Granted Patent B2

US 12,452,042 · App. 17/791,907 · Granted Oct 21, 2025

Inventor: Dai Ikarashi (Musashino, JP)

Assignee: NTT, Inc.

H04L9/085G09C1/00

Abstract

Claims (77)

1. A secure computation device for secure computation while concealing data, wherein x, y, and z are real numbers, a, b, c, δ, and ζ are real number coefficients, and a secret share value of · is [·], the secure computation device comprising:

processing circuitry configured to:

obtain a secret share value [y]=[δx 2 +ax] through the secure computation using a secret share value [x] of the real number x; and

obtain and output a secret share value [func(x)]=[y(ζy+b)+cx] of an elementary function approximation value z=func(x) of the real number x through the secure computation using the secret share value [x] and the secret share value [y],

wherein the secret share value [func(x)]=[y(ζy+b)+cx] is obtained through the secure computation while concealing data of the secure computation,

wherein a number of digits that the processing circuitry can handle is finite, and

wherein the secret share value [func(x)] does not overflow the processing circuitry.

2. A secure computation device for secure computation while concealing data, wherein x, y, z, and w are real numbers, a, b, c, d, f, g, α, β, γ, δ, and ζ are real number coefficients, and a secret share value of · is [·], the secure computation device comprising:

processing circuitry configured to:

obtain a secret share value [y]=[δx 2 +ax] through the secure computation using a secret share value [x] of the real number x;

obtain a secret share value [z]=[y(ζy+b)+cx] through the secure computation using the secret share value [x] and the secret share value [y]; and

obtain and output a secret share value [func(x)]=[γ(z(αz+d)+y(βx+f)+gx)] of an elementary function approximation value w=func(x) of the real number x through the secure computation using the secret share value [x], the secret share value [y], and the secret share value [z],

wherein the secret share value [func(x)]=[γ(z(αz+d)+y(βx+f)+gx)] is obtained through the secure computation while concealing data of the secure computation,

wherein a number of digits that the processing circuitry can handle is finite, and

wherein the secret share value [func (x)] does not overflow the processing circuit.

3. A secure computation device for secure computation while concealing data, wherein x, y, and z are real numbers, a, b, c, γ, δ, and ζ are real number coefficients, and a secret share value of · is [·], the secure computation device comprising:

processing circuitry configured to:

obtain a secret share value [y]=[δx 2 +ax] through the secure computation using a secret share value [x] of the real number x; and

obtain and output a secret share value [func(x)]=[γ(y(ζy+b)+cx)] of an elementary function approximation value z=func(x) of the real number x through the secure computation using the secret share value [x] and the secret share value [y],

wherein the secret share value [func(x)]=[γ(y(ζy+b)+cx)] is obtained through the secure computation while concealing data of the secure computation,

wherein a number of digits that the processing circuitry can handle is finite, and

wherein the secret share value [func (x)] does not overflow the processing circuitry.

4. The secure computation device according to claim 1 , wherein

the secret share value [x] is related to χ, p, and L,

χ is a real number, p is a positive integer, L is an integer equal to or greater than 2, [·] is a secret share value obtained by performing linear secret sharing on an element · on a quotient ring modulo p, and {·} is a secret share value obtained by performing linear secret sharing on an element · on a quotient ring modulo 2, and

the processing circuitry is further configured to:

obtain secret share values {χ 0 }, . . . , {χ L−1 } of an L-bit representation χ 0 . . . χ L−1 of the real number χ through the secure computation using a secret share value [χ] of the real number χ;

obtain secret share values {η 0 }, . . . , {η L−1 } of an msb flag sequence η 0 , . . . , η L−1 where a bit η msb corresponding to a most significant bit χ msb of a bit sequence χ 0 . . . χ L−1 is 1 and bits ηξ(ξ ϵ{0, . . . , L−1}) other than the bit η msb are 0 through the secure computation using the secret share values {χ 0 }, . . . , {χ L−1 };

