In this talk we will consider the problem of comparing two secret (e.g. encrypted) values, $a$ and $b$. The output must be a bit indicating whether $a < b$; no other information about $a$ or $b$ must be disclosed. We will first explain a solution to this problem, which uses some cryptographic sub-protocols, all of them based on homomorphic encryption schemes with a threshold decryption mechanism.

After that, we will discuss some real situations and problems where such a protocol for the secure comparison of secret values is necessary or useful: distributed methods to protect statistical databases, secure methods to implement majority decisions (e.g. voting schemes, private scheduling, etc.).