Apparatus for calculating matrix multiplication of homomorphic encryption and method thereof
An operation apparatus performing matrix multiplication of a homomorphic encryption is disclosed. The operation apparatus includes a memory configured to store at least one instruction and a plurality of homomorphic ciphertexts, and a processor configured to execute the at least one instruction. The processor is configured to generate first matrix data having a row of a predetermined size and a column of a predetermined size using the plurality of homomorphic ciphertexts, generate a plurality of third matrix data having a row which is the size of the predetermined column and the column of the predetermined size by arranging second matrix data having a row which is 1/n size of the predetermined column and the column of the predetermined size sequentially n-times, and perform a homomorphic multiplication operation between same rows and same columns using the first matrix data and the generated respective third matrix data.
1 . An operation apparatus, comprising:
a memory configured to store at least one instruction and a plurality of homomorphic ciphertexts; and
a processor configured to perform a homomorphic matrix multiplication operation on the plurality of homomorphic ciphertexts by executing the at least one instruction,
wherein the processor is configured to
generate first matrix data having a row of a predetermined size and a column of a predetermined size using the plurality of homomorphic ciphertexts,
generate second matrix data having a row which is 1/n size of the predetermined column and the column of the predetermined size,
generate a plurality of third matrix data having a row which is the size of the predetermined column and the column of the predetermined size by arranging a plurality of rows of the second matrix data sequentially in a predetermined row order n-times,
generate a plurality of fourth matrix data performed with a homomorphic multiplication operation between an i th row of the first matrix data and an i th row of each of the plurality of third matrix data,
generate a plurality of fifth matrix data having data in which respective column values in a row are homomorphically added with a plurality of column values of the corresponding row in a row basis of each of the plurality of fourth matrix data, and
generate a matrix multiplication operation result of the first matrix and the second matrix by applying a predetermined mask to each of the plurality of fifth matrix data.
2 . The operation apparatus according to claim 1 , wherein
the processor is configured to
perform encoding by converting a matrix of a homomorphic ciphertext input according to a size of the homomorphic ciphertext and a predetermined size of a unit matrix to a single block or multiple blocks.
3 . The operation apparatus according to claim 2 , wherein
the processor is configured to
perform, based on a converted encoding block being formed as a single block, encoding by applying zero padding to a position which remains after data of the homomorphic ciphertext is filled in the unit matrix.
4 . The operation apparatus according to claim 2 , wherein
the processor is configured to
divide, based on a converted encoding block being formed as multiple blocks, an encoding block into submatrices in the unit matrix form for a number of rows and columns of the encoded block to be multiples of rows and columns of the unit matrix, respectively, and perform encoding of the divided respective submatrices in a row-major method.
5 . The operation apparatus according to claim 1 , wherein
the processor is configured to
perform at least one from among tiling and complexification to reduce complexity in calculation of a matrix multiplication operation.
6 . The operation apparatus according to claim 1 , wherein
the mask is configured to
sequentially convert a masking position so as to correspond to an arrangement position of the third matrix data arranged sequentially in a predetermined order.
7 . An operation method for performing a matrix multiplication of a homomorphic encryption, the method comprising:
receiving input of a plurality of homomorphic ciphertexts;
performing a homomorphic matrix multiplication operation on the plurality of homomorphic ciphertexts; and
outputting an operation result,
wherein the performing the homomorphic matrix multiplication operation comprises
generating first matrix data having a row of a predetermined size and a column of a predetermined size using the plurality of homomorphic ciphertexts;
generating second matrix data having a row which is 1/n size of the predetermined column and the column of the predetermined size;
generating a plurality of third matrix data having a row which is the size of the predetermined column and a column of the predetermined size by arranging a plurality of rows of the second matrix data sequentially in a predetermined row order n-times;
generating a plurality of fourth matrix data performed with a homomorphic multiplication operation between an i th row of the first matrix data and an i th row of each of the plurality of third matrix data;
generating a plurality of fifth matrix data having data in which respective column values in a row are homomorphically added with a plurality of column values of the corresponding row in a row basis of each of the plurality of fourth matrix data; and
generating a matrix multiplication operation result of the first matrix and the second matrix by applying a predetermined mask to each of the plurality of fifth matrix data.
8 . The operation method according to claim 7 , further comprising:
performing, after receiving input of the plurality of homomorphic ciphertexts, encoding by converting a matrix of a homomorphic ciphertext input according to a size of the homomorphic ciphertext and a predetermined size of a unit matrix to a single block or multiple blocks.
9 . The operation method according to claim 8 , further comprising performing, based on a converted encoding block being formed as a single block, encoding by applying zero padding to a position which remains after data of the homomorphic ciphertext is filled in the unit matrix.
10 . The operation method according to claim 8 , further comprising
dividing, based on a converted encoding block being formed as multiple blocks, an encoding block into submatrices in the unit matrix form for a number of rows and columns in the encoding block to be multiples of rows and columns of the unit matrix, respectively, and performing encoding of the divided respective submatrices in a row-major method.
11 . The operation method according to claim 7 , further comprising
performing, after performing the homomorphic matrix multiplication operation, at least one from among tiling and complexification to reduce a complexity in calculation of a matrix multiplication.
12 . The operation method according to claim 7 , wherein
the mask comprises
sequentially converting a masking position so as to correspond to an arrangement position of the third matrix data which is sequentially arranged in a predetermined order.
13 . A non-transitory computer-readable recording medium comprising a program for executing an operation method for performing matrix multiplication of a homomorphic encryption, the operation method comprising:
receiving input of a plurality of homomorphic ciphertexts;
performing a homomorphic matrix multiplication operation on the plurality of homomorphic ciphertexts; and
outputting an operation result,
wherein the performing the homomorphic matrix multiplication operation comprises
generating first matrix data having a row of a predetermined size and a column of a predetermined size using the plurality of homomorphic ciphertexts;
generating second matrix data having a row which is 1/n size of the predetermined column and the column of the predetermined size;
generating a plurality of third matrix data having a row which is the size of the predetermined column and a column of the predetermined size by arranging a plurality of rows of the second matrix data sequentially in a predetermined row order n-times;
generating a plurality of fourth matrix data performed with a homomorphic multiplication operation between an i th row of the first matrix data and an i th row of each of the plurality of third matrix data;
generating a plurality of fifth matrix data having data in which respective column values in a row are homomorphically added with a plurality of column values of the corresponding row in a row basis of each of the plurality of fourth matrix data; and
generating a matrix multiplication operation result of the first matrix and the second matrix by applying a predetermined mask to each of the plurality of fifth matrix data.