Minerva: The curse of ECDSA nonces

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F20%3A00114222" target="_blank" >RIV/00216224:14330/20:00114222 - isvavai.cz</a>

Result on the web

<a href="https://minerva.crocs.fi.muni.cz/" target="_blank" >https://minerva.crocs.fi.muni.cz/</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.13154/tches.v2020.i4.281-308" target="_blank" >10.13154/tches.v2020.i4.281-308</a>

Result language

angličtina

Original language name

Minerva: The curse of ECDSA nonces

Original language description

We present our discovery of a group of side-channel vulnerabilities in implementations of the ECDSA signature algorithm in a widely used Atmel AT90SC FIPS 140-2 certified smartcard chip and five cryptographic libraries (libgcrypt, wolfSSL, MatrixSSL, SunEC/OpenJDK/Oracle JDK, Crypto++). Vulnerable implementations leak the bit-length of the scalar used in scalar multiplication via timing. Using leaked bit-length, we mount a lattice attack on a 256-bit curve, after observing enough signing operations. We propose two new methods to recover the full private key requiring just 500 signatures for simulated leakage data, 1200 for real cryptographic library data, and 2100 for smartcard data. The number of signatures needed for a successful attack depends on the chosen method and its parameters as well as on the noise profile, influenced by the type of leakage and used computation platform. We use the set of vulnerabilities reported in this paper, together with the recently published TPM-FAIL vulnerability [MSE+20] as a basis for real-world benchmark datasets to systematically compare our newly proposed methods and all previously published applicable lattice-based key recovery methods. The resulting exhaustive comparison highlights the methods’ sensitivity to its proper parametrization and demonstrates that our methods are more efficient in most cases. For the TPM-FAIL dataset, we decreased the number of required signatures from approximately 40 000 to mere 900.

Czech name

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Czech description

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Type

D - Article in proceedings

CEP classification

—

OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

<a href="/en/project/GA20-03426S" target="_blank" >GA20-03426S: Examining and improving security of elliptic curve cryptography</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Publication year

2020

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

IACR Transactions on Cryptographic Hardware and Embedded Systems

ISBN

—

ISSN

2569-2925

e-ISSN

—

Number of pages

28

Pages from-to

281-308

Publisher name

Ruhr-University of Bochum

Place of publication

Německo

Event location

online

Event date

Jan 1, 2020

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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