Thomas Espitau
ABSTRACT
In this paper, we investigate the security of the BLISS lattice-based signature scheme, one of the most promising candidates for postquantum-secure signatures, against side-channel attacks. Several works have been devoted to its efficient implementation on various platforms, from desktop CPUs to microcontrollers and FPGAs, and more recent papers have also considered its security against certain types of physical attacks, notably fault injection and cache attacks. We turn to more traditional side-channel analysis, and describe several attacks that can yield a full key recovery.
We first identify a serious source of leakage in the rejection sampling algorithm used during signature generation. Existing implementations of that rejection sampling step, which is essential for security, actually leak the "relative norm" of the secret key. We show how an extension of an algorithm due to Howgrave-Graham and Szydlo can be used to recover the key from that relative norm, at least when the absolute norm is easy to factor (which happens for a significant fraction of secret keys). We describe how this leakage can be exploited in practice both on an embedded device (an 8-bit AVR microcontroller) using electromagnetic analysis (EMA), and a desktop computer (recent Intel CPU running Linux) using branch tracing. The latter attack has been mounted against the open source VPN software strongSwan.
We also show that other parts of the BLISS signing algorithm can leak secrets not just for a subset of secret keys, but for 100% of them. The BLISS Gaussian sampling algorithm in strongSwan is intrinsically variable time. This would be hard to exploit using a noisy source of leakage like EMA, but branch tracing allows to recover the entire randomness and hence the key: we show that a single execution of the strongSwan signature algorithm is actually sufficient for full key recovery. We also describe a more traditional side-channel attack on the sparse polynomial multiplications carried out in BLISS: classically, multiplications can be attacked using DPA; however, our target 8-bit AVR target implementation uses repeated shifted additions instead. Surprisingly, we manage to obtain a full key recovery in that setting using integer linear programming from a single EMA trace.
Supplemental Material
- Onur Aciiccmez, Shay Gueron, and Jean-Pierre Seifert. 2007. New Branch Prediction Vulnerabilities in OpenSSL and Necessary Software Countermeasures IMACC (LNCS), Steven D. Galbraith (Ed.), Vol. Vol. 4887. Springer, 185--203.Google Scholar
- Onur Aciiccmez, cCetin Kaya Kocc, and Jean-Pierre Seifert 2007. On the Power of Simple Branch Prediction Analysis. ASIACCS, Feng Bao and Steven Miller (Eds.). ACM, 312--320.Google Scholar
- Onur Aciiccmez, cCetin Kaya Kocc, and Jean-Pierre Seifert 2007. Predicting Secret Keys Via Branch Prediction. In CT-RSA (LNCS), Masayuki Abe (Ed.), Vol. Vol. 4377. Springer, 225--242.Google Scholar
- Sedat Akleylek, Nina Bindel, Johannes A. Buchmann, Juliane Krämer, and Giorgia Azzurra Marson. 2016. An Efficient Lattice-Based Signature Scheme with Provably Secure Instantiation AFRICACRYPT (LNCS), David Pointcheval, Abderrahmane Nitaj, and Tajjeeddine Rachidi (Eds.), Vol. Vol. 9646. Springer, 44--60.Google Scholar
- Ian Beer 2016. Linux: textttperf_event_open() can race with execve(). Google Project Zero bug report. (2016). https://bugs.chromium.org/p/project-zero/issues/detail?id=807.Google Scholar
- Nina Bindel, Johannes A. Buchmann, and Juliane Krämer. 2016. Lattice-Based Signature Schemes and Their Sensitivity to Fault Attacks FDTC, Philippe Maurine and Michael Tunstall (Eds.). IEEE Computer Society, 63--77.Google Scholar
- Yuval Bistritz and Alexander Lifshitz 2010. Bounds for resultants of univariate and bivariate polynomials. Linear Algebra Appl. Vol. 432, 8 (2010), 1995--2005. Google ScholarCross Ref
Index Terms
- Side-Channel Attacks on BLISS Lattice-Based Signatures: Exploiting Branch Tracing against strongSwan and Electromagnetic Emanations in Microcontrollers
Recommendations
To BLISS-B or not to be: Attacking strongSwan's Implementation of Post-Quantum Signatures
CCS '17: Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications SecurityIn the search for post-quantum secure alternatives to RSA and ECC, lattice-based cryptography appears to be an attractive and efficient option. A particularly interesting lattice-based signature scheme is BLISS, offering key and signature sizes in the ...
Machine-Learning Side-Channel Attacks on the GALACTICS Constant-Time Implementation of BLISS
ARES '22: Proceedings of the 17th International Conference on Availability, Reliability and SecurityDue to the advancing development of quantum computers, practical attacks on conventional public-key cryptography may become feasible in the next few decades. To address this risk, post-quantum schemes that are assumed to be secure against quantum ...
Practical Lattice-Based Digital Signature Schemes
Special Issue on Embedded Platforms for Crypto and Regular PapersDigital signatures are an important primitive for building secure systems and are used in most real-world security protocols. However, almost all popular signature schemes are either based on the factoring assumption (RSA) or the hardness of the ...
Comments