AprèsSQI: Extra Fast Verification for SQIsign Using Extension-Field Signing

We optimise the verification of the SQIsign signature scheme. By using field extensions in the signing procedure, we are able to significantly increase the amount of available rational 2-power torsion in verification, which achieves a significant speed-up. This, moreover, allows several other speed-ups on the level of curve arithmetic. We show that the synergy between these high-level and low-level improvements gives significant improvements, making verification 2.07 times faster, or up to 3.41 times when using size-speed trade-offs, compared to the state of the art, without majorly degrading the performance of signing.