Research And Implementation Of Elliptic Curve Cryptosystem

With the high development of Internet, information security has gained more and more attention. An important approach to solving information security is public-key cryptology. Comparing to other public-key cryptosystems such as RSA and DSA, ECC has many advantages including high security per bit, faster computations and reduces in processing power, storage space and bandwidth. These advantages make ECC ideal for constrained environments such as PDAs,cellular phones and smart cards.In this thesis, we first discuss the algorithms of arithmetic operations over binary fields using a polynomial basis representation. Then we analyse the theory of elliptic curves over finite fields and discuss several algorithms for computing a scalar multiplication which is the central operations of ECC .The principle results in this thesis include:(l)We present a new authentication scheme based on ECDSA. In the scheme, two-way authentication may be done between two users without exposing their secret information.(2) we give a software implementation of ECDH on the elliptic curve AM 63 over the binary field GF(2163).