Algebraic Construction for Multi-Party Protocols with Focus on Threshold Signatures

Secure multi-party computation (MPC) is a field of cryptography that aims to provide methods for parties to jointly compute a function over their inputs while keeping those inputs private. Unlike of traditional cryptography where adversary is outside the system of participants, the main task (and challenge) of MPC is to protect participants from internal adversaries, who participate in protocol and can therefore send corrupted. The results presented in this thesis are three-fold. First, we study MPC from a theoretical standpoint, designing a new heuristic and a new proof system useful for proving the security of threshold signatures, a particular kind of MPC protocol. Next, we present new MPC primitives: a novel secret sharing scheme, a threshold version of Schnorr signature, a post quantum secure group action based threshold signature and finally a post quantum oblivious transfer. Lastly, we designed a coercion resistant e-voting protocol, that allows voters to freely votes without being afraid of external adversaries trying to pressure them to vote in a particular way.