ECDSA stands for Elliptic Curve Digital Signature Algorithm. It is a public-key algorithm for creating and checking digital signatures: a private key signs data, and the corresponding public key lets a verifier check the signature. NIST calls it “the elliptic curve analog of DSA” and specifies it in FIPS 186-5.
What ECDSA does
A digital signature can help a verifier confirm that data was signed by the holder of a particular private key and detect whether the signed data has changed. The signature check is mathematical; it does not, by itself, prove who controls the key or whether that person is trustworthy. A complete validation process also depends on assurances about the signer’s identity, the public key and its curve parameters, and possession of the corresponding private key.
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ECDSA is for digital signatures. Its private key creates signatures, while the matching public key is used to verify them. NIST says ECDSA keys must not be reused for another purpose, such as key establishment.
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Signing
The signer hashes the message using an approved hash function. The signing procedure combines that digest with the private key, the curve parameters, and a per-message secret number to produce a signature containing two values: (r, s). FIPS 186-5 specifies the exact procedure; implementations must follow the standard rather than rely on an informal reconstruction of the mathematics.
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Verification
The verifier needs the signed data, the signature, the claimed signer’s public key, and the matching ECDSA domain parameters. The verifier hashes the received data with the same hash function used for signing and applies the verification procedure. If the check fails, the signature is not verified for that data with the supplied key and format. That failure does not tell the verifier whether the data is factually correct.
Why the elliptic curve matters
ECDSA keys and signatures are tied to a specific set of elliptic-curve domain parameters. These include the underlying field, the curve model and coefficients, a base point G, its order n, and a cofactor h. A curve name is not just a label that can be swapped independently: verification must use parameters compatible with the key and signature.
NIST’s SP 800-186 provides recommended elliptic-curve parameters. NIST’s 2023 announcement of FIPS 186-5 says binary-field curves are deprecated and strongly recommends other, prime curves. Which curves and formats are appropriate depends on the relevant standard and the systems that need to interoperate.
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Ordinary ECDSA uses a per-message secret number during signing. Deterministic ECDSA derives that value deterministically from the message and private key, so the same message and key produce the same signature. Verification works the same way as for ECDSA.
NIST notes that deterministic ECDSA may be useful for devices that lack a reliable source of high-quality random numbers. The procedure is described in RFC 6979. Deterministic signing does not remove the need to protect private keys or implement the algorithm correctly: NIST warns about side-channel and fault attacks and stresses the importance of correct elliptic-curve group arithmetic.
What security-strength figures mean
FIPS 186-5, published in 2023, gives these ranges for the order n and corresponding minimum comparable security strengths. They are standard parameter ranges, not measurements of a particular implementation or guarantees about its security.
Order n size |
Minimum comparable security strength | Source |
|---|---|---|
| 224–255 bits | 112 bits | NIST FIPS 186-5 (2023) |
| 256–383 bits | 128 bits | NIST FIPS 186-5 (2023) |
| 384–511 bits | 192 bits | NIST FIPS 186-5 (2023) |
ECDSA’s place among signature algorithms
FIPS 186-5 specifies RSA, ECDSA, and EdDSA for signature generation and verification; DSA remains only for verifying signatures generated previously. These are distinct algorithm families, not interchangeable labels. NIST describes EdDSA as based on a Schnorr-signature variant over twisted Edwards curves, while ECDSA uses its own (r, s) signature procedure. A suitable choice depends on the applicable requirements, supported key and signature formats, curve parameters, implementation characteristics, and ecosystem compatibility.
Standards and status
FIPS 186-5 was published on February 3, 2023. Its official publication page includes a planning note dated May 12, 2025, saying NIST identified issues to correct in a future update or revision. For a current compliance decision, consult the official FIPS 186-5 publication record and its errata spreadsheet rather than assuming the 2023 text is unchanged.
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