Design And Research Of The Elliptic Curve Cryptosystem

The elliptic curve cryptosystem (ECC) is one of the three public-key cryptosystems, contrast other public-key systems, it can through short key length and reach same security intensity (For example, 160 ECC key can get the same intensity of security as 1024 RSA key), so get more concerns. It is considered to be standard of public-key cryptosystem in the new era. ECC is especially suitable for using in the fields of smart card etc., because it only needs very small memory space and computing power. Because of above-mentioned advantages too, ECC can apply to the traditional encryption field directly. This paper has done the overall introduction in the mathematics background of ECC international standards and relevant implementation algorithms, etc. Especially on how to construct the encryption system on the elliptic curves which based on limited prime number field GF(p). Latter half in this paper, the implementation model of a simple elliptic curve encryption system (SECES) which based on GF(p) has been introduced. The paper also put a deep analysis on the algorithm of point addition and point multiplication.