The Elliptic Curve Digital Signature Algorithm (ECDSA) is the elliptic curve analog of the Digital Signature Algorithm (DSA) and a federal government approved digital signature method. In this thesis work, software optimization techniques were applied to speed up the ECDSA for a particular NTST curve over GF(p). The Montgomery multiplication is used extensively in the ECDSA. By taking advantage of the algorithmic properties of the Montgomery multiplication method, special structure of the curve parameters and also applying certain fundamental and specific software optimization techniques, we have achieved an overall 26% speed improvement. Further enhancements were made by implementing the Montgomery multiplication in the ARM assembly language that resulted in 44% speed improvement. The optimizations discussed in this thesis could easily be adapted to other curves with or without changes. / Graduation date: 2002

The Elliptic Curve Digital Signature Algorithm (ECDSA) is one of the most popular algorithms to digitally sign streams or blocks of data. In this thesis we concentrate on porting and optimizing the ECDSA on the ARM7 processor for a particular NIST curve over GF(2[superscript m]). The selected curve is a binary curve of order 233. We show that for this particular curve, the ECDSA can be implemented significantly faster than the general case. The optimized algorithms have been implemented in C and the ARM assembly. The analysis and performance results indicate that by using certain machine and curve specific techniques, the ECDSA signature can be made up to 41% faster. / Graduation date: 2002