A hands-on introduction to elliptic curve cryptography. Start with curve geometry, build point addition and scalar multiplication, see why ECDLP is hard, and then use that math in ECDH, ECDSA, and ECIES.

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A comprehensive interactive introduction to Elliptic Curve Cryptography (ECC) covering the mathematical foundations and practical applications. Starting from curve geometry and point addition, it builds up to scalar multiplication and the Elliptic Curve Discrete Logarithm Problem (ECDLP) as a one-way trapdoor. The post then explains how ECC operates over finite fields for exact arithmetic, and walks through three core protocols: ECDH for key exchange, ECDSA for digital signatures, and ECIES for encryption. A comparison table shows ECC requires far smaller keys than RSA or Diffie-Hellman for equivalent security levels, explaining its adoption in TLS 1.3, Signal, SSH, and Bitcoin. The post also briefly touches on quantum computing threats and post-quantum cryptography.

An interactive intro to Elliptic Curve Cryptography (ECC)