| 摘要 |
A secret sharing system according to the present invention includes N secret sharing apparatuses. The secret sharing system according to the present invention includes fragment replacement means and reshare means. The fragment replacement means selects a number, smaller than N, of secret sharing apparatuses, generates a bijection π of {1, . . . , K}→{1, . . . , K} among the selected secret sharing apparatuses and designates a fragment aπ(k)i recorded in a selected secret sharing apparatus as a k-th fragment (i represents an identification number that indicates a selected secret sharing apparatus). The reshare means performs reshare of fragments of a numeric value used as replacements by the fragment replacement means to determine new fragments. |
| 主权项 |
1. A secret sharing system comprising N secret sharing apparatuses,
wherein it is assumed that N represents an integer equal to or greater than 3, n represents an integer equal to or greater than 1 and equal to or smaller than N, M represents an integer equal to or greater than 1, m represents an integer equal to or greater than 1 and equal to or smaller than M, K represents an integer equal to or greater than 2, k represents an integer equal to or greater than 1 and equal to or smaller than K, numeric values A1(1), . . . , AK(1), . . . , A1(M), . . . , and AK(M) are K×M numeric values whose fragments are recorded in the secret sharing apparatuses in a distributed manner, numeric values AK(1), . . . , and AK(M) are a group of k-th numeric values associated with each other, akn(m) is a fragment of a numeric value Ak(m) recorded in an n-th secret sharing apparatus, and i represents an integer equal to or greater than 1 and equal to or smaller than N that indicates secret sharing apparatuses selected from among the N secret sharing apparatuses, and the secret sharing system comprises: the plurality of N secret sharing apparatuses, each of which includes at least one processor; and a selection apparatus, that includes at least one processor, and which may be one of the secret sharing apparatuses or a separate apparatus, configured to select a number, equal to or greater than 2 and smaller than N, of secret sharing apparatuses, wherein the plurality of secret sharing apparatuses selected by the selection apparatus being configured to generate a bijection π of {1, . . . , K}→{1, . . . , K}, which is a mapping of numbers 1 to K rearranged, among the secret sharing apparatuses selected by said selection apparatus and designate and reorder fragments aπ(k)i(1), . . . , and aπ(k)i(M) of a group of π(k)-th numeric values associated with each other recorded in an i-th selected secret sharing apparatus as fragments of a group of k-th numeric values associated with each other, and the plurality of N secret sharing apparatuses being configured to perform reshare of the fragments aπ(k)i(1), . . . , and aπ(k)i(M) of numeric values Aπ(k)(1), . . . , and Aπ(k)(M) that are used as replacements by said plurality of secret sharing apparatuses selected by the selection apparatus to determine new fragments bk1(1), . . . , bkN(1), . . . , bk1(M), . . . , and bkN(M) and designate the fragments bk1(1), . . . , bkN(1), . . . , bk1(M), . . . , and bkN(M) as fragments of numeric values Bk(1), . . . , and Bk(M). |
