For the same level of security that public-key cryptosystems such as RSA have, elliptic curve cryptography (ECC) offers the benefit of smaller key sizes, hence smaller memory and processor requirements. The Diffie-Hellman key exchange, ElGamal encryption, digital signatures, and the Digital Signature Algorithm (DSA) can all be implemented in ECC. This makes ECC a very attractive algorithm for wireless devices such as handhelds and PDAs, which have limited bandwidth and processing power. Running on the same platform, ECC runs more TLS/SSL transactions per second than RSA. This chapter describes the basic concepts and definitions of elliptic curve cryptography.