Proposal of a Ramp Scheme with Anonymous Reconstruction for a One-Bit Secret Using Fermat's Little Theorem

抄録

In a secret sharing scheme, a dealer generates n shares from a secret to share the secret among n participants. We focus on an (s, t, n)-ramp scheme satisfying (i) the secret is correctly recovered by the shares of t or more arbitrary participants, and (ii) no information on a secret is revealed from the shares of s or less arbitrary participants. We propose a novel construction of a $(2,p-1,\frac{3p-7}{2})$-ramp scheme for a one-bit secret, where p ≥ 7 is an arbitrary prime number. This scheme has a property that a secret is reconstructed by arbitrary p - 1 participants in an anonymous way, i.e., without revealing their identities, by multiplying their shares.