Paper 2022/277

Security Analysis of Elliptic Curves over Sextic Extension of Small Prime Fields

Robin Salen, Vijaykumar Singh, and Vladimir Soukharev

Abstract

In this report we investigate how to generate secure elliptic curves over sextic extension of prime fields of size roughly 64 bits to achieve 128-bit security. In particular, we present one of such curves over a 64-bit prime field, which we named Cheetah, and provide its security parameter. This curve is particularly well-suited for zero-knowledge applications such as FRI-based STARK proving systems, as its base prime field has the property of having a large two-adicity, necessary for FFT-related operations and at the same time it is used for elliptic curve-based signatures. We also provide a prototype implementation of this curve in Rust, featuring constant-time arithmetic and no use of the Rust standard library for WebAssembly support.

Metadata
Available format(s)
PDF
Category
Foundations
Publication info
Preprint.
Keywords
elliptic curvesdigital signatureszero-knowledge proofsstarkblockchainfield extension
Contact author(s)
salen @ toposware com
vijaykumar singh @ toposware com
vladimir soukharev @ toposware com
History
2022-03-02: revised
2022-03-02: received
See all versions
Short URL
https://ia.cr/2022/277
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2022/277,
      author = {Robin Salen and Vijaykumar Singh and Vladimir Soukharev},
      title = {Security Analysis of Elliptic Curves over Sextic Extension of Small Prime Fields},
      howpublished = {Cryptology ePrint Archive, Paper 2022/277},
      year = {2022},
      note = {\url{https://eprint.iacr.org/2022/277}},
      url = {https://eprint.iacr.org/2022/277}
}
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