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

D 2021

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

SEDLÁČEK, Vladimír, Jesús-Javier CHI-DOMINGUEZ, Ján JANČÁR and Billy Bob BRUMLEY

Basic information

Original name

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

Authors

SEDLÁČEK, Vladimír (203 Czech Republic, guarantor, belonging to the institution), Jesús-Javier CHI-DOMINGUEZ, Ján JANČÁR (703 Slovakia, belonging to the institution) and Billy Bob BRUMLEY

Edition

Cham, Advances in Cryptology – ASIACRYPT 2021, p. 130-159, 30 pp. 2021

Publisher

Springer

Other information

Language

English

Type of outcome

Stať ve sborníku

Field of Study

10200 1.2 Computer and information sciences

Country of publisher

Switzerland

Confidentiality degree

není předmětem státního či obchodního tajemství

Publication form

electronic version available online

References:

Publisher website Website

Impact factor

Impact factor: 0.402 in 2005

RIV identification code

RIV/00216224:14330/21:00119154

Organization unit

Faculty of Informatics

ISBN

978-3-030-92061-6

ISSN

DOI

http://dx.doi.org/10.1007/978-3-030-92062-3_5

UT WoS

000926634200005

Keywords in English

elliptic curve cryptography; ECDH; side-channel analysis; RPA; ZVP; EPA; exceptional points

Abstract

V originále

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, which might be of independent research interest.

Links

GA20-03426S, research and development project

Name: Ověření a zlepšení bezpečnosti kryptografie eliptických křivek

Investor: Czech Science Foundation

MUNI/A/1549/2020, interní kód MU

Name: Zapojení studentů Fakulty informatiky do mezinárodní vědecké komunity 21 (Acronym: SKOMU)

Investor: Masaryk University

Citovat

SEDLÁČEK, Vladimír, Jesús-Javier CHI-DOMINGUEZ, Ján JANČÁR and Billy Bob BRUMLEY. A formula for disaster: a unified approach to elliptic curve special-point-based attacks. Online. In Tibouchi M., Wang H. Advances in Cryptology – ASIACRYPT 2021. Cham: Springer, 2021, p. 130-159. ISBN 978-3-030-92061-6. Available from: https://dx.doi.org/10.1007/978-3-030-92062-3_5.

@inproceedings{1787738,
   author = {Sedláček, Vladimír and ChiandDominguez, JesúsandJavier and Jančár, Ján and Brumley, Billy Bob},
   address = {Cham},
   booktitle = {Advances in Cryptology – ASIACRYPT 2021},
   doi = {http://dx.doi.org/10.1007/978-3-030-92062-3_5},
   editor = {Tibouchi M., Wang H.},
   keywords = {elliptic curve cryptography; ECDH; side-channel analysis; RPA; ZVP; EPA; exceptional points},
   howpublished = {elektronická verze "online"},
   language = {eng},
   location = {Cham},
   isbn = {978-3-030-92061-6},
   pages = {130-159},
   publisher = {Springer},
   title = {A formula for disaster: a unified approach to elliptic curve special-point-based attacks},
   url = {https://link.springer.com/chapter/10.1007%2F978-3-030-92062-3_5},
   year = {2021}
}

TY  - JOUR
ID  - 1787738
AU  - Sedláček, Vladimír - Chi-Dominguez, Jesús-Javier - Jančár, Ján - Brumley, Billy Bob
PY  - 2021
TI  - A formula for disaster: a unified approach to elliptic curve special-point-based attacks
PB  - Springer
CY  - Cham
SN  - 9783030920616
KW  - elliptic curve cryptography
KW  - ECDH
KW  - side-channel analysis
KW  - RPA
KW  - ZVP
KW  - EPA
KW  - exceptional points
UR  - https://link.springer.com/chapter/10.1007%2F978-3-030-92062-3_5
N2  - 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, which might be of independent research interest.
ER  -

SEDLÁČEK, Vladimír, Jesús-Javier CHI-DOMINGUEZ, Ján JANČÁR and Billy Bob BRUMLEY. A formula for disaster: a unified approach to elliptic curve special-point-based attacks. Online. In Tibouchi M., Wang H. \textit{Advances in Cryptology – ASIACRYPT 2021}. Cham: Springer, 2021, p.~130-159. ISBN~978-3-030-92061-6. Available from: https://dx.doi.org/10.1007/978-3-030-92062-3\_{}5.

Detailed Information on Publication Record