SECRET SHARING SYSTEM, SHARING APPARATUS, SHARE MANAGEMENT APPARATUS, ACQUISITION APPARATUS, SECRET SHARING METHOD, PROGRAM AND RECORDING MEDIUM
First Claim
Patent Images
1. A secret sharing system, comprising:
- a sharing apparatus;
Σ
α
=1L h(α
) share management apparatuses PA(α
, h(α
)), where α
=1, . . . , L, L≧
2, h(α
)=1, . . . , H(α
), H(α
)≧
2; and
an acquisition apparatus,wherein the sharing apparatus includes;
a secret sharing unit that independently shares a value corresponding to each element θ
(ψ
, i, β
)·
g2 of basis vectors bi*(ψ
) among each subset SUB(α
) consisting of H(α
) share management apparatuses PA(α
,
1), . . . , PA(α
, H(α
)) according to a predetermined secret sharing scheme to generate share information SH(ψ
, i, β
, α
, h(α
)) corresponding to each element θ
(ψ
, i, β
)·
g2, where h(α
)=1, . . . , H(α
), provided that Ψ
denotes an integer equal to or greater than 1, ψ
denotes an integer equal to or greater than 0 and equal to or smaller than Ψ
, ψ
=0, . . . , Ψ
, n(ψ
) denotes an integer equal to or greater than 1, ζ
(ψ
) denotes an integer equal to or greater than 0, a generator of a cyclic group G2 is denoted by g2, and the basis vectors bi*(ψ
)=(θ
(ψ
, i,
1)·
g2, . . . , θ
(ψ
, i, n(ψ
)+ζ
(ψ
))·
g2)ε
G2n(ψ
)+ζ
(ψ
) are n(ψ
)+ζ
(ψ
)-dimensional basis vectors for θ
(ψ
, i, β
), where i=1, . . . , n(ψ
)+ζ
(ψ
), β
=1, . . . , n(ψ
)+ζ
(ψ
), n(ψ
)≧
1, ζ
(ψ
)≧
1, elements of the basis vectors bi*(ψ
) are n(ψ
)+ζ
(ψ
) elements of the cyclic group G2,each of the share management apparatuses PA(α
, h(α
)) includes;
a share secret value generation unit that generates share secret values DSH(ψ
, α
, h(α
)) by performing a common calculation common in the subset SUB(α
) on common information shared in the subset SUB(α
) and the share information SH(ψ
, i, β
, α
, h(α
)), where h(α
)=1, . . . , H(α
), andthe acquisition apparatus includes;
a reconstruction unit that generates reconstructed secret values SUBSK(ψ
, α
) for each subset SUB(α
) from a plurality of the share secret values DSH(ψ
, α
, h(α
)) for the subset SUB(α
) by performing reconstruction processing for the subset SUB(α
) according to the secret sharing scheme; and
a synthesis unit that generates generation information D*(ψ
) from the reconstructed secret values SUBSK(ψ
, α
).
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Abstract
A sharing apparatus independently shares a value corresponding to each element θ(ψ, i, β)·g2 of basis vectors bi*(θ) among each subset SUB(α) consisting of H(α) share management apparatuses PA(α, 1), . . . , PA(α, H(α)) to generate share information SH(ψ, i, β, α, h(α)) corresponding to each element θ(ψ, i, β)·g2. The share management apparatus PA(α, h(α)) generates a share secret value DSH(ψ, α, h(α)) by performing a common calculation common in the subset SUB(α) on common information shared in the subset SUB(α) and the share information SH(ψ, i, β, α, h(α)). An acquisition apparatus generates reconstructed secret values SUBSK(ψ, α) for each subset SUB(α) by performing a reconstruction processing for the subset SUB(α) and generates generation information D*(ψ) from the reconstructed secret values SUBSK(ψ, α).
