transform the homomorphic encryption for an approximate message including an error,
perform an approximate modulus operation for the linearly transformed homomorphic encryption by using a multi-degree polynomial set such that input values within a predetermined range are approximate to an integer point,
linearly transform the homomorphic encryption which was approximately modulus operated, and
encrypt the linearly transformed homomorphic encryption which was approximately modulus operated into a form of encryption, and
wherein the multi-degree polynomial is an interpolation polynomial for a sine function or a cosine function that approximates the integer point from multiple input values within the predetermined range.
8. The operation apparatus of claim 7 ,
wherein the multi-degree polynomial is a polynomial having a degree among any one of a 7th degree to an 80th degree, and the predetermined range is from −12 to 12.
9. The operation apparatus of claim 7 ,
wherein the processor is configured to:
set a double-angle number of times and a multi-degree polynomial corresponding to the double-angle number of times, and perform an approximate modulus operation by operating the linearly transformed homomorphic encryption as many times as the set double-angle number of times by using the set multi-degree polynomial.
10. The operation apparatus of claim 7 ,
wherein the processor is configured to:
convert the homomorphic encryption into a form of polynomial, and linearly transform the homomorphic encryption by applying the converted homomorphic encryption to a predefined matrix.
11. The operation apparatus of claim 10 ,
wherein the processor is configured to:
decompose the predefined matrix into a plurality of block diagonal matrices wherein there is a value in a diagonal component and the other values are 0, and linearly transform the homomorphic encryption by applying the homomorphic encryption sequentially to the plurality of block diagonal matrices.
12. The operation apparatus of claim 11 :
wherein the processor is configured to:
linearly transform the homomorphic encryption by applying the homomorphic encryption to the plurality of block diagonal matrices in units of two continuous matrices.