COMPUTATION APPARATUS, METHOD AND PROGRAM FOR THE SAME
A computation apparatus, a method of the same, and a program which perform a secure computation using fixed-point arithmetic, and overflow is unlikely to occur and the occurrence of division by zero can be detected when an odds ratio is calculated. The computation apparatus includes an odds ratio computation unit for obtaining an odds ratio between a first group (a+b) and a second group (c+d) based on four plaintext values a, b, c, and d, by means of secure computation; a zero-division detection unit for determining, by means of secure computation, whether or not at least one of the plaintext values b and c is not zero, and detecting division by zero; and a selection unit for selecting the odds ratio if division by zero is not detected, by means of secure computation.
1 - 5 . (canceled)
6 . A computation apparatus comprising:
processing circuitry configured to:
execute an odds ratio computation processing in which the processing circuitry obtains an odds ratio between a first group (a+b) and a second group (c+d) based on four plaintext values a, b, c, and d, by means of secure computation;
execute a zero-division detection processing in which the processing circuitry determines, by means of secure computation, whether or not at least one of the plaintext values b and c is not zero, and detects division by zero; and
a selection processing in which the processing circuitry selects the odds ratio if division by zero is not detected, by means of secure computation,
wherein in the odds ratio computation processing the processing circuitry obtains ciphertexts [[ 0 ′ 1 ]] and [[ 0 ′ 2 ]] of results o′ 1 and o′ 2 of calculating a/b and d/c, respectively, by means of secure computation, and thereafter obtains a ciphertext of a result o′ of calculating o′ 1 ×o′ 2 .
7 . A computation apparatus comprising:
processing circuitry configured to:
take ciphertexts [[a]], [[b]], [[c]], and [[d]] of plaintext values a, b, c, and d as input, and obtain ciphertexts [[o′ 1 ]] and [[o′ 2 ]] of results o′ 1 and o′ 2 of calculating a/b and d/c, respectively, by [[o′ 1 ]]←[[a]]/[[b]] and [[o′ 2 ]]←[[d]]/[[c]], by means of secure computation;
take the ciphertexts [[o′ 1 ]] and [[o′ 2 ]] as input and obtain a ciphertext [[o′]] of a result o′ of computation of plaintext values o′ 1 ×o′ 2 by [[o′]]←[[o′ 1 ]]×[[o′ 2 ]], by means of secure computation;
take the ciphertexts [[b]] and [[c]] as input and obtain ciphertexts [[f 1 ]] and [[f 2 ]] of truth values f 1 and f 2 with predicates b=?0 and c=?0, respectively, by [[f 1 ]]←[[b]]=?[[0]] and [[f 2 ]]←[[c]]=?[[0]], by means of secure computation;
take the ciphertexts and as input and obtain a ciphertext [[f]] of a result f of calculating f 1 Or f 2 by [[f]]←Or([[f 1 ]], [[f 2 ]]), by means of secure computation; and
take the ciphertexts [[f]] and [[o′]] as input and obtain a ciphertext [[o]] of o that satisfies
o
=
{
⊥
if
f
=
1
o
′
otherwise
[
Math
.
4
]
by [[o]]←If Else([[f]], [[⊥]], [[o′]]), by means of secure computation, wherein ⊥ indicates an invalid value.
8 . A computation method, implemented by a computation apparatus that includes processing circuitry, comprising:
an odds ratio computation step in which the processing circuitry obtains an odds ratio between a first group (a+b) and a second group (c+d) based on four plaintext values a, b, c, and d, by means of secure computation;
a zero-division detection step in which the processing circuitry determines, by means of secure computation, whether or not at least one of the plaintext values b and c is not zero, and detects division by zero; and
a selection step in which the processing circuitry selects the odds ratio if division by zero is not detected, by means of secure computation,
wherein in the odds ratio computation step, the processing circuitry obtains ciphertexts [[o′ 1 ]] and [[o′ 2 ]] of results o′ 1 and o′ 2 of calculating a/b and d/c, respectively, by means of secure computation, and thereafter, obtains a ciphertext [[o′]] of a result o′ of calculating o′ 1 ×o′ 2 .
9 . A computation method, implemented by a computation apparatus that includes processing circuitry, comprising:
a division step in which the processing circuitry takes ciphertexts [[a]], [[b]], [[c]], and [[d]] of plaintext values a, b, c, and d as input, and obtains ciphertexts [[o′ 1 ]] and [[o′ 2 ]] of results o′ 1 and o′ 2 of calculating a/b and d/c, respectively, by [[o′ 1 ]]←[[a]]/[[b]] and [[o′ 2 ]]←[[d]]/[[c]], by means of secure computation;
a multiplication step in which the processing circuitry takes the ciphertexts [[o′ 1 ]] and [[o′ 2 ]] as input and obtains a ciphertext [[o′]] of a result o′ of computation of plaintext values o′ 1 ×o′ 2 by [[o′]]←[[o′ 1 ]]×[[o′ 2 ]], by means of secure computation;
an equality judgment step in which the processing circuitry takes the ciphertexts [[b]] and [[c]] as input and obtains ciphertexts [[f 1 ]] and [[f 2 ]] of truth values f 1 and f 2 with predicates b=?0 and c=?0, respectively, by [[f 1 ]]←[[b]]=?[[0]] and [[f 2 ]]←[[c]]=?[[0]], by means of secure computation;
a logical operation step in which the processing circuitry takes the ciphertexts [[f 1 ]] and [[f 2 ]] as input and obtains a ciphertext [[f]] of a result f of calculating f 1 Or f 2 by [[f]]←Or([[f 1 ]], [[f 2 ]]), by means of secure computation; and
a selection step in which the processing circuitry takes the ciphertexts [[f]] and [[o′]] as input and obtains a ciphertext [[o]] of o that satisfies
o
=
{
⊥
if
f
=
1
o
′
otherwise
[
Math
.
5
]
by [[o]]←If Else([[f]], [[⊥]], [[o′]]), by means of secure computation, wherein ⊥ indicates an invalid value.
10 . A non-transitory computer-readable recording medium having recorded thereon a program for causing a computer to function as the computation apparatus according to claim 6 .
11 . A non-transitory computer-readable recording medium having recorded thereon a program for causing a computer to function as the computation apparatus according to claim 7 .