18 Citations
33 Claims
-
1. A secret sharing system, comprising:
-
a sharing apparatus; Σ
α
=1L h(α
) share management apparatuses PA(α
, h(α
)), where α
=1, . . . , L, L≧
2, h(α
)=1, . . . , H(α
), H(α
)≧
2; andan acquisition apparatus, wherein the sharing apparatus includes; a secret sharing unit that independently shares a value corresponding to each element θ
(ψ
, i, β
)·
g2 of basis vectors bi*(ψ
) among each subset SUB(α
) consisting of H(α
) share management apparatuses PA(α
,
1), . . . , PA(α
, H(α
)) according to a predetermined secret sharing scheme to generate share information SH(ψ
, i, β
, α
, h(α
)) corresponding to each element θ
(ψ
, i, β
)·
g2, where h(α
)=1, . . . , H(α
), provided that Ψ
denotes an integer equal to or greater than 1, ψ
denotes an integer equal to or greater than 0 and equal to or smaller than Ψ
, ψ
=0, . . . , Ψ
, n(ψ
) denotes an integer equal to or greater than 1, ζ
(ψ
) denotes an integer equal to or greater than 0, a generator of a cyclic group G2 is denoted by g2, and the basis vectors bi*(ψ
)=(θ
(ψ
, i,
1)·
g2, . . . , θ
(ψ
, i, n(ψ
)+ζ
(ψ
))·
g2)ε
G2n(ψ
)+ζ
(ψ
) are n(ψ
)+ζ
(ψ
)-dimensional basis vectors for θ
(ψ
, i, β
), where i=1, . . . , n(ψ
)+ζ
(ψ
), β
=1, . . . , n(ψ
)+ζ
(ψ
), n(ψ
)≧
1, ζ
(ψ
)≧
1, elements of the basis vectors bi*(ψ
) are n(ψ
)+ζ
(ψ
) elements of the cyclic group G2,each of the share management apparatuses PA(α
, h(α
)) includes;a share secret value generation unit that generates share secret values DSH(ψ
, α
, h(α
)) by performing a common calculation common in the subset SUB(α
) on common information shared in the subset SUB(α
) and the share information SH(ψ
, i, β
, α
, h(α
)), where h(α
)=1, . . . , H(α
), andthe acquisition apparatus includes; a reconstruction unit that generates reconstructed secret values SUBSK(ψ
, α
) for each subset SUB(α
) from a plurality of the share secret values DSH(ψ
, α
, h(α
)) for the subset SUB(α
) by performing reconstruction processing for the subset SUB(α
) according to the secret sharing scheme; anda synthesis unit that generates generation information D*(ψ
) from the reconstructed secret values SUBSK(ψ
, α
). - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)
-
-
13. A sharing apparatus that independently shares a value corresponding to each element θ
- (ψ
, i, β
)·
g2 of basis vectors bi*(ψ
) among each subset SUB(α
) consisting of H(α
) share management apparatuses PA(α
,
1), . . . , PA(α
, H(α
)) according to a predetermined secret sharing scheme to generate share information SH(ψ
, i, β
, α
, h(α
)) corresponding to each element θ
(ψ
, i, β
)·
g2, where α
=1, . . . , L, L≧
2, h(α
)=1, . . . , H(α
), H(α
)≧
2, provided that Ψ
denotes an integer equal to or greater than 1, ψ
denotes an integer equal to or greater than 0 and equal to or smaller than Ψ
, ψ
=0, . . . , Ψ
, n(ψ
) denotes an integer equal to or greater than 1, ζ
(ψ
) denotes an integer equal to or greater than 0, a generator of a cyclic group G2 is denoted by g2, and the basis vectors bi*(ψ
)=(θ
(ψ
, i,
1)·
g2, . . . , θ
(ψ
, i, n(ψ
)+ζ
(ψ
))·
g2)ε
G2n(ψ
)+ζ
(ψ
) are n(ψ
)+ζ
(ψ
)-dimensional basis vectors for θ
(ψ
, i, β
), where i=1, . . . , n(ψ
)+ζ
(ψ
), β
=1, . . . , n(ψ
)+ζ
(ψ
), n(ψ
)≧
1, ζ
(ψ
)≧
1, the elements of the basis vectors bi*(ψ
) are n(ψ
)+ζ
(ψ
) elements of the cyclic group G2. - View Dependent Claims (28, 31)
- (ψ
-
14. A share management apparatus that generates share secret values DSH(ψ
- , α
, h(α
)) by performing a common calculation common in each subset SUB(α
) consisting of H(α
) share management apparatuses PA(α
,
1), . . . , PA(α
, H(α
)), where α
=1, . . . , L, L≧
2, h(α
)=1, . . . , H(α
), H(α
)≧
2, on common information shared in the subset SUB(α
) and share information SH(ψ
, i, β
, α
, h(α
)) obtained by independently sharing a value corresponding to each element θ
(ψ
, i, β
)·
g2 of a basis vectors bi*(ψ
) among the subset SUB(α
), provided that h(α
)=1, . . . , H(α
), denotes an integer equal to or greater than 1, ψ
denotes an integer equal to or greater than 0 and equal to or smaller than Ψ
, ψ
