Divide-and-Pair paper speeds up elliptic-curve subgroup tests, up to 10.8x on FourQ
jedisct1 · x · 2026-10-31
Consensys cryptographer Youssef El Housni and co-authors published Divide-and-Pair, a faster method for elliptic-curve subgroup membership testing (SMT), the safety check that prevents small-subgroup attacks.
- Shows Pornin's repeated-division approach and Koshelev's Tate-pairing approach sit at the extremes of a single division-pairing trade-off;
- Divide-and-Pair is always at least as fast as either and strictly faster in many cases;
- Instantiated on five widely used curves (Curve25519, Curve448, GC256A, FourQ, Jubjub) with a Go implementation in open-source gnark-crypto, achieving speedups of 1.6x, 1.3x, 1.4x, 10.8x, and 7x;
- Already integrated into gnark-crypto, used by Besu, Linea, go-ethereum and gnark-based systems.
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