https://github.com/crocs-muni/formula-for-disaster

Artifacts for the "A formula for disaster: a unified approach to elliptic curve special-point-based attacks" paper at ASIACRYPT 2021

https://github.com/crocs-muni/formula-for-disaster

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asiacrypt-2021 elliptic-curve-cryptography elliptic-curves
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Artifacts for the "A formula for disaster: a unified approach to elliptic curve special-point-based attacks" paper at ASIACRYPT 2021

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asiacrypt-2021 elliptic-curve-cryptography elliptic-curves
Created almost 5 years ago · Last pushed over 1 year ago
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README.md

A formula for disaster: a unified approach to elliptic curve special-point-based attacks

This repository contains data and scripts used in the A formula for disaster: a unified approach to elliptic curve special-point-based attacks paper at ASIACRYPT 2021.

Abstract

The Refined Power Analysis, Zero-Value Point, and Exceptional Procedure attacks introduced side-channel attack techniques against specific cases of elliptic curve cryptography. The three attacks recover bits of a static ECDH key adaptively, collecting information on whether a certain multiple of the input point was computed. We unify and generalize these attacks in a common framework, and solve the corresponding problem for a broader class of inputs. We also introduce a version of the attack against windowed scalar multiplication methods, recovering the full scalar instead of just a part of it. Finally, we systematically analyze elliptic curve point addition formulas from the Explicit-Formulas Database, classify all non-trivial exceptional points, and find them in new formulas. These results indicate the usefulness of our tooling for unrolling formulas and finding special points, potentially of independent research interest.

Contents

  • unrolling/ -> Scripts/notebooks and data of unrolled formulas from the Explicit-Formulas Database.
  • epa/ -> Scripts and data related to the Exceptional Procedure Attack.
  • rpa/ -> Scripts and data related to the Refined Power Analysis attack.
  • zvp/ -> Scripts and data related to the Zero-Value Point attack.
  • xdcp/ -> Scripts related to solving the (x)DCP problem.
  • fuzzing/ -> Scripts and data related to the fuzzing search (brute force search).

Requirements

The notebooks are Jupyter notebooks and as such require Jupyter to run. Some notebooks also require a SageMath kernel. The scripts and notebooks use the pyecsca toolkit and an export of the Explicit-Formulas Database available at efd, which is also a part of pyecsca.

Owner

  • Name: CRoCS
  • Login: crocs-muni
  • Kind: organization
  • Location: Faculty of Informatics, Masaryk University, Brno

Centre for Research on Cryptography and Security

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