A secret sharing scheme based on a systematic Reed-Solomon code and analysis of its security for a general class of sources

In this paper we investigate a secret sharing scheme based on a shortened systematic Reed-Solomon code. In the scheme L secrets S₁, S₂, ..., S_L and n shares X₁, X₂, ..., X_n satisfy certain n - k + L linear equations. Security of such a ramp secret sharing scheme is analyzed in detail. We prove that this scheme realizes a (k; n)-threshold scheme for the case of L = 1 and a ramp (k, L, n)-threshold scheme for the case of 2 ≤ L ≤ k - 1 under a certain assumption on S₁, S₂, ..., S_L.