Post-Quantum key encapsulation mechanisms based on the re-encryption framework of Fujisaki and Okamoto have proved very sensitive to Plaintext Checking Oracle (PCO) attacks. The first theoretic works on PCO attacks were rapidly followed by practical attacks on real implementations, notably on NIST standardized ML-KEM. The actual realization of a PCO relies on side-channel leakages that are inherently noisy; even more so if the implementation embeds side-channel countermeasures. In this paper we tackle the often overlooked complications caused by highly noisy PCOs. We demonstrate that the impact of wrong oracle answers can be very efficiently reduced with the use of the so-called Sequential Probability Ratio Test (SPRT). This test can be seen as an elegant and natural early abort strategy on top of the commonly used approaches based on majority-voting or the likelihood ratio test. As far as we know, this is the first use of SPRT in the context of side-channel attacks. We show that it allows to divide by a factor up to 3 the attack complexity compared to the traditional approaches. By establishing new comparisons with recently published noisy PCO attacks we emphasize that SPRT should be considered as the novel baseline for all future works in this line of research.

The present work unearths a side-channel vulnerability in the cryptographic library of Infineon Technologies, one of the most important secure element manufacturers. This vulnerability - that went unnoticed for 14 years and about 80 highest-level Common Criteria certification evaluations - is due to a non constant-time modular inversion. The attack requires physical access to the secure element (few local electromagnetic side-channel acquisitions, i.e. few minutes, are enough) in order to extract an ECDSA secret key. The attack is demonstrated on a FIDO hardware token from Yubico where it allows to create a clone of the FIDO device. Yubico acknowledged that all YubiKey 5 Series (with firmware version below 5.7) are impacted by the attack. Furthermore, strong arguments tend to indicate that all Infi-neon security microcontrollers (including TPMs) that run the Infineon cryptographic library are vulnerable to the attack.

A wide range of countermeasures have been proposed to defend against side-channel attacks, with masking being one of the most effective and commonly used techniques. While theoretical models provide formal security proofs, these often rely on assumptions—sometimes implicit—that can be difficult to assess in practice. As a result, the design of secure masked implementations frequently combines proven theoretical arguments with heuristic and empirical validation. Despite the significant body of work, the literature still lacks a cohesive and well-defined framework for translating theoretical security guarantees into practical implementations on physical devices. Specifically, there remains a gap in connecting provable results from abstract models to quantitative security guarantees at the implementation level. In this Systematization of Knowledge (SoK), we aim to provide a comprehensive methodology to transform abstract cryptographic algorithms into physically secure implementations against side-channel attacks on microcontrollers. We introduce new tools to adapt the ideal noisy leakage model to practical, real-world scenarios, and we integrate state-of-the-art techniques to build secure implementations based on this model. Our work systematizes the design objectives necessary for achieving high security levels in embedded devices and identifies the remaining challenges in concretely applying security reductions. By bridging the gap between theory and practice, we seek to provide a foundation for future research that can develop implementations with proven security against side-channel attacks, based on well-understood leakage assumptions.

. Physical side-channel attacks are powerful attacks that exploit a device’s physical em-anations to break the security of cryptographic implementations. Many countermeasures have been proposed against these attacks, especially the widely-used and efficient masking countermeasure. Nevertheless, proving the security of masked implementations is challenging. Current techniques rely on empirical approaches to validate the security of such implementations. On the other hand, the theoretical community introduced leakage models to provide formal proofs of the security of masked implementations. Meanwhile, these leakage models rely on physical assumptions that are difficult to satisfy in practice, and the literature lacks a clear framework to implement proven secure constructions on a physical device while preserving the proven security. In this paper, we present a complete methodology describing the steps to turn an abstract masking scheme proven secure in a theoretical leakage model into a physical implementation satisfying provable security against side-channel attacks in practice. We propose new tools to enforce or relax the physical assumptions the indeal noisy leakage model rely on and provide novel ways of including them in a physical implementation. We also highlight the design goals for an embedded device to reach high levels of proven security, discussing the limitations and open problems of the practical usability of the leakage models. Our goal is to show that it is possible to bridge theory and practice and to motivate further research to fully close the gap and get practical implementations proven secure against side-channel attacks on a physical device without any ideal assumption about the leakage.

