Secret sharing system, data distribution apparatus, distributed data transform apparatus, secret sharing method and program
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 fa(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 ri whose elements are L random numbers ri1. A first random number division part divides the random number vector into N shares fri(n) using a ramp secret sharing scheme S1. A second random number division part divides each of the L random numbers ri1 into N shares gri,1(n) using an arbitrary secret sharing scheme S2. A disturbance part generates a share Ui by using a share fa(i) and shares frλ(i). A reconstruction part reconstructs L pieces of disturbance information c1 from shares Uλ 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 gc1(n). A transform part generates shares ga1(i) of the information a by using a share gc1(i) and the shares grλ,1(i).
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