Consensys said a new cryptographic method called Divide-and-Pair has been published by its cryptographer Youssef El Housni together with researchers from Wuhan University of Technology, KU Leuven’s COSIC lab, and the National Academy of Sciences of Belarus. The method is designed to speed up subgroup membership testing in elliptic-curve cryptography, a check used to defend against small-subgroup attacks and one that is required on non-prime-order curves such as Curve25519.
According to Consensys, the new approach is no slower than the two mainstream methods currently used across different curves. It reported speedups of about 1.6x on Curve25519, 1.3x on Curve448, 1.4x on GC256A, 10.8x on FourQ, and 7x on Jubjub. The company also said the method has already been integrated into its open-source cryptography library gnark-crypto, which is used by Besu, Linea, Geth, and gnark-based systems including Succinct and Lighter.
The paper has been accepted by IACR Transactions on Cryptographic Hardware and Embedded Systems, or IACR TCHES, and is scheduled to be presented at CHES 2027.
Consensys said on X that its cryptographer Youssef El Housni, working with researchers from Wuhan University of Technology, KU Leuven’s COSIC laboratory, and the National Academy of Sciences of Belarus, has published a paper introducing a new method called Divide-and-Pair for faster subgroup membership testing in elliptic-curve cryptography.
The check is used to prevent small-subgroup attacks. Consensys said it is essential on non-prime-order curves such as Curve25519, but it can slow computation. The company said Divide-and-Pair is no slower than the two mainstream methods now used across different curves, while delivering speedups of about 1.6x on Curve25519, 1.3x on Curve448, 1.4x on GC256A, 10.8x on FourQ, and 7x on Jubjub.
Consensys said the method has already been integrated into its open-source cryptography library gnark-crypto. The library is used by Besu, Linea, Geth, and gnark-based systems including Succinct and Lighter.
The paper has been accepted by IACR TCHES, a top cryptography journal, and will be presented at CHES 2027.
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