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 a Billy Bob BRUMLEY

Základní údaje

Originální název

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

Autoři

SEDLÁČEK, Vladimír (203 Česká republika, garant, domácí), Jesús-Javier CHI-DOMINGUEZ, Ján JANČÁR (703 Slovensko, domácí) a Billy Bob BRUMLEY

Vydání

Cham, Advances in Cryptology – ASIACRYPT 2021, od s. 130-159, 30 s. 2021

Nakladatel

Springer

Další údaje

Jazyk

angličtina

Typ výsledku

Stať ve sborníku

Obor

10200 1.2 Computer and information sciences

Stát vydavatele

Švýcarsko

Utajení

není předmětem státního či obchodního tajemství

Forma vydání

elektronická verze "online"

Odkazy

Publisher website Website

Impakt faktor

Impact factor: 0.402 v roce 2005

Kód RIV

RIV/00216224:14330/21:00119154

Organizační jednotka

Fakulta informatiky

ISBN

978-3-030-92061-6

ISSN

DOI

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

UT WoS

000926634200005

Klíčová slova anglicky

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

Štítky

best3, core_A, firank_A

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 16. 8. 2023 13:22, RNDr. Pavel Šmerk, Ph.D.

Anotace

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.

Návaznosti

GA20-03426S, projekt VaV

Název: Ověření a zlepšení bezpečnosti kryptografie eliptických křivek

Investor: Grantová agentura ČR, Ověření a zlepšení bezpečnosti kryptografie eliptických křivek

MUNI/A/1549/2020, interní kód MU

Název: Zapojení studentů Fakulty informatiky do mezinárodní vědecké komunity 21 (Akronym: SKOMU)

Investor: Masarykova univerzita, Zapojení studentů Fakulty informatiky do mezinárodní vědecké komunity 21

Citovat

SEDLÁČEK, Vladimír, Jesús-Javier CHI-DOMINGUEZ, Ján JANČÁR a 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, s. 130-159. ISBN 978-3-030-92061-6. Dostupné z: 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 a 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, s.~130-159. ISBN~978-3-030-92061-6. Dostupné z: https://dx.doi.org/10.1007/978-3-030-92062-3\_{}5.

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