Bulletproofs: Range Proof Verification at Logarithmic Scale
Bulletproofs cut Monero range proof sizes from ~13 KB to under 800 bytes. The mechanism is a recursive inner product argument, and the math holds up.
№ 002SecurityHomomorphic Encryption vs Zero-Knowledge Proofs
HE computes on encrypted data; ZK proofs verify claims about it. Understanding the mechanical difference prevents costly architectural mistakes.
№ 003DeFiBlockchain Bridge Verification: Optimistic vs ZK Proofs
Optimistic bridges wait for objections; ZK bridges prove correctness first. The security tradeoffs are starker than most explanations admit.
№ 004AnalysisRecursive STARK Proofs: Flat Verification Costs Explained
Recursive STARKs aggregate thousands of proofs into one fixed-cost verification. The mechanism, the trade-offs, and a worked example.
№ 005SecurityConfidential Asset Protocols: Hiding Amounts on Chain
Pedersen commitments and range proofs shield transaction amounts on-chain while preserving cryptographically sound audit trails for regulators and investors.
№ 006SecuritySilent Inflation Bugs in Zero-Knowledge Proof Systems
ZK inflation bugs mint tokens from nothing while every proof verifies clean. The mechanism, the failure modes, and what a real detection framework requires.
№ 007SecurityZero-Knowledge Proofs: Proving Compliance, Not Data
Zero-knowledge proofs let crypto firms prove regulatory compliance to auditors without revealing any underlying user data. Here's the exact mechanism.
№ 008AnalysisRecursive zk-Proofs: Scalability Without Growing Costs
Recursive zk-proofs let blockchains batch thousands of transactions into one compact proof. Here's exactly how the math stays flat as volume grows.
№ 009SecurityHow zk-SNARKs Stay Small Without Breaking Soundness
zk-SNARKs produce tiny proofs that verify in milliseconds. Here's the exact mechanism that makes them compact without letting cheaters through.