The Google Titan Security Key is a FIDO U2F hardware device proposed by Google (available since July 2018) as a two-factor authentication token to sign in to applications (e.g. your Google account). We present here a side-channel attack that targets the Google Titan Security Key ’s secure element (the NXP A700X chip) by the observation of its local electromagnetic radiations during ECDSA signatures (the core cryptographic operation of the FIDO U2F protocol). This work shows that an attacker can clone a legitimate Google Titan Security Key . To understand the NXP ECDSA implementation, find a vulnerability and design a keyrecovery attack, we had to make a quick stop on Rhea (NXP J3D081 JavaCard smartcard). Freely available on the web, this product looks very much like the NXP A700X chip and uses the same cryptographic library. Rhea, as an open JavaCard platform, gives us more control to study the ECDSA implementation. We could then show that the electromagnetic side-channel signal bears partial information about the ECDSA ephemeral key. The sensitive information is recovered with a non-supervised machine learning method and plugged into a customized lattice-based attack scheme. Finally, 4000 ECDSA observations were enough to recover the (known) secret key on Rhea and validate our attack process. It was then applied on the Google Titan Security Key with success (this time with 6000 observations) as we were able to extract the long term ECDSA private key linked to a FIDO U2F account created for the experiment. Cautionary Note Two-factor authentication tokens (like FIDO U2F hardware devices) primary goal is to fight phishing attacks. Our attack requires physical access to the Google Titan Security Key , expensive equipment, custom software, and technical skills. Thus, as far as the work presented here goes, it is still safer to use your Google Titan Security Key or other impacted products as FIDO U2F two-factor authentication token to sign in to applications rather than not using one. Nevertheless, this work shows that the Google Titan Security Key (and other impacted products) would not avoid unnoticed security breach by attackers willing to put enough effort into it. Users that face such a threat should probably switch to other FIDO U2F hardware security keys, where no vulnerability has yet been discovered.

The Google Titan Security Key is a FIDO U2F hardware device proposed by Google (available since July 2018) as a two-factor authentication token to sign in to applications such as your Google account. In this paper, we present a sidechannel attack that targets the Google Titan Security Key ’s secure element (the NXP A700x chip) by the observation of its local electromagnetic radiations during ECDSA signatures. This work shows that an attacker can clone a legitimate Google Titan Security Key. As a side observation, we identified a novel correlation between the elliptic curve group order and the lattice-based attack success rate.

The Google Titan Security Key is a FIDO U2F hardware device proposed by Google (available since July 2018) as a two-factor authentication token to sign in to applications such as your Google account. In this paper, we present a side-channel attack that targets the Google Titan Security Key's secure element (the NXP A700x chip) by the observation of its local electromagnetic radiations during ECDSA signatures. This work shows that an attacker can clone a legitimate Google Titan Security Key. As a side observation, we identified a novel correlation between the elliptic curve group order and the lattice-based attack success rate.

In a series of recent articles (from 2011 to 2017), Schindler et al. show that exponent/scalar blinding is not as effective a countermeasure as expected against side-channel attacks targeting RSA modular exponentiation and ECC scalar multiplication. Precisely, these works demonstrate that if an attacker is able to retrieve many randomizations of the same secret, this secret can be fully recovered even when a significative proportion of the blinded secret bits are erroneous. With a focus on ECC, this paper improves the best results of Schindler et al. in the specific case of structured-order elliptic curves. Our results show that larger blinding material and higher error rates can be successfully handled by an attacker in practice. This study also opens new directions in this line of work by the proposal of a three-steps attack process that isolates the attack critical path (in terms of complexity and success rate) and hence eases the development of future solutions.

Mammalian pyruvate dehydrogenase (PDH) activity is tightly regulated by phosphorylation and dephosphorylation, which is catalyzed by PDH kinase isomers and PDH phosphatase isomers, respectively. PDH phosphatase isomer 1 (PDP1) is a heterodimer consisting of a catalytic subunit (PDP1c) and a regulatory subunit (PDP1r). Here, the crystal structure of bovine PDP1c determined at 2.1 Å resolution is reported. The crystals belonged to space group P3221, with unit-cell parameters a = b = 75.3, c = 173.2 Å. The structure was solved by molecular-replacement methods and refined to a final R factor of 21.9% (Rfree = 24.7%). The final model consists of 402 of a possible 467 amino-acid residues of the PDP1c monomer, two Mn2+ ions in the active site, an additional Mn2+ ion coordinated by His410 and His414, two MnSO4 ion pairs at special positions near the crystallographic twofold symmetry axis and 226 water molecules. Several new features of the PDP1c structure are revealed. The requirements are described and plausible bases are deduced for the interaction of PDP1c with PDP1r and other components of the pyruvate dehydrogenase complex.

