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What is ECDSA?
ECDSA (Elliptic Curve Digital Signature Algorithm) is the signature method Bitcoin and Ethereum accounts use to prove a transaction was approved by the right private key. It is built on the mathematics of elliptic curves, which allows short keys and short signatures.
What it means for you
Every ECDSA signature needs a fresh secret number. Wallet software that reuses or leaks that number lets anyone who sees the signatures calculate the private key. You cannot spot this from outside, so it comes down to the quality of the wallet software or device doing the signing.
How it works
FIPS 186-5 specifies ECDSA. The private key is a number d and the public key is the curve point Q = dG, where G is a fixed generator point. To sign, the signer picks a new secret number k for each message, takes r from the x-coordinate of the point kG, and computes s = k^-1(h + d*r) mod n, where h is the message hash. The verifier checks (r, s) against Q. RFC 6979 shows that a known k lets anyone solve for d, and defines deterministic ECDSA, which derives k from the key and the message. Bitcoin uses ECDSA on the curve secp256k1.
Sources: NIST FIPS 186-5: Digital Signature Standard, RFC 6979: Deterministic usage of DSA and ECDSA, Bitcoin developer guide: transactions · checked 4 October 2026
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