SECURE RANDOM NUMBER GENERATION SYSTEM, SECURE COMPUTATION APPARATUS, SECURE RANDOM NUMBER GENERATION METHOD, AND PROGRAM

1 . A secure random number generation system comprising a plurality of secure computation apparatuses and generating a concealed value [r] of a random number r, the random number r following a discrete Laplace distribution with parameter α,

wherein, α is a number that is larger than 0 and smaller than 1, and N is an integer of 2 or more,

the secure computation apparatuses each comprise:

processing circuitry configured to:

generate a concealed value stream [b 0 ], [b 1 ], . . . , [b N ] that is constituted by a concealed value [b 0 ] of a random number bit b 0 that follows a Bernoulli distribution with probability (1−α)/(1+α) and concealed values [b 0 ], . . . , [b N ] of random number bits b 1 , . . . , b N that each follow a Bernoulli distribution with probability (1−α);

obtain a concealed value [L] of a position L at which 1 is first set from the head of the random number bits b 0 , b 1 , . . . , b N ; and

obtain a result [L·s] obtained by multiplying the concealed value [L] by a concealed value [s] of a random sign s, as a concealed value [r] of the random number r.

2 . The secure random number generation system according to claim 1 ,

wherein, Z p is a finite field of order p and i is each of integers from 0 to N,

the processor circuitry is further configured to:

set a section I in which |I|/p is close to the probability of the Bernoulli distribution;

generate a concealed value [r i ] of a random number r i on the finite field Z p , for each integer i; and

generate a result obtained by judging whether or not the random number r i is included in the section I using the concealed value [r i ], for each integer i, as the concealed value [b i ].

3 . The secure random number generation system according to claim 2 ,

wherein

the processor circuitry is further configured to:

generate a concealed value stream [c 0 ], [c 1 ], . . . , [c N ], the result of computing [b 0 ] OR . . . OR [b i ] for each integer i being a concealed value [c i ]; and

generate a result of computing Σ i (1−[c i ]) as the concealed value [L].

4 . A secure computation apparatus being to be used in a secure random number generation system, the secure random number generation system generating a concealed value [r] of a random number r s the random number r following a discrete Laplace distribution with parameter α,

wherein, α is a number that is larger than 0 and smaller than 1, and N is an integer of 2 or more,

the secure computation apparatus comprises:

processor circuitry configured to:

generate a concealed value stream [b 0 ], [b 1 ], . . . , [b N ] that is constituted by a concealed value [b 0 ] of a random number bit b 0 that follows a Bernoulli distribution with probability (1−α)/(1+α) and concealed values [b 1 ], . . . , [b N ] of random number bits b 1 , . . . , b N that each follow a Bernoulli distribution with probability (1−α);

obtain a concealed value [L] of a position L at which 1 is first set from the head of the random number bits b 0 , b 1 , . . . , b N ; and

obtain a result [L·s] obtained by multiplying the concealed value [L] by a concealed value [s] of a random sign s, as a concealed value [r] of the random number r.

5 . A secure random number generation method being to be executed by a secure random number generation system comprising a plurality of secure computation apparatuses, the secure random number generation system generating a concealed value [r] of a random number r, the random number r following a discrete Laplace distribution with parameter α,

wherein, α is a number that is larger than 0 and smaller than 1 and N is an integer of 2 or more,

the secure random number generation method comprising:

generating, by processor circuitry of each of the secure computation apparatuses, a concealed value stream [b 0 ], [b 1 ], . . . , [b N ] that is constituted by a concealed value [b 0 ] of a random number bit b 0 that follows a Bernoulli distribution with probability (1−α)/(1+α) and concealed values [b 1 ], . . . , [b N ] of random number bits b 1 , . . . , b N that each follow a Bernoulli distribution with probability (1−α);

obtaining, by the processor circuitry, a concealed value [L] of a position L at which 1 is first set from the head of the random number bits b 0 , b 1 , . . . , b N ; and

obtaining, by the processor circuitry, a result [L·s] obtained by multiplying the concealed value [L] by a concealed value [s] of a random sign s, as a concealed value [r] of the random number r.

6 . A non-transitory computer recording medium on which a program for causing a computer to operate as the secure computation apparatus according to claim 4 is recorded.