obtain a secret share value {ρ i }={ρ i+1 V χi } where 0≤i<L−1 and a secret share value {ρ L−1 }={χ L−1 } through the secure computation using the secret share values {χ 0 }, . . . , {χ L −1 };

obtain a secret share value [θ] of a count value θ indicating the number of elements being 1 among ρ 0 , . . . , ρ L−1 through the secure computation using secret share values {ρ 0 }, . . . , {ρ L−1 };

obtain a secret share value [ν] of an msb flag value ν=η 0 . . . η L−1 obtained by bit-connecting the msb flag sequence η 0 , . . . , η L−1 through the secure computation using the secret share values {η 0 }, . . . , {η L−1 };

obtain the secret share value [x]=[χ][ν] through the secure computation using the secret share value [χ] and the secret share value [ν]; and

obtain and output [log χ]=[func(x)]−[θ] through the secure computation using the secret share value [func(x)] and the secret share value [θ].

5. A secure computation method for secure computation while concealing data, wherein x, y, and z are real numbers, a, b, c, δ, and ζ are real number coefficients, and a secret share value of · is [·], the secure computation method, performed by processing circuitry, comprising:

obtaining a secret share value [y]=[δx 2 +ax] through the secure computation using a secret share value [x] of the real number x; and

obtaining and outputting a secret share value [func(x)]=[y(ζy+b)+cx] of an elementary function approximation value z=func(x) of the real number x through the secure computation using the secret share value [x] and the secret share value [y],

wherein the secret share value [func(x)]=[y(ζy+b)+cx] is obtained through the secure computation while concealing data of the secure computation,

wherein a number of digits that the processing circuitry can handle is finite, and

wherein the secret share value [func(x)] does not overflow the processing circuitry.

6. A secure computation method for secure computation while concealing data, wherein x, y, z, and w are real numbers, a, b, c, d, f, g, α, β, γ, δ, and ζ are real number coefficients, and a secret share value of · is [·], the secure computation method, performed by processing circuitry, comprising:

obtaining a secret share value [y]=[δx 2 +ax] through the secure computation using a secret share value [x] of the real number x;

obtaining a secret share value [z]=[y(ζy+b)+cx] through the secure computation using the secret share value [x] and the secret share value [y]; and

obtaining and outputting a secret share value [func(x)]=[γ(z(αz+d)+y(βx+f)+gx)] of an elementary function approximation value w=func(x) of the real number x through the secure computation using the secret share value [x], the secret share value [y], and the secret share value [z],

wherein the secret share value [func(x)]=[γ(z(αz+d)+y(βx+f)+gx)] is obtained through the secure computation while concealing data of the secure computation,

wherein a number of digits that the processing circuitry can handle is finite, and

wherein the secret share value [func(x)] does not overflow the processing circuitry.

7. A secure computation method for secure computation while concealing data, wherein x, y, and z are real numbers, a, b, c, γ, δ, and ζ are real number coefficients, and a secret share value of · is [·], the secure computation method, performed by processing circuitry, comprising:

obtaining a secret share value [y]=[δx 2 +ax] through the secure computation using a secret share value [x] of the real number x; and

obtaining and outputting a secret share value [func(x)]=[γ(y(ζy+b)+cx)] of an elementary function approximation value z=func(x) of the real number x through the secure computation using the secret share value [x] and the secret share value [y],

wherein the secret share value [func(x)]=[γ(y(ζy+b)+cx)] is obtained through the secure computation while concealing data of the secure computation,

wherein a number of digits that the processing circuitry can handle is finite, and

wherein the secret share value [func(x)] does not overflow the processing circuitry.

8. A non-transitory computer-readable recording medium storing a program for causing a computer to perform the method of claim 5 .