Pyruvate dehydrogenase complex (PDC) is a large multienzyme complex that catalyzes the irreversible conversion of pyruvate to acetyl-coenzyme A with reduction of NAD+. Distinctive from PDCs in lower forms of life, in mammalian PDC, dihydrolipoyl acetyltransferase (E2; E2p in PDC) and dihydrolipoamide dehydrogenase binding protein (E3BP) combine to form a complex that plays a central role in the organization, regulation, and integration of catalytic reactions of PDC. However, the atomic structure and organization of the mammalian E2p/E3BP heterocomplex are unknown. Here, we report the structure of the recombinant dodecahedral core formed by the C-terminal inner-core/catalytic (IC) domain of human E2p determined at 3.1 Å resolution by cryo electron microscopy (cryoEM). The structure of the N-terminal fragment and four other surface areas of the human E2p IC domain exhibit significant differences from those of the other E2 crystal structures, which may have implications for the integration of E3BP in mammals. This structure also allowed us to obtain a homology model for the highly homologous IC domain of E3BP. Analysis of the interactions of human E2p or E3BP with their adjacent IC domains in the dodecahedron provides new insights into the organization of the E2p/E3BP heterocomplex and suggests a potential contribution by E3BP to catalysis in mammalian PDC.

The probing security model is very popular to prove the side-channel security of cryptographic implementations protected by masking. A common approach to secure nonlinear functions in this model is to represent them as polynomials over a binary field and to secure their nonlinear multiplications thanks to a method introduced by Ishai, Sahai and Wagner at Crypto 2003. Several schemes based on this approach have been published, leading to the recent proposal of Coron, Roy and Vivek which is currently the best known method when no particular assumption is made on the algebraic structure of the function. In the present paper, we revisit this idea by trading nonlinear multiplications for low-degree functions. Specifically, we introduce an algebraic decomposition approach in which a nonlinear function is represented as a sequence of functions with low algebraic degrees. We therefore focus on the probing-secure evaluation of such low-degree functions and we introduce three novel methods to tackle this particular issue. The paper concludes with a comparative analysis of the proposals, which shows that our algebraic decomposition method outperforms the method of Coron, Roy and Vivek in several realistic contexts.

Many applications of embedded devices require the generation of cryptographic secret parameters during the life cycle of the product. In such an unsafe context, several papers have shown that key generation algorithms are vulnerable to side-channel attacks. This is in particular the case of the generation of the secret prime factors in RSA. Until now, the threat has been demonstrated against naive implementations whose operations' flow depends on secret data, and a simple countermeasure is to avoid such kind of dependency. In this paper, we propose a new attack that renders this defence strategy ineffective. It is in particular able to break secure implementations recommended by the ANSI X9.31 and FIPS 186-4 standards. We analyse its efficiency for various realistic attack contexts and we demonstrate its practicality through experiments against a smart-card implementation. Possible countermeasures are eventually proposed, drawing the following main conclusion: prime generation algorithms should avoid the use of a prime sieve combined with a deterministic process to generate the prime candidates from a random seed.

Implementations of cryptographic algorithms are vulnerable to Side-Channel Analyses extracting information from the device behaviour. When such an attack targets the manipulation of several, say d, intermediate variables then it is said to be a d th-order one. A privileged way to circumvent this type of attacks is to split any key-dependent variable into n shares, with n > d, and to adapt the internal processing in order to securely operate on these shares. The latter step is often very tricky and few schemes have been proposed which address this issue in a sound way.

The resistance of a cryptographic implementation with regards to side-channel analysis is often quantified by measuring the success rate of a given attack. This approach cannot always be followed in practice, especially when the implementation includes some countermeasures that may render the attack too costly for an evaluation purpose, but not costly enough from a security point of view. An evaluator then faces the issue of estimating the success rate of an attack he cannot mount. The present paper addresses this issue by presenting a methodology to estimate the success rate of higher-order side-channel attacks targeting implementations protected by masking. Specifically, we generalize the approach initially proposed at SAC 2008 in the context of first-order side-channel attacks. The principle is to approximate the distribution of an attack's score vector by a multivariate Gaussian distribution, whose parameters are derived by profiling the leakage. One can then accurately compute the expected attack success rate with respect to the number of leakage measurements. We apply this methodology to higher-order side-channel attacks based on the widely used correlation and likelihood distinguishers. Moreover, we validate our approach with simulations and practical attack experiments against masked AES implementations running on two different microcontrollers.

