ChainCatcher report: ConsenSys posted on X that its cryptographer Youssef El Housni, along with collaborators from Wuhan University of Technology, KU Leuven, and the National Academy of Sciences of Belarus, has proposed a new method for subgroup membership detection 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 the system to small-subgroup attacks. In contrast, NIST P-series curves have prime order and do not require this check. This method treats two known approaches as endpoints of a single parameter range, selecting optimal settings for each curve while maintaining or exceeding the speed of previous methods. According to ConsenSys, the speedup factors for each curve are approximately: Curve25519 at 1.6x, Curve448 at 1.3x, GC256A at 1.4x, FourQ at 10.8x, and Jubjub at 7x.
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.
ConsenSys Researchers Propose Divide-and-Pair Method to Accelerate Subgroup Membership Checks
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Summary
On-chain news breaks as ConsenSys cryptographers Youssef El Housni and collaborators from Wuhan University of Technology, KU Leuven, and the National Academy of Sciences of Belarus propose a new method for subgroup membership checks. Dubbed Divide-and-Pair, the technique accelerates verification on elliptic curves such as Curve25519 and Curve448, with speed improvements ranging from 1.3x to 10.8x. The method has been integrated into gnark-crypto, a library used in Besu, Linea, and go-ethereum. A related paper is set to be published in IACR Transactions on Cryptographic Hardware and Embedded Systems and will be presented at CHES 2027.
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