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Lookup tables with AffinePoint for Projective scalar multiplication #14

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Nashtare opened this issue Feb 25, 2022 · 0 comments · Fixed by #19
Closed

Lookup tables with AffinePoint for Projective scalar multiplication #14

Nashtare opened this issue Feb 25, 2022 · 0 comments · Fixed by #19

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@Nashtare
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Mixed addition (AffinePoint + ProjectivePoint) is about 88% faster than regular ProjectivePoint addition.
This could lead to beneficial gains in scalar multiplication, by storing in the LookupTable multiples of the base point in Affine coordinates, rather than Projective coordinates. This can be done efficiently by creating first the array of ProjectivePoint multiples, and then doing a batch normalization to convert them all in Affine coordinates with 1 field inversion.

Unfortunately, we currently have a relatively expensive Fp6 inversion which makes this approach only beneficial for scalar multiplication with the hardcoded basepoint. But it may be worth investigating, and keep it under the hood in case inversion is improved.

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