Elliptic Curve Cryptography over Binary Finite Field GF(2^m)

摘要

The rapid growth of information technology that has resulted in significant advances in cryptography to protect the integrity and confidentiality of data is astounding. Elliptic curve cryptography is gaining wide acceptance as an alternative to the conventional cryptosystems (DES, RSA, AES, etc.). Elliptic curve cryptosystems require less computational power, memory, communication bandwidth and network connectivity. Elliptic curve ciphers today are based in smartcards, Personal Digital Assistants (PDAs), pagers and mobile phones and can be easily implemented with processors clocked in single digits of MHz. This study describes the basic design principle of Elliptic Curve Crypto (ECC) protocols. The ECC processor is normally used to perform elliptic curve operations for: EC Diffie-Hellman, EC ElGamal and ECDSA protocols. As an example we will implement ECC defined over binary finite field GF(2^m).