# elliptic curve cryptography

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## elliptic curve cryptography

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.
References in periodicals archive ?
Research Issues on Elliptic Curve Cryptography and Its applications", International Journal of Computer Science and Network Security, 9(6): 19-22.
TinyECC: A Configurable Library for Elliptic Curve Cryptography in Wireless Sensor Networks, 2011.
A (relatively easy to understand) primer on elliptic curve cryptography," ars technica, October 2013.
The users in a group are maintained by using the Tree based Elliptic curve cryptography.
Software Implementation of Elliptic Curve Cryptography over Binary Fields, University of Paderborn, Germany
The size of the parameters (essentially the key size) for elliptic curve cryptography (ECC) needed to ensure security (under our current state of understanding) is much lower for ECC than for RSA or ElGamal (another alternative cryptographic method," he said.
Adopted by the National Security Agency (NSA) for classified and sensitive but unclassified government communications, Elliptic Curve Cryptography (ECC) provides the most security per bit of any known public-key scheme.
Public key cryptography performance is significantly enhanced by using special instructions, while elliptic curve cryptography algorithms can utilize new non-arithmetic instructions.
Elliptic curve cryptography is a proven alternative to traditional algorithms associated with PKI and the applications that employ public key operations and provides processing efficiencies that are well suited to emerging markets and security requirements.
In addition, the blade eases the transition from 4G to 5G mobile networks, as well as improves the performance of elliptic curve cryptography (ECC) and 2K keys with SSL.
NCP's VPN client suite and gateway now come equipped with support for elliptic curve cryptography (ECC) to safeguard VPN connections.
The topics include an entity relationship extraction model based on a chameleon clustering algorithm, a practical relay attack on contactless transactions using near-field communication mobile phones, an RFID path-checking protocol based on ordered multisignatures, a mobile RFID-based mutual authentication protocol using elliptic curve cryptography for security patrolling applications, and the cryptanalysis of two ultralightweight RFID authentication protocols.

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