| The groundbreaking idea of public key cryptography and the rapid expansion of the internet in the 80s opened a new research area for finite field arithmetic. The large size of fields in cryptography demands new algorithms for efficient arithmetic and new metrics for estimating finite field operation performance. The area, power, and timing constraints on hand-held and embedded devices necessitate accurate models to achieve expected goals. Additionally, cryptosystems need to protect their secrets and hide their internal operation states against side-channel attacks. Fault-injection attacks or random errors reduce the security of a cryptosystem and can help a cryptanalyst to extract a system's secrets.;This dissertation covers various aspects of finite field arithmetic to provide predictable, efficient, and secure elements for cryptography. We provide architecture for an elliptic curve processor (ECP), which is essentially a finite field processor. We also provide finite field multipliers over polynomial and optimal normal bases for pipeline and parallel architectures.;To further analyze the behavior of finite field multipliers, we formalize timing, area, and energy consumption over binary extension fields. To ensure robustness of the multiplication operation, we provide concurrent error detection (CED) schemes for polynomial and normal base multipliers and provide the probability of error detection. |
