Classical Access Structures of Ramp Secret Sharing Based on Quantum Stabilizer Codes In this paper we consider to use the quantum stabilizer codes as secret sharing schemes for classical secrets. We give necessary and sufficient conditions for qualified and forbidden sets in terms of quantum stabilizers. Then we give a GilbertVarshamovetype sufficient condition for existence of secret sharing schemes with given parameters, and by using that sufficient condition, we show that roughly 19% of participants can be made forbidden independently of the size of classical secret, in particular when an nbit classical secret is shared among n participants having 1qubit share each. We also consider how much information is obtained by an intermediate set and express that amount of information in terms of quantum stabilizers. All the results are stated in terms of linear spaces over finite fields associated with the quantum stabilizers.

Strongly Secure Ramp Secret Sharing Schemes from Any Linear Secret Sharing Schemes A secret sharing scheme (SSS) is a cryptographic tool to protect a secret from loss and leakage by dividing it into shares. A ramp SSS can improve the efficiency in terms of the sizes of shares by allowing partial information about the secret to leak out. In order to prevent the partial information from being recovered explicitly, the notion of the strong security has been introduced. However, there have been proposed few methods to construct strongly secure ramp SSSs for general access structures and they are not always sufficient. In this paper, we show that any linear ramp SSS can be transformed into a strongly secure scheme with the same access structure preserving the information ratio.