International Association for Cryptologic Research

International Association
for Cryptologic Research


Jonathan Komada Eriksen


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.
Cryptographic Smooth Neighbors
We revisit the problem of finding two consecutive $B$-smooth integers by giving an optimised implementation of the Conrey-Holm\-strom-McLaughlin ``smooth neighbors'' algorithm. While this algorithm is not guaranteed to return the complete set of $B$-smooth neighbors, in practice it returns a very close approximation to the complete set but does so in a tiny fraction of the time of its exhaustive counterparts. We exploit this algorithm to find record-sized solutions to the pure twin smooth problem, and subsequently to produce instances of cryptographic parameters whose corresponding isogeny degrees are significantly smoother than prior works. Our methods seem well-suited to finding parameters for the SQISign signature scheme, especially for instantiations looking to minimize the cost of signature generation. We give a number of examples, among which are the first parameter sets geared towards efficient SQISign instantiations at NIST's security levels III and V.