Elliptic curve cryptosystems: A survey

Elliptic curves have been a subject of much mathematical study since early in the past century. Recently, through the work of Koblitz and Miller, they have found application in the area of publickey cryptography. The basic reason is that, elliptic curves over finite fields provide an abundance of finite abelian groups which could be used as a basis for public-key cryptosystems. The objective of this thesis is to survey the field of elliptic curve public-key cryptography as it exists now, with an attempt to identify key ideas and contributions. We are particularly interested in elliptic curve cryptosystems defined over Zp (p > 3 and prime) and the ring Zn (n is a product of two large distinct primes).