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ECDSA stands for Elliptic Curve Digital Signature Algorithm. It is a public-key algorithm for creating and checking digital signatures: a private key signs, and the corresponding public key verifies. NIST describes it as “the elliptic curve analog of DSA.”
What ECDSA is used for
An ECDSA signature can help a verifier establish that data was signed by the holder of a particular private key and detect whether the signed data has changed. A mathematical signature check is only one part of accepting a signature: the verifier also needs trustworthy information about the signer’s identity, public key, curve parameters, and possession of the private key.
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ECDSA is a signature algorithm, not a method for encrypting data. Its keys are intended for digital signatures and must not be reused for another purpose, such as key establishment.
How ECDSA signing and verification work
Signing
The signer hashes the message with a hash function and uses the private key, the curve parameters, and a per-message secret number to calculate a signature. That signature consists of two values, written as (r, s). FIPS 186-5 specifies the exact generation procedure; the brief description here is conceptual, not an implementation recipe.
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Verification
The verifier uses the signer’s public key and the relevant curve parameters, hashes the received data with the same hash function used for signing, and applies ECDSA’s verification procedure to the signature. If the check fails, the signature cannot be verified for that data with the supplied key and signature format. Failure does not, by itself, establish whether the data is otherwise correct.
Why the curve parameters matter
ECDSA operates within a defined elliptic-curve domain. Its parameters include the underlying field, the curve model and coefficients, a base point G, the order n, and the cofactor h. The public key and verification process are tied to those parameters, so a curve name is not an interchangeable label: the verifier must use the domain parameters that belong with the key.
Deterministic ECDSA
In deterministic ECDSA, the per-message secret number is derived deterministically from the message and private key. For a given message and key, this produces a deterministic signature; verification is unchanged. NIST notes that this variant may be desirable for devices that lack a reliable source of high-quality random numbers. RFC 6979 describes a procedure for generating the number deterministically.
Deterministic generation does not remove the need to protect the private key or to implement the algorithm correctly. NIST warns about side-channel and fault attacks and stresses the importance of correct elliptic-curve arithmetic.
Security-strength ranges in FIPS 186-5
FIPS 186-5 gives the following ranges for the order n and their comparable security strengths. These are standard parameter ranges, not measurements of a particular implementation or guarantees about its security.
Order n size |
Comparable security strength | Source and date |
|---|---|---|
| 224–255 bits | At least 112 bits | NIST FIPS 186-5, 2023 |
| 256–383 bits | At least 128 bits | NIST FIPS 186-5, 2023 |
| 384–511 bits | At least 192 bits | NIST FIPS 186-5, 2023 |
Which standards specify ECDSA?
NIST FIPS 186-5 specifies ECDSA for signature generation and verification. Its publication page says it was published on February 3, 2023. NIST SP 800-186 provides recommended elliptic-curve parameters. NIST’s FIPS 186-5 release notice says binary-field curves are deprecated and strongly recommends other, prime curves.
For a compliance decision, check the current NIST publication record and errata: the FIPS 186-5 page includes a planning note dated May 12, 2025, saying NIST had identified issues to correct in a future update or revision. A standards citation alone should not be treated as confirmation that a particular implementation or deployment meets applicable requirements.
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ECDSA is one signature family, not a synonym for digital signatures
FIPS 186-5 also specifies RSA and EdDSA for signatures. EdDSA is based on a variant of Schnorr signatures over twisted Edwards curves; ECDSA uses its own (r, s) procedure. These algorithms have different mathematical constructions and deployment requirements. Which one fits depends on the required standard, ecosystem support, key and signature formats, implementation characteristics, and security requirements; they should not be treated as interchangeable without that context.
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