2DT-GLS: Faster and exception-free scalar multiplication in the GLS254 binary curve

Marius A. Aardal; Diego F. Aranha

Paper 2022/748

2DT-GLS: Faster and exception-free scalar multiplication in the GLS254 binary curve

Marius A. Aardal, Aarhus University

Diego F. Aranha

, Aarhus University

Abstract

We revisit and improve performance of arithmetic in the binary GLS254 curve by introducing the 2DT-GLS scalar multiplication algorithm. The algorithm includes theoretical and practice-oriented contributions of potential independent interest: (i) for the first time, a proof that the GLS scalar multiplication algorithm does not incur exceptions, such that faster incomplete formulas can be used; (ii) faster dedicated atomic formulas that alleviate the cost of precomputation; (iii) a table compression technique that reduces the storage needed for precomputed points; (iv) a refined constant-time scalar decomposition algorithm that is more robust to rounding. We also present the first GLS254 implementation for Armv8. With our contributions, we set new speed records for constant-time scalar multiplication by $34.5\%$ and $6\%$ on 64-bit Arm and Intel platforms, respectively.

Metadata

Available format(s): PDF
Category: Implementation
Publication info: Published elsewhere. SAC 2022
Keywords: ECC binary elliptic curves software implementation GLS254
Contact author(s): maardal @ cs au dk
dfaranha @ cs au dk
History: 2022-10-01: last of 4 revisions; 2022-06-13: received; See all versions
Short URL: https://ia.cr/2022/748
License: CC BY

BibTeX

@misc{cryptoeprint:2022/748,
      author = {Marius A. Aardal and Diego F. Aranha},
      title = {2DT-GLS: Faster and exception-free scalar multiplication in the GLS254 binary curve},
      howpublished = {Cryptology ePrint Archive, Paper 2022/748},
      year = {2022},
      note = {\url{https://eprint.iacr.org/2022/748}},
      url = {https://eprint.iacr.org/2022/748}
}