Fast 4 way vectorized ladder for the complete set of Montgomery curves

Year 2022, Volume: 11 Issue: 2, 12 - 24, 30.06.2022

Hüseyin Hışıl Berkan Eğrice Mert Yassı

Abstract

This paper introduces 4 way vectorization of Montgomery ladder on any Montgomery form elliptic curve. Our algorithm takes 2M^4+1S^4 (M^4: A vector of four field multiplications, S^4: A vector of four field squarings) per ladder step for variable-scalar variable-point multiplication. This paper also introduces new formulas for doing arithmetic over GF(2^255-19).

Keywords

Montgomery ladder, elliptic curves, genus 1, Kummer lines, Diffie-Hellman key exchange, public key cryptography.

Supporting Institution

Yasar University

Project Number

SRP-057

Thanks

We thank Erdem Alkım, Sedat Akleylek, and members of the Cyber Security and Cryptology Laboratory, Ondokuz Mayis University, for providing us access to OMU-i9, a Skylake i9-7900X machine. We developed the AVX-512 implementation on OMU-i9. The measurements relating to were both taken on OMU-i9.

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