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What is ECDSA used for?
ECDSA—the Elliptic Curve Digital Signature Algorithm—is used to generate and verify digital signatures. A signature can help detect unauthorized changes to signed data and support authentication of the signatory. It does not, by itself, prove that a real-world person or organization owns the public key used to verify it.
FIPS 186-5 specifies ECDSA for signatures and says its keys must not be reused for another purpose. NIST states: “ECDSA keys shall not be used for any other purpose (e.g., key establishment).” Use separate keys for signing and for purposes such as key establishment.
How do I generate an ECDSA signature safely?
At a high level, signing uses an ECDSA key pair and domain parameters, hashes the data with an appropriate approved hash function, obtains a per-message secret value, and computes the signature. Follow the applicable standard and your cryptographic library’s documented interface rather than implementing the elliptic-curve arithmetic yourself.
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- Establish parameters and keys. Select domain parameters that meet the applicable standards and deployment requirements, then generate and protect the signing private key and corresponding public key.
- Hash the exact data. Use an appropriate approved hash function, and ensure the verifier uses the same hash function and the same data representation.
- Generate the per-message secret. Ordinary ECDSA uses a random secret value for each signature. Treat this value as sensitive; errors in its generation or handling can undermine the private key.
- Compute and encode the signature. Use a conforming implementation and the signature format required by the protocol or application. Interoperability depends on agreeing on details such as encoding, not merely on choosing ECDSA.
- Optionally verify the result. FIPS 186-5 allows a signer to verify its own signature as a final check for otherwise undetected computation errors. This can be useful when a signature is high value, will be checked by multiple verifiers, or may not be checked until much later.
Does deterministic ECDSA remove the need for randomness?
It removes the need to obtain a fresh random per-message secret for each signature: deterministic ECDSA derives that value as a function of the message and private key, using a specified procedure. FIPS 186-5 points to RFC 6979 for deterministic generation and says verification is unchanged. NIST notes: “The use of deterministic ECDSA may be desirable for devices that do not have a good source of quality random numbers.”
| Approach | Per-message secret | Verification |
|---|---|---|
| Ordinary ECDSA | Requires a random per-message secret value. | Uses the standard ECDSA verification process. |
| Deterministic ECDSA | Derives the value from the message and private key according to the deterministic procedure. | Uses the same verification process as ordinary ECDSA. |
Deterministic signing does not make the private key safe, fix faulty arithmetic, or eliminate implementation risks. It addresses how the per-message secret is obtained—not key management or the correctness of the signing implementation.
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How do I choose an ECDSA curve?
ECDSA domain parameters include the field, curve model and coefficients, base point, subgroup order, and cofactor. FIPS 186-5 refers readers to NIST SP 800-186 for recommended curves for Federal Government use. Curve selection should follow the standards that apply to your deployment, required interoperability, validation requirements, and security target; the ranges below are not a complete curve-selection recipe.
| Subgroup-order bit length in FIPS 186-5 | Approximate security strength |
|---|---|
| 224–255 bits | At least 112 bits |
| 256–383 bits | At least 128 bits |
| 384–511 bits | At least 192 bits |
These are the standard’s parameter ranges. NIST relates approximate ECDSA security strength to half the subgroup-order bit length. Confirm that a candidate curve is approved or otherwise suitable for the relevant jurisdiction and protocol rather than choosing from bit length alone.
What should I verify besides the signature?
A successful signature check establishes that the signature verifies for the data, public key, parameters, and format supplied to the verifier. It does not establish that the data is true, that the public key belongs to the claimed signer, or that the key was used by that signer at the relevant time.
- Obtain the claimed signer’s public key and ECDSA domain parameters from a source appropriate to the application.
- Validate the identity-to-key binding. Establish that the public key belongs to the person, service, or organization named as signer; a mathematically valid signature does not supply this assurance.
- Check parameter and public-key validity. Confirm the domain parameters and public key meet the applicable requirements.
- Hash the data being verified with the same hash function used at signing, using the correct data representation.
- Run signature verification with the corresponding public key, parameters, and expected signature format.
- Assess signing-time key possession and context. For acceptance, obtain assurance that the signer possessed the corresponding private key when the signature was generated, and apply any application-specific authorization or freshness checks.
If verification fails, the signature cannot be verified for the supplied data, key, parameters, and format. That result does not determine whether the data itself is correct.
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Why can a correct ECDSA primitive still be insecure?
Security depends on the implementation and the surrounding key-management system as well as the algorithm. NIST highlights side-channel and fault attacks that can expose internal data or key material without breaking the cryptographic primitive, and emphasizes correct elliptic-curve group arithmetic. These concerns are particularly relevant to hardware, embedded and IoT devices, and smartcards.
- Keep private keys secret and restrict access to signing operations.
- Use a maintained, conforming cryptographic implementation instead of writing your own curve arithmetic.
- Evaluate protections against side-channel leakage and fault attacks for the actual deployment environment.
- Where applicable, check the NIST Cryptographic Algorithm Validation Program prerequisites and relevant validation records. The program lists FIPS 186-5 ECDSA key-generation, key-verification, signature-generation, and signature-verification modes, as well as deterministic signature generation; a listing is evidence about a particular validation context, not blanket approval of every product or configuration.
Is ECDSA secure against quantum computers?
No. NIST’s February 3, 2023 announcement accompanying FIPS 186-5 and SP 800-186 says: “The algorithms in these standards are not expected to provide resistance from attacks from a large-scale quantum computer.” Do not treat ECDSA as post-quantum secure; if that threat model matters, use standards and migration guidance intended for post-quantum security.
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