Optimized Frobenius and Cyclotomic Cubing for Enhanced Pairing Computation

Leila Ben Abdelghani; Nadia El Mrabet; Loubna Ghammam; Lina Mortajine

Paper 2025/468

Optimized Frobenius and Cyclotomic Cubing for Enhanced Pairing Computation

Leila Ben Abdelghani, University of Monastir

Nadia El Mrabet

, Ecole des Mines de Saint Etienne

Loubna Ghammam

, ITK Engineering GmbH

Lina Mortajine, ITK Engineering GmbH

Abstract

Efficient implementation of pairing-based cryptosystems relies on high-performance arithmetic in finite fields $\mathbb{F}_{p}$ and their extensions $\mathbb{F}_{p^k}$, where $k$ denotes the embedding degree. A small embedding degree is crucial since a part of the arithmetic for pairing computation occurs in $\mathbb{F}_{{p}^k}$, including squaring, multiplication, and Frobenius operations. In this paper, we present a fast and efficient method for computing the Frobenius endomorphism in the finite field $\mathbb{F}_{p^k}$, along with an analysis of its computational complexity. Furthermore, we introduce an optimization for cyclotomic cubing operations tailored to several pairing-friendly elliptic curves, which are essential for the calculation of Tate pairing and its derivatives.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint.
Keywords: Optimal Ate Pairing Frobenius maps Kronecker products Finite fields Cyclotomic cubing
Contact author(s): leila benabdelghani @ fsm rnu tn
nadia el-mrabet @ emse fr
loubna ghammam @ itk-engineering de
lina mortajine @ itk-engineering de
History: 2025-10-29: revised; 2025-03-12: received; See all versions
Short URL: https://ia.cr/2025/468
License: CC0

BibTeX

@misc{cryptoeprint:2025/468,
      author = {Leila Ben Abdelghani and Nadia El Mrabet and Loubna Ghammam and Lina Mortajine},
      title = {Optimized Frobenius and Cyclotomic Cubing for Enhanced Pairing Computation},
      howpublished = {Cryptology {ePrint} Archive, Paper 2025/468},
      year = {2025},
      url = {https://eprint.iacr.org/2025/468}
}