Odaily Planet Daily reports that ConsenSys has announced that its cryptographer Youssef El Housni, in collaboration with Wuhan University of Technology, KU Leuven, and the National Academy of Sciences of Belarus, has proposed a new method for subgroup membership testing called "Divide-and-Pair." On non-prime-order curves such as Curve25519, not all points belong to the target subgroup; skipping this check may expose systems to small-subgroup attacks, whereas NIST P-series curves, being of prime order, do not require this check. The method treats two known approaches as endpoints within the same parameter range and selects optimal settings for each curve, achieving speeds no slower than existing methods. According to ConsenSys, the speed improvements for each curve are approximately: 1.6x for Curve25519, 1.3x for Curve448, 1.4x for GC256A, 10.8x for FourQ, and 7x for Jubjub.
This method has been integrated into the open-source library gnark-crypto. The library currently runs on Besu, Linea, go-ethereum, and systems based on gnark such as Succinct and Lighter. The related paper has been accepted by IACR Transactions on Cryptographic Hardware and Embedded Systems (TCHES) and will be presented at CHES 2027.