International Association for Cryptologic Research

International Association
for Cryptologic Research


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

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
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Presentation: Slides
Conference: ASIACRYPT 2021
Abstract: 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.
Video from ASIACRYPT 2021
  title={A formula for disaster: a unified approach to elliptic curve special-point-based attacks},
  author={Vladimir Sedlacek and Jesús-Javier Chi-Domínguez and Jan Jancar and Billy Bob Brumley},