Paper 2024/038
On Computing the Multidimensional Scalar Multiplication on Elliptic Curves
, ITK Engineering GmbH, Im Speyerer Tal 6 R ̈ulzheim76761Germany., Laboratory of Secure System and Architecture (SSA), Ecole des Mines de Saint Etienne, 880 Rte de Mimet, Campus Georges Charpak Provence, 13120, Gardanne, France.Abstract
Multiscalar multiplication on elliptic curves is used in wide cryptographic domains such as digital signatures, zero knowledge proofs, and verifiable computation, where it enables efficient and secure cryptographic protocols. In this work, we present two methods for optimizing multi scalar multiplication over elliptic curves. The first method is used when $3^d - 1$ points of the target curve can be stored. The second method is suitable for large values of $d$, where storing $3^d - 1$ points becomes infeasible. Our first method achieves up to $24\%$ better performance on elliptic curves with efficient tripling, speeding up ECDSA signing by $2.88\times$ and verification by $1.67\times$. The second method achieves an efficiency improvement of $11.34\%$ compared to the similar existing approach. These improvements are supported by operation counts and practical benchmarks.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Preprint.
- Keywords
- Elliptic curvesmultidimensional scalar multiplicationscalar multiplicationcomplexity
- Contact author(s)
-
haddajiwalid95 @ gmail com
ubna ghammam @ itk-engineering de
nadia elmrabet @ emse fr
leila benabdelghani @ fsm rnu tn - History
- 2026-02-09: last of 3 revisions
- 2024-01-09: received
- See all versions
- Short URL
- https://ia.cr/2024/038
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2024/038,
author = {Walid Haddaji and Loubna Ghammam and Nadia El Mrabet and Leila Ben Abdelghani},
title = {On Computing the Multidimensional Scalar Multiplication on Elliptic Curves},
howpublished = {Cryptology {ePrint} Archive, Paper 2024/038},
year = {2024},
url = {https://eprint.iacr.org/2024/038}
}
