Elliptic Curve Discrete Logarithm Based Cryptography

This chapter examines the elliptic curve discrete logarithm-based (ECDLP) pubic-key cryptosystems and digital signatures. These include Elliptic curve Dif?e-Helman-Meerkle key-exchange; Elliptic curve Massey-Omura three-pass protocol; Elliptic curve ElGamal cryptography; Elliptic curve RSA cryptosystem; Menezes-Vanstone elliptic curve cryptography; and Elliptic curve digital signature algorithm (ECDSA). The most widely used RSA crypto system cannot only be used for both encryption and digital signatures, but also has a natural analog of elliptic curve cryptography. The elliptic curve digital signature algorithm (ECDSA) is the elliptic curve analog of the digital signature algorithm (DSA). The chapter also introduces elliptic curve cryptography (ECC) and the digital signature algorithm (ECDSA), whose security are based on the infeasibility of the Elliptic Curve Discrete Logarithm Problem.