- Diffie-Hellman allows two parties to establish a shared secret over an insecure channel.
- Elliptic Curve Cryptography (ECC) offers equivalent security to RSA with significantly smaller key sizes.
- 256-bit ECC key offers comparable security to a 3072-bit RSA key.
### Elliptic Curve Cryptography (ECC)
ECC defined over finite fields utilizes points on curves satisfying equations of the form:
$$y^2 = x^3 + ax + b \pmod p$$
#### Point Addition & Scalar Multiplication
Given a generator point $G$, multiplying by a scalar private key $k$ yields public key point $Q = k \cdot G$. Computing $k$ from $Q$ and $G$ is the **Elliptic Curve Discrete Logarithm Problem (ECDLP)**.