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Abstract

A secret sharing system transforms shares in ramp secret sharing to shares in homomorphic secret sharing. On a data distribution apparatus, a division part divides information a into N shares f_a(n) using an arbitrary ramp secret sharing scheme S1. On each of distributed data transform apparatuses, a random number selecting part generates a random number vector r_i whose elements are L random numbers r_i1. A first random number division part divides the random number vector into N shares f_ri(n) using a ramp secret sharing scheme S1. A second random number division part divides each of the L random numbers r_i1 into N shares g_ri,1(n) using an arbitrary secret sharing scheme S2. A disturbance part generates a share U_i by using a share f_a(i) and shares f_rλ(i). A reconstruction part reconstructs L pieces of disturbance information c₁ from shares U_λ by using the ramp secret sharing scheme S1. A redivision part divides each piece of disturbance information c₁ into N using the secret sharing scheme S2 to generate shares g_c1(n). A transform part generates shares g_a1(i) of the information a by using a share g_c1(i) and the shares g_rλ,1(i).

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