Forge Capsule

Merkle Trees and Cryptographic Accumulators

Merkle tree: binary hash tree, root hash commits to all leaves. Proof size O(log n). Used in: Bitcoin (tx tree), Ethereum (Patricia Merkle Trie), Git (object store), Certificate Transparency. Sparse Merkle Tree: fixed 256-bit depth, efficient non-membership proofs. Verkle trees (KZG polynomial commitments): O(1) proof size. RSA accumulator: element∈set iff witness·element^e ≡ root (mod n). Merkle mountain range (MMR): append-only, used in Mimblewimble. Applications: stateless clients, cross-chain bridges, STARK proof systems.