Random number generation is important in many fields today. It is particularly important in the field of cryptography when generating nonce values, cryptographic keys, and other data required in many cryptographic applications. The proliferation of small, handheld devices that are typically connected to large networks via a wireless connection requires...
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...
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...
During the last few years we have seen formidable advances in digital and mobile
communication technologies such as cordless and cellular telephones, personal
communication systems, Internet connection expansion, etc. The vast majority
of digital information used in all these applications is stored and also processed
within a computer system, and...
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...
Instant Messaging (IM) has grown rapidly among network users. It has even become a very important tool for the industry around the world. It is used in scheduling meetings, exchanging business information and clients information, and so on. Instant Messaging has been developed by private sectors or providers such as...
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...