International Association
for Cryptologic Research

We present a set of physical profiled attacks against CRYSTALS-Dilithium that accumulate noisy knowledge on secret keys over multiple signatures, finally leading to a full key recovery attack. The methodology is composed of two steps. The first step consists of observing or inserting a bias in the posterior distribution of sensitive variables. The second step is an information processing phase which is based on belief propagation and effectively exploits that bias. The proposed concrete attacks rely on side-channel information, induced faults or possibly a combination of the two. Interestingly, the adversary benefits most from this previous knowledge when targeting the released signatures, however, the latter are not strictly necessary. We show that the combination of a physical attack with the binary knowledge of acceptance or rejection of a signature also leads to exploitable information on the secret key. Finally, we demonstrate that this approach is also effective against shuffled implementations of CRYSTALS-Dilithium.

<p> Raccoon is a lattice-based scheme submitted to the NIST 2022 call for additional post-quantum signatures. One of its main selling points is that its design is intrinsically easy to mask against side-channel attacks. So far, Raccoon's physical security guarantees were only stated in the abstract probing model. In this paper, we discuss how these probing security results translate into guarantees in more realistic leakage models. We also highlight that this translation differs from what is usually observed (e.g., in symmetric cryptography), due to the algebraic structure of Raccoon's operations. For this purpose, we perform an in-depth information theoretic evaluation of Raccoon's most innovative part, namely the AddRepNoise function which allows generating its arithmetic shares on-the-fly. Our results are twofold. First, we show that the resulting shares do not enforce a statistical security order (i.e., the need for the side-channel adversary to estimate higher-order moments of the leakage distribution), as usually expected when masking. Second, we observe that the first-order leakage on the (large) random coefficients manipulated by Raccoon cannot be efficiently turned into leakage on the (smaller) coefficients of its long-term secret. Concretely, our information theoretic evaluations for relevant leakage functions also suggest that Raccoon's masked implementations can ensure high security with less shares than suggested by a conservative analysis in the probing model. </p>

FrodoKEM is a lattice-based Key Encapsulation Mechanism (KEM) based on unstructured lattices. From a security point of view this makes it a conservative option to achieve post-quantum security, hence why it is favored by several European authorities (e.g., German BSI and French ANSSI). Relying on unstructured instead of structured lattices (e.g., CRYSTALS-Kyber) comes at the cost of additional memory usage, which is particularly critical for embedded security applications such as smart cards. For example, prior FrodoKEM-640 implementations (using AES) on Cortex-M4 require more than 80 kB of stack making it impossible to run on some embedded systems. In this work, we explore several stack reduction strategies and the resulting time versus memory trade-offs. Concretely, we reduce the stack consumption of FrodoKEM by a factor 2–3x compared to the smallest known implementations with almost no impact on performance. We also present various time-memory trade-offs going as low as 8 kB for all AES parameter sets, and below 4 kB for FrodoKEM-640. By introducing a minor tweak to the FrodoKEM specifications, we additionally reduce the stack consumption down to 8 kB for all the SHAKE versions. As a result, this work enables FrodoKEM on more resource constrained embedded systems.

CRYSTALS-Dilithium has been selected by the NIST as the new standard for post-quantum digital signatures. In this work, we revisit the side-channel countermeasures of Dilithium in three directions. First, we improve its sensitivity analysis by classifying intermediate computations according to their physical security requirements. Second, we provide improved gadgets dedicated to Dilithium, taking advantage of recent advances in masking conversion algorithms. Third, we combine these contributions and report performance for side-channel protected Dilithium implementations. Our benchmarking results additionally put forward that the randomized version of Dilithium can lead to significantly more efficient implementations (than its deterministic version) when side-channel attacks are a concern.

The post-quantum digital signature scheme CRYSTALS-Dilithium has been recently selected by the NIST for standardization. Implementing CRYSTALSDilithium, and other post-quantum cryptography schemes, on embedded devices raises a new set of challenges, including ones related to performance in terms of speed and memory requirements, but also related to side-channel and fault injection attacks security. In this work, we investigated the latter and describe a differential fault attack on the randomized and deterministic versions of CRYSTALS-Dilithium. Notably, the attack requires a few instructions skips and is able to reduce the MLWE problem that Dilithium is based on to a smaller RLWE problem which can be practically solved with lattice reduction techniques. Accordingly, we demonstrated key recoveries using hints extracted on the secret keys from the same faulted signatures using the LWE with side-information framework introduced by Dachman-Soled et al. at CRYPTO’20. As a final contribution, we proposed algorithmic countermeasures against this attack and in particular showed that the second one can be parameterized to only induce a negligible overhead over the signature generation.

