Bulletproof

A compact zero-knowledge proof, most used as a range proof (proving a hidden number lies in a valid range without revealing it), that requires no trusted setup. Bulletproofs let confidential transactions keep amounts private while proving no illegal (negative/overflowing) value was created — the soundness backbone of private-amount systems like Monero, which adopted them to shrink proof size. The trade-off is small, setup-free proofs at the cost of relatively heavy verification.