As the information-processing and telecommunications revolutions now underway will continue to change our life styles in the rest of the 21st century, our personal and economic lives rely more and more on our ability to transact over the electronic medium in a secure way. The privacy, authenticity, and integrity of...
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...
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...