Encryption processing apparatus and encryption processing method
An encryption processing apparatus processes a ciphertext. The ciphertext is a fully homomorphic cyphertext 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 able to be subjected to a predetermined operation between integers without being decrypted. The apparatus includes a processor that performs a calculation process of applying a predetermined polynomial to a ciphertext. The calculation process performs a first process of reducing an error of an input ciphertext by using the predetermined polynomial and a second process of extracting the new ciphertext from a ciphertext obtained as a result of the first process. The calculation process computes the new ciphertext that is different in input value at high speed by performing the second process a plurality of number of times on the ciphertext obtained as the result of the first process.
1 . An encryption processing apparatus that processes a ciphertext, the apparatus comprising:
a processor that performs a calculation process of applying a predetermined polynomial to a fully homomorphic ciphertext to obtain a new ciphertext, the ciphertext being the 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 the fully homomorphic ciphertext is able to be subjected to a predetermined operation between integers without being decrypted, wherein the calculation process performs:
a first process of reducing an error of an input ciphertext by using the predetermined polynomial, and
a second process of extracting the new ciphertext from a ciphertext obtained as a result of the first process, wherein the processor improves speed of computation of computes the new ciphertext that is different in input value at high speed by performing the second process a plurality of number of times on a ciphertext obtained as the result of the first process,
wherein the predetermined operation is an operation of transforming coordinates of a point on a plane from polar coordinates to orthogonal coordinates;
the calculation process
performs the first process on a first ciphertext that is input corresponding to a declination angle θ of the point to obtain a second ciphertext,
performs the second process on the second ciphertext at a first position to obtain a third ciphertext corresponding to cos θ, as the new ciphertext, and
performs the second process on the second ciphertext at a second position to obtain a fourth ciphertext corresponding to sin θ, as the new ciphertext; and
the processor further
performs homomorphic multiplication between the third ciphertext and a fifth ciphertext that is input corresponding to a distance from an origin to obtain a sixth ciphertext corresponding to an x-coordinate value, and
performs homomorphic multiplication between the fourth ciphertext and the fifth ciphertext to obtain a seventh ciphertext corresponding to a y-coordinate value.
2 . The encryption processing apparatus according to claim 1 , wherein the calculation process preforms a process of reducing a number of coefficients of the ciphertext, prior to obtaining a new ciphertext.
3 . The encryption processing apparatus according to claim 1 , wherein the process performed by the processor performs the predetermined operation to perform a process involved in fuzzy authentication or fuzzy search using the input ciphertext that is input.
4 . The encryption processing apparatus according to claim 1 , wherein the processor further performs the predetermined operation to process a query based on the input ciphertext to an encrypted database that is input.
5 . An encryption processing method, executed by a processor, of processing a ciphertext, the method comprising:
a calculation process of applying a predetermined polynomial to a fully homomorphic ciphertext to obtain a new ciphertext, the ciphertext being the 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 the fully homomorphic ciphertext is able to be subjected to a predetermined operation between integers without being decrypted, wherein
the calculation process performs a first process of reducing an error of an input ciphertext by using the predetermined polynomial; and
a second process of extracting the new ciphertext from a ciphertext obtained as a result of the first process, wherein speed of computation of computes the new ciphertext that is different in input value at high speed is improved by performing the second process a plurality of times on a ciphertext obtained as the result of the first process,
wherein the predetermined operation is an operation of transforming coordinates of a point on a plane from polar coordinates to orthogonal coordinates;
the calculation process
performs the first process on a first ciphertext that is input corresponding to a declination angle θ of the point to obtain a second ciphertext,
performs the second process on the second ciphertext at a first position to obtain a third ciphertext corresponding to cos θ, as the new ciphertext, and
performs the second process on the second ciphertext at a second position to obtain a fourth ciphertext corresponding to sin θ, as the new ciphertext; and
the processor further
performs homomorphic multiplication between the third ciphertext and a fifth ciphertext that is input corresponding to a distance from an origin to obtain a sixth ciphertext corresponding to an x-coordinate value, and
performs homomorphic multiplication between the fourth ciphertext and the fifth ciphertext to obtain a seventh ciphertext corresponding to a y-coordinate value.
6 . A non-transitory computer-readable recording medium storing a program for causing a processor to perform an encryption process of processing a ciphertext, the encryption process including:
a calculation process of applying a predetermined polynomial to a fully homomorphic ciphertext to obtain a new ciphertext, the ciphertext being the 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 the fully homomorphic ciphertext is able to be subjected to a predetermined operation between integers without being decrypted, wherein
the calculation process performs a first process of reducing an error of an input ciphertext by using the predetermined polynomial; and
a second process of extracting the new ciphertext from a ciphertext obtained as a result of the first process, wherein the processor improves speed of computation of computes the new ciphertext that is different in input value at high speed by performing the second process a plurality of number of times on a ciphertext obtained as the result of the first process,
wherein the predetermined operation is an operation of transforming coordinates of a point on a plane from polar coordinates to orthogonal coordinates;
the calculation process
performs the first process on a first ciphertext that is input corresponding to a declination angle θ of the point to obtain a second ciphertext,
performs the second process on the second ciphertext at a first position to obtain a third ciphertext corresponding to cos θ, as the new ciphertext, and
performs the second process on the second ciphertext at a second position to obtain a fourth ciphertext corresponding to sin θ, as the new ciphertext; and
the processor further
performs homomorphic multiplication between the third ciphertext and a fifth ciphertext that is input corresponding to a distance from an origin to obtain a sixth ciphertext corresponding to an x-coordinate value, and
performs homomorphic multiplication between the fourth ciphertext and the fifth ciphertext to obtain a seventh ciphertext corresponding to a y-coordinate value.