A Linear Algebraic Approach to Strongly Secure Ramp Secret Sharing for General Access Structures

Secret sharing is a cryptographic technique to share a secret among participants in such a way that only authorized subsets are able to recover the secret. Ramp secret sharing schemes can achieve better information ratio than perfect schemes while some partial information on a secret which is composed of several sub-secrets leaks out. The notion of strong security has been introduced to control the amount of information on every subset of the sub-secrets unauthorized sets can obtain. In this paper, we reduce the construction of strongly secure ramp secret sharing for general access structures to a linear algebraic problem. As a result, we show that previous results on strongly secure network coding imply two constructions of a linear transformation which makes a given linear ramp scheme strongly secure. They are explicit or provide a deterministic algorithm while the previous method which works for any linear ramp scheme is probabilistic.