Fast Elliptic Curve Scalar Multiplications in SN(T)ARK Circuits

2026
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Authors: Liam Eagen; Youssef El Housni; Simon Masson; Thomas Piellard
Published in: Progress in Cryptology – LATINCRYPT 2025
Publisher: Springer Nature Switzerland

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Abstract

This chapter delves into the optimization of elliptic curve scalar multiplications within SNARK (Succinct Non-interactive Argument of Knowledge) and STARK (Scalable Transparent Argument of Knowledge) circuits, crucial for privacy-preserving and scalable blockchain applications. The text explores various techniques for scalar decomposition, including lattice reduction and the extended Euclidean algorithm, to reduce the computational cost of proving scalar multiplications. It provides detailed algorithms and implementations for different elliptic curves used in production, demonstrating significant speed-ups in proving times. The chapter also discusses the trade-offs between witness generation and proving times, offering practical insights for developers working on blockchain technologies. Additionally, it compares the performance of the proposed techniques with previous state-of-the-art implementations, highlighting the advantages and potential applications of the new methods.

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Title: Fast Elliptic Curve Scalar Multiplications in SN(T)ARK Circuits
Authors: Liam Eagen
Youssef El Housni
Simon Masson
Thomas Piellard
Publisher: Springer Nature Switzerland
Book: Progress in Cryptology – LATINCRYPT 2025
Print ISBN: 978-3-032-06753-1

Electronic ISBN: 978-3-032-06754-8

Copyright Year: 2026
DOI: https://doi.org/10.1007/978-3-032-06754-8_4

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