Secret sharing schemes allow a dealer to distribute shares of a secret value among a set of parties so that only "qualified" subsets of parties can recover the secret value. Blakley [1] and Shamir [2] initiated the study of threshold secret sharing schemes, in which a set of parties is qualified if and only if it contains some minimum threshold of parties. Ito, Saito, and Nishizeki [3] subsequently proposed secret sharing schemes for general access structures, i.e., arbitrary qualified sets.

This presentation will cover a selection of secret sharing constructions, lower bounds, and major open questions. It is intended to be accessible to a general audience -- I hope there will be something for everyone, whether this is your first foray into secret sharing or your fiftieth!

[1] G. R. Blakley. Safeguarding cryptographic keys. Proc. of the 1979 AFIPS National Computer Conference. AFIPS Press, 1979.

[2] A. Shamir. How to share a secret. Communications of the ACM, 22:612–613, 1979.

[3] M. Ito, A. Saito, and T. Nishizeki. Secret sharing schemes realizing general access structure. In Proc. of the IEEE Global Telecommunication Conf, 1987. Journal version: Multiple assignment scheme for sharing secret. J. of Cryptology, 6(1):15-20, 1993.

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