crypto: Multiply Fq2 with the Karatsuba method - #1644
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multiply(Fq2) was schoolbook, 4 base field multiplications, while every other level of the tower already used Karatsuba. Trading one multiplication for three additions pays here because a Montgomery multiplication costs several times an addition: about 6% off the ECPAIRING instruction count.
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Pull request overview
Optimizes BN254 Fq2 multiplication using Karatsuba’s method.
Changes:
- Reduces base-field multiplications from four to three.
- Documents the algorithm and potential lazy-reduction optimization.
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Codecov Report✅ All modified and coverable lines are covered by tests. Additional details and impacted files@@ Coverage Diff @@
## master #1644 +/- ##
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Coverage 97.71% 97.71%
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Files 171 171
Lines 15607 15609 +2
Branches 3610 3610
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+ Hits 15251 15253 +2
Misses 269 269
Partials 87 87
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Reverted because causes performance regressions. |
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multiply(Fq2) was schoolbook, 4 base field multiplications, while Fq6 and
Fq12 already used Karatsuba. At Fq2 the trade is one multiplication for
three additions, which pays because a Montgomery multiplication costs
several times an addition.
About 6% off the ECPAIRING instruction count, measured with paired
interleaved A/B runs of both binaries.
A TODO records the step left on the table: holding the three products at
double width and reducing once per output coefficient instead of after
every multiplication. That needs a wide multiplication and a standalone
Montgomery reduction in ModArith.
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