Detailed Information on Publication Record

JANČÁR, Ján, Vladimír SEDLÁČEK, Petr ŠVENDA and Marek SÝS. Minerva: The curse of ECDSA nonces. Online. In Amir Moradi, Mehdi Tibouchi. IACR Transactions on Cryptographic Hardware and Embedded Systems. Německo: Ruhr-University of Bochum, 2020, p. 281-308. ISSN 2569-2925. Available from: https://dx.doi.org/10.13154/tches.v2020.i4.281-308.

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Basic information
Original name	Minerva: The curse of ECDSA nonces
Authors	JANČÁR, Ján (703 Slovakia, guarantor, belonging to the institution), Vladimír SEDLÁČEK (203 Czech Republic, belonging to the institution), Petr ŠVENDA (203 Czech Republic, belonging to the institution) and Marek SÝS (703 Slovakia, belonging to the institution).
Edition	Německo, IACR Transactions on Cryptographic Hardware and Embedded Systems, p. 281-308, 28 pp. 2020.
Publisher	Ruhr-University of Bochum

Other information
Original language	English
Type of outcome	Proceedings paper
Field of Study	10201 Computer sciences, information science, bioinformatics
Country of publisher	Germany
Confidentiality degree	is not subject to a state or trade secret
Publication form	electronic version available online
WWW	Website
RIV identification code	RIV/00216224:14330/20:00114222
Organization unit	Faculty of Informatics
ISSN	2569-2925
Doi	http://dx.doi.org/10.13154/tches.v2020.i4.281-308
Keywords in English	ECDSA; Hidden Number Problem; side-channel attack; lattice attack; smartcard
Tags	best1, core_A, firank_A
Tags	International impact, Reviewed
Changed by	Changed by: RNDr. Pavel Šmerk, Ph.D., učo 3880. Changed: 31/5/2022 14:26.

Abstract
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.

Abstract

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.

Links
GA20-03426S, research and development project	Name: Ověření a zlepšení bezpečnosti kryptografie eliptických křivek
GA20-03426S, research and development project	Investor: Czech Science Foundation