## elliptic curve cryptography - Computer Definition

A public key cryptography method that provides fast decryption and digital signature processing. Elliptic curve cryptography (ECC) uses points on an elliptic curve to derive a 163-bit public key that is equivalent in strength to a 1024-bit RSA key. The public key is created by agreeing on a standard generator point in an elliptic curve group (elliptic curve mathematics is a branch of number theory) and multiplying that point by a random number (the private key). Although the starting point and public key are known, it is extremely difficult to backtrack and derive the private key. Once the public key is computed by ECC, it can be used in various ways to encrypt and decrypt. One way is to encrypt with the public key and decrypt with the private one. Another is to use the Diffie-Hellman method which uses a key exchange to create a shared secret key by both parties. Finally, ECC allows a digital signature to be signed with a private key and verified with the public key. For an in-depth look at elliptic curve cryptography, visit Certicom's website at www.certicom.com. There are live examples that show the math and methods. See Diffie-Hellman.