Unconditionally secure cryptographic protocols from coding-theoretic primitives

This dissertation presents new cryptographic protocols, which can be divided into two families. Protocols in the first family achieve unilateral security: this means that they protect legitimate users against an external attacker. Concretely, we assume that two users wish to communicate securely over a given communication system, where an external attacker eavesdrops and tampers with some of the wires of the system. We contribute to the topic by presenting protocols with improved efficiency and a simpler definition compared to previous work, and we design interactive protocols that achieve security against a stronger attacker.

Protocols of the second type achieve multilateral security, meaning that they protect users against each other. This is the case for multi-party computation or MPC, where several users wish to compute a function on private inputs while keeping inputs private and without appealing to a trusted third party; we contribute to this topic by adding a cheater-detection functionality to a well-established MPC protocol.

A key component that underlies these scenarios is secret sharing; we investigate this topic by casting in particular a new light on its connections with coding theory. This allows us to better harness the features of recent code constructions to obtain improved secret-sharing schemes.