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AssigneeNippon Telegraph and Telephone Corporation
InventorDai IKARASHI
Estimating the term…
Computational complexity is reduced in accordance with given k and n. A random number generation unit 12 generates random numbers r0 to rk-2 ∈GF(xq). A share generation unit 14 generates shares b0 to bn-1 by calculating a product of a vector a=(r0, . . . , rk-2, s), having the random numbers r0 to rk-2 and plaintext s∈GF(xq) as its elements, and a matrix A. A share selection unit 15 generates a vector b′=(bp0, . . . , bpk-1) having, as its elements, k shares bp0 to bpk-1 selected from the shares b0 to bn-1. An inverse-matrix generation unit 16 generates an inverse matrix A′−1 of a k-degree square matrix having the p0-th to pk-1-th rows of the matrix A. A plaintext calculation unit 17 restores the plaintext s by multiplying the k-th row of the inverse matrix A′−1 and the vector b′.
A secret sharing method in which x is an element X of an irreducible polynomial f[X] that generates an extension field GF(xq), n and k are integers equal to or larger than 2 and satisfy n≥2k−1, p0 to pk-1 are different integers equal to or larger than 0 and smaller than n, and A is an n-by-k matrix defined by a formula given below:
A secret sharing system comprising a distributing apparatus and a restoring apparatus;
A distributing apparatus in which x is an element X of an irreducible polynomial f[X] that generates an extension field GF(xq), n and k are integers equal to or larger than 2 and satisfy n≥2k−1, p0 to pk-1, are different integers equal to or larger than 0 and smaller than n;
(canceled)
A non-transitory computer readable medium including computer executable instructions that make a distributing apparatus, wherein x is an element X of an irreducible polynomial f[X] that generates an extension field GF(xq), n and k are integers equal to or larger than 2 and satisfy n≥2k−1, p0 to pk-1 are different integers equal to or larger than 0 and smaller than n;
Dependencies are inferred from the claim text.