## CryptoDB

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

Authors: Vladimir Sedlacek , Masaryk University, Ca’ Foscari University of Venice Jesús-Javier Chi-Domínguez , Technology Innovation Institute (TII) Jan Jancar , Masaryk University Billy Bob Brumley , Tampere University DOI: 10.1007/978-3-030-92062-3_5 Search ePrint Search Google Slides ASIACRYPT 2021 The Refined Power Analysis, Zero-Value Point, and Exceptional Procedure attacks introduced side-channel 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, which we released publicly, for unrolling formulas and finding special points, and potentially for independent future work.
##### BibTeX
@inproceedings{asiacrypt-2021-31416,
title={A formula for disaster: a unified approach to elliptic curve special-point-based attacks},
publisher={Springer-Verlag},
doi={10.1007/978-3-030-92062-3_5},
author={Vladimir Sedlacek and Jesús-Javier Chi-Domínguez and Jan Jancar and Billy Bob Brumley},
year=2021
}