TABLE GENERATION APPARATUS, TABLE GENERATION METHOD AND PROGRAM

1 . A table generation apparatus configured to create a table in which a distribution of noise z satisfies a condition for achieving (ε, δ)-differential privacy and approximates a discrete Laplace distribution, when a sum of one or more elements that are randomly selected from the table is used to define the noise z, the table generation apparatus comprising:

circuitry configured to

create a probability density function that satisfies the condition and is represented by a third array, based on (i) a first array in which the one or more elements are initialized, (ii) a second array that is defined by the first array, and (iii) the third array that is created from the second array by a predetermined convolution operation; and

create the table by using the first array.

2 . The table generation apparatus according to claim 1 , wherein when the first array is defined as C, a length of the first array C is set to L+1, and L is an integer of zero or more, the circuitry is configured to create the table that stores C[L−|k|] pieces of each k=−L, −L+1, . . . , L.

3 . The table generation apparatus according to claim 1 , wherein when the first array is defined as C, the second array is defined as C sym , and the third array is defined as C sym *n , the circuitry is configured to

define the second array C sym by C sym [i]=C sym [(2L+2)−i]=C[i](i=0, . . . , L) for L (where L is an integer of zero or more),

calculate real numbers c 0 and c 1 satisfying C sym *n [L+1]=c 1 C[L+1]+c 0 ,

set a maximum integer that does not exceed (e ε Csym *n [L]−c 0 )/c 1 to C[L+1] for predetermined value of ε that is greater than 0,

repeat incrementing L by one until an end condition is satisfied, and

create C sym *n [k+L]/(a sum of Csym *n [j] from j=0 to j=2L−1) as the probability density function.

4 . The table generation apparatus according to claim 3 , wherein the end condition is that L+1≥Δ (where Δ is greater than or equal to 1 and is an integer representing sensitivity) and that (a sum of C sym *n [j] from j=0 to j=Δ−1)/(a sum of C sym *n [j] from j=0 to j=2L−1) is less than δ (where δ is a predetermined value greater than 0).

5 . The table generation apparatus according to claim 3 , wherein the end condition is that a predetermined number of repetitions is reached.

6 . A table generation method for creating a table in which a distribution of noise z satisfies a condition for achieving (ε, δ)-differential privacy and approximates a discrete Laplace distribution, when a sum of one or more elements that are randomly selected from the table is used to the noise z, the table generation method comprising:

creating a probability density function that satisfies the condition and is represented by a third array, based on (i) a first array in which the one or more elements are initialized, (ii) a second array that is defined by the first array, and (iii) the third array that is created from the second array by a predetermined convolution operation; and

creating the table by using the first array.

7 . A non-transitory computer readable storage medium storing a program that causes a computer to execute the table generation method of claim 6 .