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**2022/748**

**Title:**

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

**Authors:**
Marius A. Aardal and Diego F. Aranha

**Abstract:**

We revisit and improve performance of arithmetic in the binary GLS254 curve by introducing the 2D-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 6\% and 34.5\% on respectively 64-bit Intel and Arm platforms.

**ePrint:**
https://eprint.iacr.org/2022/748

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