ECDSA Sign & Verify

By Anish Nath - Security Engineer & Cryptography Expert | @anish2good | Last Updated: January 23, 2025
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Generate EC Key Pair
Sign / Verify Configuration
PEM format (BEGIN EC PRIVATE KEY)
PEM format (BEGIN PUBLIC KEY)
Output

Signature output will appear here

Enter a message and click "Generate Signature" or "Verify Signature"

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Understanding ECDSA

Elliptic Curve Digital Signature Algorithm (ECDSA) is a cryptographic algorithm used to ensure that data can only be signed by its rightful owners. It's widely used in cryptocurrencies like Bitcoin and Ethereum, as well as TLS/SSL, SSH, and secure messaging protocols.

What is ECDSA?

ECDSA is a variant of the Digital Signature Algorithm (DSA) that uses elliptic curve cryptography. It provides the same level of security as RSA but with significantly smaller key sizes, making it more efficient for:

  • Mobile devices - Less computational power required
  • IoT devices - Smaller memory footprint
  • Blockchain - Faster transaction verification
  • TLS handshakes - Reduced bandwidth and latency

How ECDSA Works

Signing Process
  1. Hash the message using SHA-256 (or similar)
  2. Generate a random number k (critical for security)
  3. Calculate point R = k × G on the curve
  4. Calculate r = R.x mod n
  5. Calculate s = k⁻¹(hash + r × privateKey) mod n
  6. Signature is the pair (r, s)
Verification Process
  1. Hash the message using the same algorithm
  2. Calculate w = s⁻¹ mod n
  3. Calculate u1 = hash × w mod n
  4. Calculate u2 = r × w mod n
  5. Calculate point P = u1 × G + u2 × PublicKey
  6. Signature valid if P.x mod n == r

Key Concepts

Private Key

A secret 256-bit integer known only to the owner. Used to generate signatures. In Bitcoin, this is derived from a random number. Must be kept absolutely secret.

Public Key

Derived from the private key using elliptic curve point multiplication: PublicKey = privateKey × G. Can be shared publicly and used to verify signatures.

Signature

Proves that the signer has the private key without revealing it. Consists of two values (r, s) typically encoded as DER format or concatenated raw bytes.

ECDSA vs RSA

Feature ECDSA (256-bit) RSA (3072-bit) Winner
Security Level 128-bit 128-bit Tie
Key Size 256 bits (32 bytes) 3072 bits (384 bytes) ECDSA
Signature Size 64 bytes 384 bytes ECDSA
Sign Speed Fast Slow ECDSA
Verify Speed Moderate Fast RSA
Adoption Growing (TLS 1.3, Bitcoin) Legacy (widespread) Depends

Popular EC Curves

Curve Bits Security Usage Notes
secp256k1 256 128-bit Bitcoin, Ethereum, Litecoin Koblitz curve, efficient for verification
P-256 (secp256r1) 256 128-bit TLS, WebAuthn, FIDO2, Apple NIST standard, most widely supported
P-384 (secp384r1) 384 192-bit Government, NSA Suite B Required for TOP SECRET classification
P-521 (secp521r1) 521 256-bit High-security applications Maximum NIST curve security
Ed25519 256 128-bit SSH, Signal, Tor EdDSA variant, deterministic signatures
brainpoolP256r1 256 128-bit European standards, German BSI Alternative to NIST curves

Real-World Applications

Cryptocurrency

Bitcoin, Ethereum use ECDSA for transaction signing

TLS/SSL

HTTPS certificates and key exchange

SSH

Secure shell authentication keys

Mobile Auth

FIDO2, WebAuthn, passkeys

OpenSSL Commands

# List available curves
openssl ecparam -list_curves

# Generate EC key pair (secp256k1 for Bitcoin compatibility)
openssl ecparam -name secp256k1 -genkey -noout -out ec-private.pem

# Extract public key
openssl ec -in ec-private.pem -pubout -out ec-public.pem

# View key details
openssl ec -in ec-private.pem -text -noout

# Sign a message (creates binary signature)
openssl dgst -sha256 -sign ec-private.pem -out signature.bin message.txt

# Convert signature to Base64
base64 signature.bin > signature.b64

# Verify signature
openssl dgst -sha256 -verify ec-public.pem -signature signature.bin message.txt

# Generate key for P-256 (NIST) curve
openssl ecparam -name prime256v1 -genkey -noout -out p256-key.pem

Security Best Practices

DON'T:
  • Never reuse the random nonce k - leads to private key recovery
  • Never share your private key
  • Don't use weak random number generators
  • Don't ignore signature malleability in blockchain apps
  • Don't use deprecated curves (e.g., secp112r1)
DO:
  • Use deterministic signatures (RFC 6979) when possible
  • Use well-tested cryptographic libraries
  • Verify signatures before trusting data
  • Use curves with at least 256-bit security
  • Keep private keys in secure hardware (HSM) when possible
Critical Security Note: The security of ECDSA depends entirely on the randomness of the nonce k. In 2010, Sony's PlayStation 3 private key was compromised because they used the same k value for multiple signatures. Always use cryptographically secure random number generators or deterministic signature schemes (RFC 6979).
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