A (t, n) secret sharing scheme [1, 2] allows a secret to be shared among n users in such a way that only t or more users can reconstruct the secret, but any t − 1 or less users have absolutely no information about the secret. One common drawback of almost all known secret sharing schemes is that they are one-time schemes. That is, once any t or more users reconstruct the secret by pooling their...

In a Multistage Secret Sharing (MSSS) scheme, the authorized subsets of participants could reconstruct a number of secrets in consecutive stages. A One-Stage Multisecret Sharing (OSMSS) scheme is a special case of MSSS schemes that all secrets are recovered simultaneously. In these schemes, in addition to the individual shares, the dealer should provide the participants with a number of public ...

Alice disposes of some number of secrets. She is willing to disclose one of them to Bob. Although she agrees to let him choose wich secret he wants, she is not willing to allow him to gain any information on more than one secret. On the other hand, Bob does not want Alice to know which secret he wishes. This is a useful building block in crypto-protocols. For instance, it can be used to easily ...