SCALLOP: Scaling the CSI-FiSh
نویسندگان
چکیده
We present SCALLOP: SCALable isogeny action based on Oriented supersingular curves with Prime conductor, a new group isogenies of curves. Similarly to CSIDH and OSIDH, we use the an imaginary quadratic order’s class set oriented Compared CSIDH, main benefit our construction is that it easy compute class-group structure; this data required uniquely represent — efficiently act by arbitrary elements, which requirement in, e.g., CSI-FiSh signature scheme Beullens, Kleinjung Vercauteren. The index-calculus algorithm used in structure has complexity L(1/2), ruling out groups much larger than CSIDH-512, limitation particularly problematic light ongoing debate regarding quantum security cryptographic actions. Hoping solve issue, consider order large prime conductor inside field small discriminant. This family orders lets us easily determine size group, and, carefully choosing even exercise significant control particular supporting highly smooth choices. Although evaluating resulting still subexponential asymptotic complexity, careful choice parameters leads practical speedup demonstrate practice for level equivalent CSIDH-1024, parameter currently firmly reach index-calculus-based methods. However, implementation takes 35 s (resp. 12.5 min) single group-action evaluation at CSIDH-512-equivalent CSIDH-1024-equivalent) level, showing that, while feasible, SCALLOP does not achieve realistically usable performance yet.
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ژورنال
عنوان ژورنال: Lecture Notes in Computer Science
سال: 2023
ISSN: ['1611-3349', '0302-9743']
DOI: https://doi.org/10.1007/978-3-031-31368-4_13