Researches On Electronic Transaction Algorithms Based On (Hyper) Elliptic Curves Cryptosystems

SET, short for Secure Electronic Transaction, is a standard that will enable secure credit card transactions on the Internet. It was launched in 1996 by MasterCard International and Visa International and supported by Microsoft, Netscape, Verisign, and others. By the employment of digital signatures, SET will enable merchants to verify that buyers are who they claim to be. And it will protect buyers by providing a mechanism with their credit card number to be transferred directly to the credit card issuer for verification and billing without the merchant being able to see the number.Since elliptic curve cryptosystems (ECC) were proposed in around 1985, ECC has been studied for about twenty years and has been recently applied in many commercial purposes. In 1989, Koblitz generalized the concept of elliptic curve cryptosystems to hyperelliptic curves of higher genus. (Hyper) Elliptic Curve are useful in cryptography as they maintain the same level of security than other cryptosystems but taking smaller sizes.This is especially important for small-footprint devices with limited computational capacities, memory and low-bandwidth network connections, such as smart cards. And by the use of (hyper) elliptic curve cryptosystems, the implementation of a SET protocol can be accelerated.The main works of this dissertation can be described as follows:(1) Some improving remarks of SET protocol(2) An electronic transaction algorithm based on elliptic curve cryptosystem is proposed.(3) SET protocol based on elliptic hyperelliptic curve cryptosystem is proposed.(4) The Implementation of hyperelliptic curve cryptosystem algorithm in Maple.