We revisit the popular adage that side-channel countermeasures must be combined to be efficient, and study its application to bitslice masking and shuffling. Our main contributions are twofold. First, we improve this combination: by shuffling the shares of a masked implementation rather than its tuples, we can amplify the impact of the shuffling exponentially in the number of shares, while this impact was independent of the masking security order in previous works. Second, we evaluate the masking and shuffling combination’s performance vs. security tradeoff under sufficient noise conditions: we show that the best approach is to mask first (i.e., fill the registers with as many shares as possible) and shuffle the independent operations that remain. We conclude that with moderate but sufficient noise, the “bitslice masking + shuffling” combination of countermeasures is practically relevant, and its interest increases when randomness is expensive and many independent operations are available for shuffling. When these conditions are not met, masking only is the best option. As additional side results, we improve the best known attack against the shuffling countermeasure from ASIACRYPT 2012. We also recall that algorithmic countermeasures like masking and shuffling, and therefore their combination, cannot be implemented securely without a minimum level of physical noise.

The performance of higher-order masked implementations of lattice-based based key encapsulation mechanisms (KEM) is currently limited by the costly conversions between arithmetic and Boolean masking. While bitslicing has been shown to strongly speed up masked implementations of symmetric primitives, its use in arithmetic-to-Boolean and Boolean-to-arithmetic masking conversion gadgets has never been thoroughly investigated. In this paper, we first show that bitslicing can indeed accelerate existing conversion gadgets. We then optimize these gadgets, exploiting the degrees of freedom offered by bitsliced implementations. As a result, we introduce new arbitrary-order Boolean masked addition, arithmetic-to-Boolean and Boolean-to-arithmetic masking conversion gadgets, each in two variants: modulo 2k and modulo p (for any integers k and p). Practically, our new gadgets achieve a speedup of up to 25x over the state of the art. Turning to the KEM application, we develop the first open-source embedded (Cortex-M4) implementations of Kyber768 and Saber masked at arbitrary order. The implementations based on the new bitsliced gadgets achieve a speedup of 1.8x for Kyber and 3x for Saber, compared to the implementation based on state-of-the-art gadgets. The bottleneck of the bitslice implementations is the masked Keccak-f[1600] permutation.

In order to lower costs, the fabrication of Integrated Circuits (ICs) is increasingly delegated to offshore contract foundries, making them exposed to malicious modifications, known as hardware Trojans. Recent works have demonstrated that a strong form of Trojan-resilience can be obtained from untrusted chips by exploiting secret sharing and Multi-Party Computation (MPC), yet with significant cost overheads. In this paper, we study the possibility of building a symmetric cipher enabling similar guarantees in a more efficient manner. To reach this goal, we exploit a simple round structure mixing a modular multiplication and a multiplication with a binary matrix. Besides being motivated as a new block cipher design for Trojan resilience, our research also exposes the cryptographic properties of the modular multiplication, which is of independent interest.

We explore the concrete side-channel security provided by state-of-theart higher-order masked software implementations of the AES and the (candidate to the NIST Lightweight Cryptography competition) Clyde, in ARM Cortex-M0 and M3 devices. Rather than looking for possibly reduced security orders (as frequently considered in the literature), we directly target these implementations by assuming their maximum security order and aim at reducing their noise level thanks to multivariate, horizontal and analytical attacks. Our investigations point out that the Cortex-M0 device has so limited physical noise that masking is close to ineffective. The Cortex-M3 shows a better trend but still requires a large number of shares to provide strong security guarantees. Practically, we first exhibit a full 128-bit key recovery in less than 10 traces for a 6-share masked AES implementation running on the Cortex-M0 requiring 232 enumeration power. A similar attack performed against the Cortex-M3 with 5 shares require 1,000 measurements with 244 enumeration power. We then show the positive impact of lightweight block ciphers with limited number of AND gates for side-channel security, and compare our attacks against a masked Clyde with the best reported attacks of the CHES 2020 CTF. We complement these experiments with a careful information theoretic analysis, which allows interpreting our results. We also discuss our conclusions under the umbrella of “backwards security evaluations” recently put forwards by Azouaoui et al. We finally extrapolate the evolution of the proposed attack complexities in the presence of additional countermeasures using the local random probing model proposed at CHES 2020.

