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Elliptic Curve Digital Signature Algorithm

Creates digital signatures with elliptic-curve keys.

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Quick Facts

Compact metadata for implementation and discovery.

Category: Cryptography
Difficulty: Advanced
Family: Digital Signature
Tier: Specialized
Status: Verified
Review: Source Checked
Sources: 1
Formulas: 1
Relationships: 4
Code example: Not ready
Visualization: Ready
Aliases: ECDSA

Overview

ECDSA signs message digests using elliptic-curve arithmetic and verifies signatures with the public key.

Core Concepts

security primitivecurve point operationsignature verificationsecurity assumptiondigital signaturekey materialmessage transformation

Quick facts

Complexity

Runtime and memory behavior at a glance.

Best

O(k^2)

Average

O(k^2)

Worst

O(k^3)

Space

O(k)

When to Use

Use Elliptic Curve Digital Signature Algorithm when you need to sign a message digest.
Use it for tLS certificates with inputs like private or public key.
Use it only through reviewed libraries when the security goal matches the primitive.
Use it when the Digital Signature tradeoff is acceptable for the problem size.

When Not to Use

Avoid custom implementations for production security or when key, nonce, and padding rules are unclear.
Avoid it when O(k^3) worst-case behavior is too costly for the expected input size.
Avoid it when the required output is not signature.

What It Does

Signs a message digest
Verifies signatures with a public key

Use Cases

TLS certificates
Code signing
Blockchain transactions

Inputs

Private or public key
Message digest
Nonce for signing

Outputs

Signature
Verification result

Key Formulas (1)

ECDSA signature scalar

s = inverse(k) · (hash(message) + r · private_key) mod n

s = inverse(k) * (hash(message) + r * private_key) mod n

Computes the signature value from the message hash, nonce, and private key.

Pseudocode

1.Hash the message
2.Generate a per-signature nonce
3.Compute a curve point from the nonce
4.Combine the digest, private key, and nonce into a signature pair
5.Verify the pair with the public key

Canonical Example

Input: message = 'pay $10', key material = configured securely
Output: protected value such as a digest, signature, shared secret, or ciphertext
Explanation: Elliptic Curve Digital Signature Algorithm: The primitive transforms the message according to a specific security purpose.

Implementation Notes

Keep the input contract explicit: Private or public key; Message digest; Nonce for signing.
Use this step as the implementation spine: Hash the message.
Then preserve the next state change: Generate a per-signature nonce.
Validate parameters, key sizes, nonces, salts, and error handling against the library's recommended API.

Common Pitfalls

Reusing or biasing the signing nonce can reveal the private key.
Confusing encryption, hashing, signatures, and authentication codes as interchangeable tools.
Returning signature without handling empty, invalid, or boundary inputs.

Interactive Mechanism Walkthrough

Graph Frontier & Edge Relaxation

Show a private key creating a signature that a public key verifies.

Step 1 of 5: Hash the message

signature-flow

Notes

Elliptic Curve Digital Signature Algorithm operates in O(k^2) time and O(k) space within the Digital Signature family. Key governing relation: s = inverse(k) * (hash(message) + r * private_key) mod n. Often compared with Elliptic Curve Diffie-Hellman and EdDSA.