Secret Sharing

Abstract

In this chapter, we introduce the problem of secret-sharing. We present the generalized secret-sharing scheme of Ito et al. [98] and the threshold secret-sharing scheme of Shamir [135]. While secret-sharing schemes find extensive application in MPC, we showcase here another important application, namely perfectly-secure message transmission. We conclude with demonstrating what can go wrong in a secret-sharing scheme in the face of malicious adversaries. Consider the following application. There is a bank with three managers. There is a locker in the bank, which needs to be opened every day using the help of the managers. Each of the managers has got a password to operate the locker. However, no one trusts any single manager. So we want to design a system where the locker can be opened only if at least two of the managers enter their respective passwords, but the locker should remain inaccessible if only a single manager tries to open it. Similarly, consider a scenario where the passcode of a country’s nuclear missile is shared among the top three entities of the country, say the president, vice-president and the prime-minister in such a way that the missile can be launched only when at least two of these three entities agree to do the same.