Consensys says new subgroup membership check boosts FourQ performance by about 10.8x
Consensys said its cryptographer Youssef El Housni, working with collaborators from Wuhan University of Technology, KU Leuven, and the National Academy of Sciences of Belarus, has introduced a new subgroup membership testing method called Divide-and-Pair. The method targets curves such as Curve25519, where not every point belongs to the target subgroup and skipping the check can expose implementations to small-subgroup attacks. Consensys noted that NIST P-series curves have prime order and do not require this check. According to the company, the new approach treats two existing methods as opposite ends of the same parameter range and selects the best setting for each curve, with performance no worse than prior techniques. Reported speedups were about 1.6x for Curve25519, 1.3x for Curve448, 1.4x for GC256A, 10.8x for FourQ, and 7x for Jubjub. Consensys also said the method has been integrated into the open-source gnark-crypto library, which is currently used in Besu, Linea, go-ethereum, and gnark-based systems including Succinct and Lighter. The related paper has been accepted by IACR Transactions on Cryptographic Hardware and Embedded Systems and is set to appear at CHES 2027.