We revisit Unterstein et al.’s leakage-resilient authenticated encryption scheme from CHES 2020. Its main goal is to enable secure software updates by leveraging unprotected (e.g., AES, SHA256) coprocessors available on low-end microcontrollers. We show that the design of this scheme ignores an important attack vector that can significantly reduce its security claims, and that the evaluation of its leakage-resilient PRF is quite sensitive to minor variations of its measurements, which can easily lead to security overstatements. We then describe and analyze a new mode of operation for which we propose more conservative security parameters and show that it competes with the CHES 2020 one in terms of performances. As an additional bonus, our solution relies only on AES-128 coprocessors, an

We take advantage of a recently published open source implementation of the AES protected with a mix of countermeasures against side-channel attacks to discuss both the challenges in protecting COTS devices against such attacks and the limitations of closed source security evaluations. The target implementation has been proposed by the French ANSSI (Agence Nationale de la Sécurité des Systèmes d’Information) to stimulate research on the design and evaluation of side-channel secure implementations. It combines additive and multiplicative secret sharings into an affine masking scheme that is additionally mixed with a shuffled execution. Its preliminary leakage assessment did not detect data dependencies with up to 100,000 measurements. We first exhibit the gap between such a preliminary leakage assessment and advanced attacks by demonstrating how a countermeasures’ dissection exploiting a mix of dimensionality reduction, multivariate information extraction and key enumeration can recover the full key with less than 2,000 measurements. We then discuss the relevance of open source evaluations to analyze such implementations efficiently, by pointing out that certain steps of the attack are hard to automate without implementation knowledge (even with machine learning tools), while performing them manually is straightforward. Our findings are not due to design flaws but from the general difficulty to prevent side-channel attacks in COTS devices with limited noise. We anticipate that high security on such devices requires significantly more shares.

This paper defines Spook: a sponge-based authenticated encryption with associated data algorithm. It is primarily designed to provide security against side-channel attacks at a low energy cost. For this purpose, Spook is mixing a leakageresistant mode of operation with bitslice ciphers enabling efficient and low latency implementations. The leakage-resistant mode of operation leverages a re-keying function to prevent differential side-channel analysis, a duplex sponge construction to efficiently process the data, and a tag verification based on a Tweakable Block Cipher (TBC) providing strong data integrity guarantees in the presence of leakages. The underlying bitslice ciphers are optimized for the masking countermeasures against side-channel attacks. Spook is an efficient single-pass algorithm. It ensures state-of-the-art black box security with several prominent features: (i) nonce misuse-resilience, (ii) beyond-birthday security with respect to the TBC block size, and (iii) multiuser security at minimum cost with a public tweak. Besides the specifications and design rationale, we provide first software and hardware implementation results of (unprotected) Spook which confirm the limited overheads that the use of two primitives sharing internal components imply. We also show that the integrity of Spook with leakage, so far analyzed with unbounded leakages for the duplex sponge and a strongly protected TBC modeled as leak-free, can be proven with a much weaker unpredictability assumption for the TBC. We finally discuss external cryptanalysis results and tweaks to improve both the security margins and efficiency of Spook.

Triggered by the increasing deployment of embedded cryptographic devices (e.g., for the IoT), the design of authentication, encryption and authenticated encryption schemes enabling improved security against side-channel attacks has become an important research direction. Over the last decade, a number of modes of operation have been proposed and analyzed under different abstractions. In this paper, we investigate the practical consequences of these findings. For this purpose, we first translate the physical assumptions of leakage-resistance proofs into minimum security requirements for implementers. Thanks to this (heuristic) translation, we observe that (i) security against physical attacks can be viewed as a tradeoff between mode-level and implementation-level protection mechanisms, and (i}) security requirements to guarantee confidentiality and integrity in front of leakage can be concretely different for the different parts of an implementation. We illustrate the first point by analyzing several modes of operation with gradually increased leakage-resistance. We illustrate the second point by exhibiting leveled implementations, where different parts of the investigated schemes have different security requirements against leakage, leading to performance improvements when high physical security is needed. We finally initiate a comparative discussion of the different solutions to instantiate the components of a leakage-resistant authenticated encryption scheme.