9. The secure computation device according to claim 2 , wherein

the secret share value [x] is related to χ, p, and L,

χ is a real number, p is a positive integer, L is an integer equal to or greater than 2, [·] is a secret share value obtained by performing linear secret sharing on an element · on a quotient ring modulo p, and {·} is a secret share value obtained by performing linear secret sharing on an element · on a quotient ring modulo 2, and

the processing circuitry is further configured to:

obtain secret share values {χ 0 }, . . . , {χ L−1 } of an L-bit representation χ 0 . . . χ L−1 of the real number χ through the secure computation using a secret share value [χ] of the real number x;

obtain secret share values {η 0 }, . . . , {η L−1 } of an msb flag sequence η 0 , . . . , η L−1 where a bit η msb corresponding to a most significant bit χ msb of a bit sequence χ 0 . . . χ L−1 is 1 and bits ηξ(ξ ϵ{0, . . . , L−1}) other than the bit η msb are 0, through the secure computation using the secret share values {η 0 }, . . . , {η L−1 };

obtain a secret share value {ρ i }={ρ i+1 V χi } where 0≤i<L−1 and a secret share value {ρ L−1 }={χ L−1 } through the secure computation using the secret share values {χ 0 }, . . . , {χ L −1 };

obtain a secret share value [θ] of a count value θ indicating the number of elements being 1 among ρ 0 , . . . , ρ L−1 through the secure computation using secret share values {ρ 0 ), . . . , {p L−1 };

obtain a secret share value [ν] of an msb flag value ν=η 0 . . . n L−1 obtained by bit-connecting the msb flag sequence η 0 , . . . , η L−1 through the secure computation using the secret share values {η 0 }, . . . , {η L−1 };

obtain the secret share value [x]=[χ][ν] through the secure computation using the secret share value [χ] and the secret share value [ν]; and

obtain and output [log χ]=[func(x)]−[θ] through the secure computation using the secret share value [func(x)] and the secret share value [θ].

10. The secure computation device according to claim 3 , wherein

the secret share value [x] is related to χ, p, and L,

χ is a real number, p is a positive integer, L is an integer equal to or greater than 2, [·] is a secret share value obtained by performing linear secret sharing on an element · on a quotient ring modulo p, and {·} is a secret share value obtained by performing linear secret sharing on an element · on a quotient ring modulo 2, and

the processing circuitry is further configured to:

obtain secret share values {χ 0 }, . . . , {χ L−1 } of an L-bit representation χ 0 . . . χ L−1 of the real number χ through the secure computation using a secret share value [χ] of the real number x;

obtain secret share values {η 0 }, . . . , {η L−1 } of an msb flag sequence η 0 , . . . , η L−1 where a bit η msb corresponding to a most significant bit χ msb of a bit sequence χ 0 . . . χ L−1 is 1 and bits ηξ(ξ ϵ{0, . . . , L−1}) other than the bit η msb are 0 through the secure computation using the secret share values {χ 0 }, . . . , {χ L−1 };

obtain a secret share value {ρ i }={ρ i +V χi } where 0≤i<L−1 and a secret share value {ρ L−1 }={χ L−1 } through the secure computation using the secret share values {χ 0 }, . . . , {χ L −1 };

obtain a secret share value [θ] of a count value θ indicating the number of elements being 1 among ρ 0 , . . . , ρ L−1 through the secure computation using secret share values {ρ 0 }, . . . , {ρ L−1 };

obtain a secret share value [ν] of an msb flag value ν=η 0 . . . η L−1 obtained by bit-connecting the msb flag sequence η 0 , . . . , η L−1 through the secure computation using the secret share values {η 0 }, . . . , {η L−1 };

obtain the secret share value [x]=[χ][ν] through the secure computation using the secret share value [χ] and the secret share value [ν]; and

obtain and output [log χ]=[func(x)]−[θ] through the secure computation using the secret share value [func(x)] and the secret share value [θ].

11. A non-transitory computer-readable recording medium storing a program for causing a computer to perform the method of claim 6 .

12. A non-transitory computer-readable recording medium storing a program for causing a computer to perform the method of claim 7 .

Assignments (2)

Continuity (1)

References Cited (12)