=0, . . . , Ψ
, n(ψ
) denotes an integer equal to or greater than 1, ζ
(ψ
) denotes an integer equal to or greater than 0, a generator of a cyclic group G2 is denoted by g2, and the basis vectors are n(ψ
)+ζ
(ψ
)-dimensional basis vectors bi*(ψ
)=(θ
(ψ
, i,
1)·
g2, . . . , θ
(ψ
, i, n(ψ
)+ζ
(ψ
))·
g2)ε
G2n(ψ
)+ζ
(ψ
) for θ
(ψ
, i, β
), where i=1, . . . , n(ψ
)+ζ
(ψ
), β
=1, . . . , n(ψ
)+ζ
(ψ
), n(ψ
)≧
1, ζ
(ψ
)≧
1, the elements of the basis vectors bi*(ψ
) are n(ψ
)+ζ
(ψ
) elements of the cyclic group G2. - View Dependent Claims (29, 32)
- , α
-
15. An acquisition apparatus, comprising:
-
a reconstruction unit that generates reconstructed secret values SUBSK(ψ
, α
) for each subset SUB(α
) from a plurality of share secret values DSH(ψ
, α
, h(α
)) for the subset SUB(α
) by performing a reconstruction processing for the subset SUB(α
) according to a predetermined secret sharing scheme, provided that Ψ
denotes an integer equal to or greater than 1, ψ
denotes an integer equal to or greater than 0 and equal to or smaller than Ψ
, ψ
=0, . . . , Ψ
, SUB(α
) denotes the subset consisting of H(α
) share management apparatuses PA(α
,
1), . . . , PA(α
, H(α
)), α
=1, . . . , L, L≧
2, h(α
)=1, . . . , H(α
), H(α
)≧
2; anda synthesis unit that generates generation information D*(ψ
) from the reconstructed secret values SUBSK(ψ
, α
). - View Dependent Claims (30, 33)
-
-
16. A secret sharing method performed by a sharing apparatus, Σ
-
α
=1L h(α
) share management apparatuses PA(α
, h(α
)), where α
=1, . . . , L, L≧
2, h(α
)=1, . . . , H(α
), H(α
)≧
2, and an acquisition apparatus, the method comprising;(A) a step of independently sharing, at the sharing apparatus, a value corresponding to each element θ
(ψ
, i, β
)·
g2 of basis vectors bi*(ψ
) among each subset SUB(α
) consisting of H(α
) share management apparatuses PA(α
,
1), . . . , PA(α
, H(α
)) according to a predetermined secret sharing scheme to generate share information SH(ψ
, i, β
, α
, h(α
)) corresponding to each element θ
(ψ
, i, β
)·
g2, where h(α
)=1, . . . , H(α
), provided that Ψ
denotes an integer equal to or greater than 1, ψ
denotes an integer equal to or greater than 0 and equal to or smaller than Ψ
, ψ
=0, . . . , Ψ
, n(ψ
) denotes an integer equal to or greater than 1, ζ
(ψ
) denotes an integer equal to or greater than 0, a generator of a cyclic group G2 is denoted by g2, and the basis vectors bi*(ψ
)=(θ
(ψ
, i,
1)·
g2, θ
(ψ
, i, n(ψ
)+ζ
(ψ
))·
g2)ε
G2n(ψ
)+ζ
(ψ
) are an n(ψ
)+ζ
(ψ
)-dimensional basis vectors for θ
(ψ
, i, β
), where i=1, . . . , n(ψ
)+ζ
(ψ
), β
=1, . . . , n(ψ
)+ζ
(ψ
), n(ψ
)≧
1, ζ
(ψ
)≧
1, the elements of the basis vectors bi*(ψ
) are n(ψ
)+ζ
(ψ
) elements of the cyclic group G2;(B) a step of generating, at each of the share management apparatuses PA(α
, h(α
)), share secret values DSH(ψ
, α
, h(α
)) by performing a common calculation common in the subset SUB(α
) on common information shared in the subset SUB(α
) and the share information SH(ψ
, i, β
, α
, h(α
)), where h(α
)=1, . . . , H(α
);(C) a step of generating, at the acquisition apparatus, reconstructed secret values SUBSK(ψ
, α
) for each subset SUB(α
) from a plurality of the share secret values DSH(ψ
, α
, h(α
)) for the subset SUB(α
) by performing a reconstruction processing for the subset SUB(α
) according to the secret sharing scheme; and(D) a step of generating, the acquisition apparatus, generation information D*(ψ
) from the reconstructed secret values SUBSK(ψ
, α
). - View Dependent Claims (17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27)
-
α
Specification
-
- Resources
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Current AssigneeNippon Telegraph and Telephone Corporation
-
Original AssigneeNippon Telegraph and Telephone Corporation
-
InventorsNishimaki, Ryo, Suzuki, Koutarou
-
Granted Patent
-
Time in Patent OfficeDays
-
Field of Search
-
US Class Current380/278
-
CPC Class CodesH04L 9/0836 using tree structure or hie...H04L 9/085 Secret sharing or secret sp...H04L 9/0861 Generation of secret inform...H04L 9/3073 involving pairings, e.g. id...
