Rings and trees: how to prove coin ownership
summary
Compares three concrete ownership proofs: CLSAG (Monero today) uses linkable ring signatures with size and verification linear in ring size (e.g., a 16-member ring yields ~16 elements — millions become infeasible); Groth-style one-of-many proofs (Firo / Sigma / Spark) give logarithmic on‑chain proof size but still require linear verification over the bucket, enabling thousands but not millions; Merkle proofs (Zcash, proposed FCMP++ with curve‑trees and a bulletproofs-based circuit) scale to full‑chain membership with logarithmic or constant proofs (trusted setup for constant) and far larger anonymity sets.
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chapters (10)
- 0:00Introduction
- 1:09Proving coin ownership matters
- 3:58Cryptographic approaches to ownership
- 9:35CLSAG ring signatures in Monero
- 11:00Groth-Bal proofs and bucketed sets
- 14:50Merkel proofs and tree structures
- 19:46Monero’s FCMP++ upgrade
- 22:14Trade-offs across protocols
- 23:20Quantum risks for cryptographic proofs
- 26:50AI tools in cryptographic research
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