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, ..., SLand n shares X1, X2, ..., Xn 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, ..., SL.