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.
Consensys said it has introduced a new subgroup membership testing method called Divide-and-Pair. The work was led by its cryptographer Youssef El Housni with collaborators from Wuhan University of Technology, KU Leuven, and the National Academy of Sciences of Belarus.
The method addresses a security check used on non-prime-order curves such as Curve25519, where not every point belongs to the target subgroup. If that check is skipped, implementations can face small-subgroup attacks. Consensys said NIST P-series curves have prime order, so the check is not required there.
Reported speed gains across curves
According to Consensys, the method frames two known approaches as opposite ends of the same parameter range and picks the optimal setting for each curve. It said performance is no worse than existing methods.
- Curve25519: about 1.6x
- Curve448: about 1.3x
- GC256A: about 1.4x
- FourQ: about 10.8x
- Jubjub: about 7x
Integrated into gnark-crypto
Consensys said the method has already been integrated into the open-source gnark-crypto library. The library is currently used in Besu, Linea, go-ethereum, and gnark-based systems including Succinct and Lighter.
Paper accepted for publication
The related paper has been accepted by IACR Transactions on Cryptographic Hardware and Embedded Systems (TCHES) and will be presented at CHES 2027.
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