Elliptic Curve Cryptography Calculator

Point Addition Result: -

Scalar Multiplication Result: -

Public Key: -

Understanding Elliptic Curve Cryptography

What is ECC?

Elliptic Curve Cryptography is a public-key cryptography approach based on the algebraic structure of elliptic curves over finite fields.

Curve Equation: y² = x³ + ax + b (mod p)

Point Addition: P + Q = R

Scalar Multiplication: kP = P + P + ... + P (k times)

  • a, b are curve parameters
  • p is the prime field characteristic
  • k is the private key
  • kP is the public key

Advanced ECC Concepts

  • Curve Properties:
    • Group Law
    • Point at Infinity
    • Order and Cofactor
    • Discrete Logarithm Problem
  • Security Considerations:
    • Key Size Selection
    • Side-Channel Attacks
    • Safe Curves
    • Implementation Security
  • Applications:
    • Digital Signatures (ECDSA)
    • Key Agreement (ECDH)
    • Blockchain Technology
    • TLS/SSL Security

Common Curves and Standards

secp256k1

Used in Bitcoin

P-256

NIST Standard

Curve25519

Modern, Safe Curve

brainpoolP256r1

BSI Standard