Why prime fields? Why binary fields?
From this document, now I can answer one of the questions from the previous posting:
Why prime fields?
- Commonly used for software implementations because
the integer arithmetic is more optimized in today’s
microprocessors - Desktops: favour fast multipliers
- Embedded: varies based on processor architecture
- Hardware implementations benefit from the full size
operands but the area impact may be significant - Hardware implementations carry chain timing challenges
Why binary fields?
- Not as efficient in SW implementations compared to
prime fields where large multipliers are available- Integer multipliers can deal with word size data
- Not true for smaller processors with inefficient integer
multipliers
- Even more challenging for custom SW implementations if
m is a large value- Challenging for SW implementations with reduced register
space
- Usually use a sliding window dbl/add to speed up
multiplication
Crypto Code 
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