Masking is a widely used countermeasure to protect block cipher implementations against side-channel attacks. The principle is to split every sensitive intermediate variable occurring in the computation into d+1 shares, where d is called the masking order and plays the role of a security parameter. A masked implementation is then said to achieve d th-order security if any set of d (or less) intermediate variables does not reveal key-dependent information. At CHES 2010, Rivain and Prouff have proposed a higher-order masking scheme for AES that works for any arbitrary order d . This scheme, and its subsequent extensions, are based on an improved version of the shared multiplication processing published by Ishai et al. at CRYPTO 2003. This improvement enables better memory/timing performances but its security relies on the refreshing of the masks at some points in the algorithm. In this paper, we show that the method proposed at CHES 2010 to do such mask refreshing introduces a security flaw in the overall masking scheme. Specifically, we show that it is vulnerable to an attack of order ⌈ d/2 ⌉ +1 whereas the scheme is supposed to achieve d th-order security. After exhibiting and analyzing the flaw, we propose a new solution which avoids the use of mask refreshing, and we prove its security. We also provide some implementation trick that makes our proposed solution, not only secure, but also faster than the original scheme.

Since the introduction of side channel attacks in the nineties, a large amount of work has been devoted to their effectiveness and efficiency improvements. On the one side, general results and conclusions are drawn in theoretical frameworks, but the latter ones are often set in a too ideal context to capture the full complexity of an attack performed in real conditions. On the other side, practical improvements are proposed for specific contexts but the big picture is often put aside, which makes them difficult to adapt to different contexts. This paper tries to bridge the gap between both worlds. We specifically investigate which kind of issues is faced by a security evaluator when performing a state of the art attack. This analysis leads us to focus on the very common situation where the exact time of the sensitive processing is drown in a large number of leakage points. In this context we propose new ideas to improve the effectiveness and/or efficiency of the three considered attacks. In the particular case of stochastic attacks, we show that the existing literature, essentially developed under the assumption that the exact sensitive time is known, cannot be directly applied when the latter assumption is relaxed. To deal with this issue, we propose an improvement which makes stochastic attack a real alternative to the classical correlation power analysis. Our study is illustrated by various attack experiments performed on several copies of three micro-controllers with different CMOS technologies respectively 350, 130 and 90 nanometers.

In this paper we study the collision-correlation attack published by Clavier etal. at CHES 2011 on a 1st-order Boolean masking scheme and show its lack of robustness against unknown and high level of measurement noise. In order to improve the attack, we follow the approach that Gérard and Standaert proposed in a recent paper at CHES 2012. Then we address the problem of heterogeneous leakage pointed out by Gérard and Standaert (when the leakage noise is different from one Sbox output to the others due for instance to implementation particularities or resynchronisation reasons), by inserting an efficient termination algorithm in the key-recovery phase of the attack. In a last contribution, we compare (over simulations and real experiments) the enhanced collision-correlation attack and the 2nd-order CPA attack. Similarly to the results of Gérard and Standaert, we show - in the context of masked implementations - the superiority of 2nd-order CPA when its leakage model is not too far from the real leakage function.

Side-channel attacks usually apply a divide-and-conquer strategy, separately recovering different parts of the secret. Their efficiency in practice relies on the adversary ability to precisely assess the success or unsuccess of each of these recoveries. This makes the study of the attack success rate a central problem in side channel analysis. In this paper we tackle this issue in two different settings for the most popular attack, namely the Correlation Power Analysis (CPA). In the first setting, we assume that the targeted subkey is known and we compare the state of the art formulae expressing the success rate as a function of the leakage noise and the algebraic properties of the cryptographic primitive. We also make the link between these formulae and the recent work of Fei et al. at CHES 2012. In the second setting, the subkey is no longer assumed to be known and we introduce the notion of confidence level in an attack result, allowing for the study of different heuristics. Through experiments, we show that the rank evolution of a subkey hypothesis can be exploited to compute a better confidence than considering only the final result.