crypto: Share the Fq12 accumulator across pairing pairs - #1638
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pairing_check ran an independent Miller loop per pair, paying 64 Fq12 squarings each, although the recurrence f ← f²·line is multiplicative across pairs so a single accumulator serves all of them. Collect the surviving pairs and run one loop over the NAF digits, squaring once per iteration and folding every pair's line value into the shared f. For N pairs this drops (N−1)×64 squarings plus the N−1 Fq12 multiplications that combined the per-pair results, cutting about 13% off the ECPAIRING instruction count on the benchmark inputs, which carry 2 to 4 pairs.
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## master #1638 +/- ##
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Coverage 97.71% 97.71%
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Branches 3610 3615 +5
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pairing_check ran an independent Miller loop per pair and multiplied the
results, paying 64 Fq12 squarings each. The recurrence f ← f²·line is
multiplicative across pairs, so a single accumulator serves all of them
and the squaring is paid once per iteration rather than once per pair.
For N pairs this drops (N−1)×64 squarings plus the N−1 Fq12
multiplications that combined the per-pair results, and lets an
all-infinity input skip the final exponentiation. About 13% off the
ECPAIRING instruction count on the benchmark inputs, which carry 2 to 4
pairs.
Supersedes the draft #1544, reimplemented rather than rebased because it
predates the JacPoint rename and the Point removal. One caveat: the
per-pair state needs a vector, so a single-pair call pays an allocation
and saves no squarings.
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