Consensys proposes a new subgroup membership testing method, achieving roughly 10.8x speedup for FourQ curve detection

Odaily reports: Consensys has announced that its cryptographer Youssef El Housni, together with collaborators from Wuhan University of Technology, KU Leuven, and the National Academy of Sciences of Belarus, has proposed a new subgroup membership testing method called Divide-and-Pair. On non-prime-order curves such as Curve25519, not all points belong to the target subgroup; skipping this check can expose systems to small-subgroup attacks. NIST P-series curves are prime-order and do not require this check. The method treats two known schemes as the two ends of the same parameter range, selecting the optimal setting for each curve, with speed no lower than existing methods. According to Consensys, the speedup factors for each curve are: approximately 1.6x for Curve25519, approximately 1.3x for Curve448, approximately 1.4x for GC256A, approximately 10.8x for FourQ, and approximately 7x for Jubjub.

The method has been integrated into the open-source library gnark-crypto. The library currently runs in Besu, Linea, go-ethereum, as well as gnark-based systems such as Succinct and Lighter. The related paper has been accepted by IACR Transactions on Cryptographic Hardware and Embedded Systems (TCHES) and will be published at CHES 2027.