ECDSA optimizations on an ARM processor for a NIST curve over GF(p)

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

TITLE: ECDSA Optimizations on an ARM Processor for a NIST Curve Over GF(p)

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 NIST 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. © Copyright by Haluk Kent Tani