Secret Sharing

Secret sharing becomes indispensable whenever secret information needs to be kept collectively by a group of participants in such a way that only a qualified subgroup is able to reconstruct the secret. An example of such a scheme is a (t, n) threshold secret sharing in which there are n participants holding their shares of the secret and every t (t ≤ n) participants can collectively recreate the secret while any (t − 1) participants cannot get any information about the secret. The need for secret sharing arises if the storage system is not reliable, so there is a high likelihood that some pieces of information will be lost. Secret sharing is also useful if the owner of the secret does not trust any single person. Instead, the owner can deposit the secret with a group so that only a sufficiently large subgroup of members can reconstruct the secret. Threshold schemes were independently proposed by Blakley [41] and Shamir [464].