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Currently, we're using AMCL's BIG and its associated modular functions for modular arithmetic. However, it looks like those functions are just using the classical algorithms (and, in fact, some of them have comments that explicitly say they're slow!).
AMCL also has finite-field types, which allow reduction modulo the field order. So maybe those are more efficient?
This isn't a pressing concern, even when we start trying to be more efficient, because modular arithmetic is not the processor hog (the curve stuff, especially the pairing computations) are the killers.
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