| Elliptic curve cryptography was proposed independently by Neil Koblitz and Victor Miller in the middle of 80's. The security of Elliptic Curve Cryptography depends upon the elliptic curve discrete logarithm problem. For providing the same strength, it uses a smaller key size than that for RSA. This advantage makes it particularly suitable for some devices and applications, which have a resource constraint.; Digital Signature Systems are one of the most important applications of cryptography. In Y2K IEEE has included two Elliptic Cryptography based methods in its new standard P1363. The elliptic curve cryptosystem uses "point" operations like point doubling and addition. As a consequence, optimization of, point operations plays a key role in determining the efficiency of computation. Today's technology easily permits the fabrication of multiple simple "processors" on a single chip. For such devices, a serial-parallel computation has been proposed by Adnan and Mohammad [AM03][AM03a] for a faster computation of elliptic algorithms. This thesis presents a new optimized point operations algorithm for elliptic curve cryptosystems over GF(2 n). We have designed and implemented the new algorithm for a more efficient digital signature system. |
