ECDSA

ECDSA (Elliptic Curve Digital Signature Algorithm) is the signature scheme that uses elliptic-curve cryptography to sign messages. A signing key is a random 256-bit integer; the public key is a point on the curve derived from multiplying the curve generator by that scalar. Signing a message hash produces a two-integer (r, s) tuple; verifying checks r and s against the hash, curve parameters, and public key.

LearnCoin uses ECDSA over the secp256k1 curve — the same combination Bitcoin and Ethereum use. GCP KMS signs SHA-256 digests of canonicalized credentials and returns DER-encoded (r, s) pairs. The resulting signatures fit into MerkleProof2019's proofValue encoding.

ECDSA has well-known pitfalls. The per-signature nonce k must be unpredictable — leak k and the private key is recoverable. RFC 6979 specifies a deterministic k derived from the message hash and private key, eliminating the nonce-reuse attack surface. GCP KMS handles this inside the HSM.