International Association
for Cryptologic Research

Maria Corte-Real Santos , University College London

Jonathan Komada Eriksen , Norwegian University of Science and Technology

Michael Meyer , University of Regensburg

Francisco Rodríguez-Henríquez , Cryptography Research Center, Technology Innovation Institute

DOI: 10.62056/ayojbhey6b

URL: https://cic.iacr.org//p/1/3/39

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Isogeny-based schemes often come with special requirements on the field of definition of the involved elliptic curves. For instance, the efficiency of SQIsign, a promising candidate in the NIST signature standardisation process, requires a large power of two and a large smooth integer $T$ to divide $p^2-1$ for its prime parameter $p$. We present two new methods that combine previous techniques for finding suitable primes: sieve-and-boost and XGCD-and-boost. We use these methods to find primes for the NIST submission of SQIsign. Furthermore, we show that our methods are flexible and can be adapted to find suitable parameters for other isogeny-based schemes such as AprèsSQI or POKE. For all three schemes, the parameters we present offer the best performance among all parameters proposed in the literature.