Encryption processing apparatus and encryption processing method

An encryption processing apparatus that processes a ciphertext,

• the ciphertext being a fully homomorphic ciphertext that has, as a plaintext associated with an integer, a value obtained by adding an error with a predetermined variance to a predetermined value and that is subjected to a predetermined operation between integers without being decrypted,
• the apparatus comprising a processor that performs a process including
• obtaining, based on a subtraction result of homomorphic subtraction of a second ciphertext as a divisor from a first ciphertext as a dividend, a binary third ciphertext determining whether the subtraction result is positive or negative,
• performing an operation process that subtracts a result of homomorphic multiplication between the third ciphertext and the second ciphertext from the first ciphertext in a homomorphic manner to obtain a new ciphertext,
• obtaining a new third ciphertext by using an operation result of the operation process as a new first ciphertext, and repeating the operation process using the new first ciphertext, the second ciphertext, and the new third ciphertext,
• accumulating the third ciphertext to a predetermined initial value to obtain a new ciphertext, every time the third ciphertext is obtained, and
• outputting the new ciphertext obtained by accumulation of the third ciphertext at a time at which the operation process has been repeated a predetermined number of times in total, as a result of division of the first ciphertext by the second ciphertext.

A non-transitory computer-readable recording medium storing a program for causing a processor to perform an encryption processing method of processing a ciphertext,

• the ciphertext being a fully homomorphic ciphertext that has, as a plaintext associated with an integer, a value obtained by adding an error with a predetermined variance to a predetermined value and that is subjected to a predetermined operation between integers without being decrypted, wherein
• the encryption process includes
• obtaining, based on a subtraction result of homomorphic subtraction of a second ciphertext as a divisor from a first ciphertext as a dividend, a binary third ciphertext determining whether the subtraction result is positive or negative,
• performing an operation process that subtracts a result of homomorphic multiplication between the third ciphertext and the second ciphertext from the first ciphertext in a homomorphic manner to obtain a new ciphertext,
• obtaining a new third ciphertext by using an operation result of the operation process as a new first ciphertext, and repeating the operation process using the new first ciphertext, the second ciphertext, and the new third ciphertext, and
• outputting the new ciphertext output after a predetermined number of repetitions of the operation process in total, as a result of division or a remainder operation of the first ciphertext by the second ciphertext.

A non-transitory computer-readable recording medium storing a program for causing a processor to perform an encryption processing method of processing a ciphertext,

• the ciphertext being a fully homomorphic ciphertext that has, as a plaintext associated with an integer, a value obtained by adding an error with a predetermined variance to a predetermined value and that is subjected to a predetermined operation between integers without being decrypted, wherein
• the encryption process includes
• obtaining, based on a subtraction result of homomorphic subtraction of a second ciphertext as a divisor from a first ciphertext as a dividend, a binary third ciphertext determining whether the subtraction result is positive or negative,
• performing an operation process that subtracts a result of homomorphic multiplication between the third ciphertext and the second ciphertext from the first ciphertext in a homomorphic manner to obtain a new ciphertext,
• obtaining a new third ciphertext by using an operation result of the operation process as a new first ciphertext, and repeating the operation process using the new first ciphertext, the second ciphertext, and the new third ciphertext,
• accumulating the third ciphertext to a predetermined initial value to obtain a new ciphertext, every time the third ciphertext is obtained, and
• outputting the new ciphertext obtained by accumulation of the third ciphertext at a time at which the operation process has been repeated a predetermined number of times in total, as a result of division of the first ciphertext by the second ciphertext.