King Fahd University of Petroleum & Minerals,
Email: gutub@kfupm.edu.sa
Abstract:
Modular inversion is a fundamental process
in several cryptographic systems. It can be computed in software or hardware,
but hardware computation has been proven to be faster and more secure. This
research focused on improving an old scalable inversion hardware architecture
proposed in 2004 for finite field GF(p). The architecture comprises two parts, a computing unit
and a memory unit. The memory unit holds all the data bits of computation
whereas the computing unit performs all the arithmetic operations in word
(digit) by word bases such that the design is scalable.
The main objective of this paper is to show
the cost and benefit of modifying the memory unit to include shifting, which
was previously one of the tasks of the scalable computing unit. The study
included remodeling the entire hardware architecture removing the shifter from
the scalable computing part and embedding it in the non-scalable memory unit
instead. This modification resulted in a speedup to the complete inversion
process with an area increase due to the new memory shifting unit. Several
design schemes have been compared giving the user the complete picture to
choose from depending on the application need.