One important open question in side-channel analysis is to find out whether all the leakage samples in an implementation can be exploited by an adversary, as suggested by masking security proofs. For attacks exploiting a divide-and-conquer strategy, the answer is negative: only the leakages corresponding to the first/last rounds of a block cipher can be exploited. Soft Analytical Side-Channel Attacks (SASCA) have been introduced as a powerful solution to mitigate this limitation. They represent the target implementation and its leakages as a code (similar to a Low Density Parity Check code) that is decoded thanks to belief propagation. Previous works have shown the low data complexities that SASCA can reach in practice. In this paper, we revisit these attacks by modeling them with a variation of the Random Probing Model used in masking security proofs, that we denote as the Local Random Probing Model (LRPM). Our study establishes interesting connections between this model and the erasure channel used in coding theory, leading to the following benefits. First, the LRPM allows bounding the security of concrete implementations against SASCA in a fast and intuitive manner. We use it in order to confirm that the leakage of any operation in a block cipher can be exploited, although the leakages of external operations dominate in known-plaintext/ciphertext attack scenarios. Second, we show that the LRPM is a tool of choice for the (nearly worst-case) analysis of masked implementations in the noisy leakage model, taking advantage of all the operations performed, and leading to new tradeoffs between their amount of randomness and physical noise level. Third, we show that it can considerably speed up the evaluation of other countermeasures such as shuffling.

Leakage detection is a common tool to quickly assess the security of a cryptographic implementation against side-channel attacks. The Test Vector Leakage Assessment (TVLA) methodology using Welch’s t-test, proposed by Cryptography Research, is currently the most popular example of such tools, thanks to its simplicity and good detection speed compared to attack-based evaluations. However, as any statistical test, it is based on certain assumptions about the processed samples and its detection performances strongly depend on parameters like the measurement’s Signal-to-Noise Ratio (SNR), their degree of dependency, and their density, i.e., the ratio between the amount of informative and non-informative points in the traces. In this paper, we argue that the correct interpretation of leakage detection results requires knowledge of these parameters which are a priori unknown to the evaluator, and, therefore, poses a non-trivial challenge to evaluators (especially if restricted to only one test). For this purpose, we first explore the concept of multi-tuple detection, which is able to exploit differences between multiple informative points of a trace more effectively than tests relying on the minimum p-value of concurrent univariate tests. To this end, we map the common Hotelling’s T2-test to the leakage detection setting and, further, propose a specialized instantiation of it which trades computational overheads for a dependency assumption. Our experiments show that there is not one test that is the optimal choice for every leakage scenario. Second, we highlight the importance of the assumption that the samples at each point in time are independent, which is frequently considered in leakage detection, e.g., with Welch’s t-test. Using simulated and practical experiments, we show that (i) this assumption is often violated in practice, and (ii) deviations from it can affect the detection performances, making the correct interpretation of the results more difficult. Finally, we consolidate our findings by providing guidelines on how to use a combination of established and newly-proposed leakage detection tools to infer the measurements parameters. This enables a better interpretation of the tests’ results than the current state-of-the-art (yet still relying on heuristics for the most challenging evaluation scenarios).

Leakage certification aims at guaranteeing that the statistical models used in side-channel security evaluations are close to the true statistical distribution of the leakages, hence can be used to approximate a worst-case security level. Previous works in this direction were only qualitative: for a given amount of measurements available to an evaluation laboratory, they rated a model as “good enough” if the model assumption errors (i.e., the errors due to an incorrect choice of model family) were small with respect to the model estimation errors. We revisit this problem by providing the first quantitative tools for leakage certification. For this purpose, we provide bounds for the (unknown) Mutual Information metric that corresponds to the true statistical distribution of the leakages based on two easy-to-compute information theoretic quantities: the Perceived Information, which is the amount of information that can be extracted from a leaking device thanks to an estimated statistical model, possibly biased due to estimation and assumption errors, and the Hypothetical Information, which is the amount of information that would be extracted from an hypothetical device exactly following the model distribution. This positive outcome derives from the observation that while the estimation of the Mutual Information is in general a hard problem (i.e., estimators are biased and their convergence is distribution-dependent), it is significantly simplified in the case of statistical inference attacks where a target random variable (e.g., a key in a cryptographic setting) has a constant (e.g., uniform) probability. Our results therefore provide a general and principled path to bound the worst-case security level of an implementation. They also significantly speed up the evaluation of any profiled side-channel attack, since they imply that the estimation of the Perceived Information, which embeds an expensive cross-validation step, can be bounded by the computation of a cheaper Hypothetical Information, for any estimated statistical model.