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> Hm, why aren't compilers generating that instruction?

Thats polynomial multiply. Its (almost) a multiplication in GF2 for elliptical curves. Thats not a "normal" multiply.

"PMULL" is basically a bitshift and XOR. Your traditional "MUL" is bitshift and ADD. Its called "polynomial multiply" because bitshift-and-xor has very similar properties to bitshift-and-add (it distributes over XOR, associative, communative, etc. etc).

Bitshift-and-xor has a few features that are better for cryptography. But its NOT the multiplication you are taught in grade school.

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EDIT: With that being said... those "better features" for cryptography would make PMULL probably a better function for random-number generation. PMULL will return a different result than the real multiplication, but you'll have an easier time making a field (aka: reversable 1-to-1 bijections) out of PMULL than MUL...




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