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millerLoopLines inverts P.Y without a guard, so a G1 point at infinity (0,0) makes Pair, PairingCheck and MillerLoop unsatisfiable on BW6-761. BN254 and BLS12-381 already select yInv=0 for Y=0 (Consensys-Incorporated#1559), which turns the lines for that point into 1. Do the same here.
yelhousni
approved these changes
Sep 29, 2026
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On BW6-761,
Pair,PairingCheckandMillerLoopfail when one of the G1 points is the point at infinity (0,0). gnark-crypto accepts the same inputs.Before:
After: both pass.
millerLoopLinescomputes1/P.Ydirectly. The BN254 and BLS12-381 pairings selectyInv = 0whenP.Y == 0(added in #1559), which makes every line evaluation for that point equal to 1 so the point contributes nothing to the product. BW6-761 didn't get that guard; this adds the same three lines.The BW6-761 pairing row in
internal/stats/latest_stats.csvgoes up by 74 (groth16) / 145 (plonk) constraints and is regenerated.Tests:
TestPairG1Infinity(e(0,Q1)·e(P2,Q2) compared to gnark-crypto) andTestPairingCheckG1Infinity(e(0,Q1)·e(0,Q2) == 1), both failing on master.std/algebra/emulated/sw_bw6761,internal/statsand the BW6-in-BN254 recursion tests pass.