Encryption processing device and encryption processing method

An encryption processing method of processing a ciphertext executed by a processor, the ciphertext being a fully homomorphic ciphertext that has a value obtained by adding an error with a predetermined variance to a predetermined value, as a plaintext associated with an integer and that enables a predetermined operation between integers to be performed without decryption, the method comprising:

• preparing a first polynomial and a second polynomial respectively including a second function and a third function and the fourth polynomial and storing the first polynomial and the second polynomial, and the fourth polynomial in the storage device, the second function and the third function being generated by decomposing a first function as a calculation object;
• rotating coefficients of the first polynomial based on a first ciphertext stored in the storage device to obtain the third polynomial, extracting a predetermined coefficient of the third polynomial to obtain a second ciphertext and storing the second ciphertext in the storage device;
• rotating coefficients of the fourth polynomial based on the first ciphertext to obtain a fifth polynomial, extracting a predetermined coefficient of the fifth polynomial to obtain a fifth ciphertext, rotating coefficients of the second polynomial based on a sixth ciphertext obtained by homomorphically adding the first ciphertext and the fifth ciphertext, to obtain a sixth polynomial, extracting a predetermined coefficient of the sixth polynomial to obtain a third ciphertext and storing the third ciphertext in the storage device;
• and
• performing a homomorphic operation using the second ciphertext and the third ciphertext that are stored in the storage device to obtain a fourth ciphertext corresponding to a result of calculation of the first function using the first ciphertext as input.

A non-transitory computer-readable recording medium storing therein an encryption processing program for causing a processor to execute an encryption process of processing a ciphertext, the ciphertext being a fully homomorphic ciphertext that has a value obtained by adding an error with a predetermined variance to a predetermined value, as a plaintext associated with an integer and that enables a predetermined operation to be performed between integers without decryption, wherein

• the encryption process includes
• preparing a first polynomial and a second polynomial respectively including a second function and a third function and a fourth polynomial and storing the first polynomial and the second polynomial, and the fourth polynomial in the storage device, the second function and the third function being generated by decomposing a first function as a calculation object,
• rotating coefficients of the first polynomial based on a first ciphertext stored in the storage device to obtain the third polynomial, extracting a predetermined coefficient of the third polynomial to obtain a second ciphertext and storing the second ciphertext in the storage device,
• rotating coefficients of the fourth polynomial based on the first ciphertext to obtain a fifth polynomial, extracting a predetermined coefficient of the fifth polynomial to obtain a fifth ciphertext, rotating coefficients of the second polynomial based on a sixth ciphertext obtained by homomorphically adding the first ciphertext and the fifth ciphertext, to obtain a sixth polynomial, extracting a predetermined coefficient of the sixth polynomial to obtain a third ciphertext and storing the third ciphertext in the storage device, and
• performing a homomorphic operation using the second ciphertext and the third ciphertext that are stored in the storage device to obtain a fourth ciphertext corresponding to a result of calculation of the first function using the first ciphertext as input.