Monero’s transaction protocol uses several cryptographic constructions working in tandem; these include linkable ring signatures, Pedersen commitments, and range proofs. Each component of the transaction model introduces costs that affect network performance and user experience. In this talk, we will review past and present efforts to improve transaction space and time efficiency. We’ll discuss Bulletproofs for range proofs, changes to Pedersen element communication for output size reduction, and compact LSAG signatures for ring signature optimization. No prior experience with these constructions is assumed, so this talk will be accessible to everyone! Sarang Noether is a mathematician and cryptographer who conducts research and development for the Monero Research Lab. He has extensive worldwide teaching and speaking experience in mathematics, technology, and applied cryptography.