We describe novel methods for obtaining fast software implementations of the arithmetic operations in the finite field GF(p) and GF(p[superscript k]). In GF(p) we realize an extensive speedup in modular addition and subtraction routines and some small speedup in the modular multiplication routine with an arbitrary prime modulus p which...
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...
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...
In recent years, the elliptic curve cryptosystems (ECC) have received attention
due to their increased security with smaller key size which brings the advantage of less
storage area and less bandwidth. Elliptic curve cryptography provides a methodology
for obtaining high-speed, efficient, and scalable implementations of network security
protocols. In addition...
In this thesis, we study the Karatsuba-Ofman Algorithm (KOA), which is a recursive multi-precision multiplication method, and improve it for certain special applications. This thesis is in two parts. In the first part, we derive an efficient algorithm from the KOA to multiply the operands having a precision of 2[superscript...
The computation of the inverse of a number in finite fields, namely Galois Fields GF(p) or GF(2ⁿ), is one of the most complex arithmetic operations in cryptographic applications. In this work, we investigate the GF(p) inversion and present several phases in the design of efficient hardware implementations to compute the...