An Advanced Signature Scheme: Schnorr algorithm and its Benefits to the Bitcoin Ecosystem
This thesis has been realized for the Master of Science in Mathematical Engineering at Politecnico di Milano.
ECDSA (Elliptic Curve Digital Signature Algorithm) is currently used as digital signature scheme for Bitcoin: its drawbacks are well known and it could be better to avoid them. The Schnorr signature algorithm, although still lacking a standardization, is superior in every aspect to ECDSA. Starting from the mathematical and cryptographic foundations, the aim of this work is to present the two schemes, delve into their technicalities and compare them; then study the benefits to higher level constructions allowed by Schnorr (multi-signatures, threshold signatures, cross-chain atomic swaps and the Lightning Network). The discussion proceeds according to the recent BIP (Bitcoin Improvement Proposal) by Pieter Wuille and others about Schnorr's standardization for Bitcoin.