Digital signature

The standard scheme in Bitcoin and Ethereum is ECDSA over the secp256k1 curve. It is not deterministic by default: each signature requires a random nonce, and as a best practice it must never be reused or predictable, since that would leak the private key. In Ethereum the signature adds a recovery component. Schnorr over secp256k1 (BIP-340) arrived with Bitcoin's Taproot upgrade in 2021 and brings non-malleability and signature aggregation. EdDSA with Ed25519 is deterministic, fast to verify and more robust against nonce failures; all three schemes offer about 128 bits of security. The current NIST standard is FIPS 186-5.

It is what authorizes transactions: holding the private key equals controlling the funds and identity tied to the address. It connects wallets, accounts and asset control, and is the piece that backs ownership in any tokenized infrastructure.

Bitcoin and Ethereum use ECDSA over secp256k1 for their accounts; Schnorr and Taproot have run on Bitcoin since 2021; Solana, Cardano and Stellar use Ed25519, also present in SSH and TLS. Typed EIP-712 signatures, over readable structured data, are the basis of Web3 logins and of off-chain anchored attestations. The signature is applied over the hash produced by a cryptographic hash function, and in a zk-SNARK or zk-STARK the possession of a valid signature can be proven without revealing it, useful for anonymous identity.