Conditional Disclosure of Secrets and d-Uniform Secret Sharing with Constant Information Rate

Consider the following secret-sharing problem. Your goal is to distribute a long file s between n servers such that (d − 1)-subsets cannot recover the file, (d + 1)-subsets can recover the file, and d-subsets should be able to recover s if and only if they appear in some predefined list L. How small can the information ratio (i.e., the number of bits stored… CONTINUE READING