CryptoDB
Cryptographic Smooth Neighbors
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Presentation: | Slides |
Conference: | ASIACRYPT 2023 |
Abstract: | 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. |
BibTeX
@inproceedings{asiacrypt-2023-33453, title={Cryptographic Smooth Neighbors}, publisher={Springer-Verlag}, author={Giacomo Bruno and Maria Corte-Real Santos and Craig Costello and Jonathan Komada Eriksen and Michael Meyer and Michael Naehrig and Bruno Sterner}, year=2023 }