Fast Side-Channel Security Evaluation of ECC Implementations: Shortcut Formulas for Horizontal Side-channel Attacks against ECSM with the Montgomery ladder

Horizontal attacks are a suitable tool to evaluate the (nearly) worst-case side-channel security level of ECC implementations, due to the fact that they allow extracting a large amount of information from physical observations. Motivated by the difficulty of mounting such attacks and inspired by evaluation strategies for the security of symmetric cryptography implementations, we derive shortcut formulas to estimate the success rate of horizontal differential power analysis attacks against ECSM implementations, for efficient side-channel security evaluations. We then discuss the additional leakage assumptions that we exploit for this purpose, and provide experimental confirmation that the proposed tools lead to good predictions of the attacks\u27 success

Post-Quantum Authenticated Encryption against Chosen-Ciphertext Side-Channel Attacks

Over the last years, the side-channel analysis of Post-Quantum Cryptography (PQC) candidates in the NIST standardization initiative has received increased attention. In particular, it has been shown that some post-quantum Key Encapsulation Mechanisms (KEMs) are vulnerable to Chosen-Ciphertext Side-Channel Attacks (CC-SCA). These powerful attacks target the re-encryption step in the Fujisaki-Okamoto (FO) transform, which is commonly used to achieve CCA security in such schemes. To sufficiently protect PQC KEMs on embedded devices against such a powerful CC-SCA, masking at increasingly higher order is required, which induces a considerable overhead. In this work, we propose to use a conceptually simple construction, the ΕtS KEM, that alleviates the impact of CC-SCA. It uses the Encrypt-then-Sign (EtS) paradigm introduced by Zheng at ISW ’97 and further analyzed by An, Dodis and Rabin at EUROCRYPT ’02, and instantiates a postquantum authenticated KEM in the outsider-security model. While the construction is generic, we apply it to the CRYSTALS-Kyber KEM, relying on the CRYSTALSDilithium and Falcon signature schemes. We show that a CC-SCA-protected EtS KEM version of CRYSTALS-Kyber requires less than 10% of the cycles required for the CC-SCA-protected FO-based KEM, at the cost of additional data/communication overhead. We additionally show that the cost of protecting the EtS KEM against fault injection attacks, necessarily due to the added signature verification, remains negligible compared to the large cost of masking the FO transform at higher orders. Lastly, we discuss relevant embedded use cases for our EtS KEM construction

Key Enumeration from the Adversarial Viewpoint: When to Stop Measuring and Start Enumerating?

In this work, we formulate and investigate a pragmatic question related to practical side-channel attacks complemented with key enumeration. In a real attack scenario, after an attacker has extracted side-channel information, it is possible that despite the entropy of the key has been signicantly reduced, she cannot yet achieve a direct key recovery. If the correct key lies within a sufficiently small set of most probable keys, it can then be recovered with a plaintext and the corresponding ciphertext, by performing enumeration. Our proposal relates to the following question: how does an attacker know when to stop acquiring side-channel observations and when to start enumerating with a given computational effort? Since key enumeration is an expensive (i.e. time-consuming) task, this is an important question from an adversarial viewpoint. To answer this question, we present an efficient (heuristic) way to perform key-less rank estimation, based on simple entropy estimations using histograms

Exploiting Small-Norm Polynomial Multiplication with Physical Attacks: Application to CRYSTALS-Dilithium

We present a set of physical attacks against CRYSTALS-Dilithium that accumulate noisy knowledge on secret keys over multiple signatures, finally leading to a full 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 of an information processing phase which is based on belief propagation, which allows effectively exploiting that bias. The proposed concrete attacks rely on side-channel information, injection of fault attacks, or a combination of the two. Interestingly, the adversary benefits from the knowledge on the released signature, but is not dependent on it. 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

Systematic Study of Decryption and Re-Encryption Leakage: the Case of Kyber

The side-channel cryptanalysis of Post-Quantum (PQ) key encapsulation schemes has been a topic of intense activity over the last years. Many attacks have been put forward: Simple Power Analysis (SPAs) against the re-encryption of schemes using the Fujisaki-Okamoto (FO) transform are known to be very powerful; Differential Power Analysis (DPAs) against the decryption are also possible. Yet, to the best of our knowledge, a systematic and quantitative investigation of their impact for designers is still missing. In this paper, we propose to capture these attacks with shortcut formulas in order to compare their respective strength in function of the noise level. Taking the case of Kyber for illustration, we then evaluate the (high) cost of preventing them with masking and the extent to which different parts of an implementation could benefit from varying security levels. We finally discuss tweaks to improve the situation and enable a better leveling of the countermeasures. Our conclusions confirm that current solutions for side-channel secure PQ key encapsulation schemes like Kyber are unlikely to be efficient in low-noise settings without (design or countermeasures) improvements

The Side-Channel Metrics Cheat Sheet

Side-channel attacks exploit a physical observable originating from a cryptographic device in order to extract its secrets. Many practically relevant advances in the field of side-channel analysis relate to security evaluations of cryptographic functions and devices. Accordingly, many metrics have been adopted or defined to express and quantify side-channel security. These metrics can relate to one another, but also conflict in terms of effectiveness, assumptions and security goals. In this work, we review the most commonly used metrics in the field of side-channel analysis. We provide a self-contained presentation of each metric, along with a discussion of its limitations. We practically demonstrate the metrics on examples of relevant implementations of the Advanced Encryption Standard (AES), and make the software implementation of the presented metrics available to the community as open source. This work, being beyond a survey of the current status of metrics, will allow researchers and practitioners to produce a well-informed security evaluation through a better understanding of its supporting and summarizing metrics

From MLWE to RLWE: A Differential Fault Attack on Randomized & Deterministic Dilithium

The post-quantum digital signature scheme CRYSTALS-Dilithium has been recently selected by the NIST for standardization. Implementing CRYSTALS-Dilithium, 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

Protecting Dilithium against Leakage: Revisited Sensitivity Analysis and Improved Implementations

CRYSTALS-Dilithium has been selected by the NIST as the new stan- dard 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 ran- domized version of Dilithium can lead to significantly more efficient implementations (than its deterministic version) when side-channel attacks are a concern

Shortcut side-channel security evaluations : application to elliptic curve cryptography, masking and shuffling

Since 1996, numerous attacks have been shown to uncover secrets by exploiting a device's physical behavior or emanation, such as power consumption, electromagnetic radiation, execution time, or temperature. Until then, the adversary was always assumed to be constrained by black box assumptions, but we are aware now that he is considerably more powerful than expected. These new attacks, called side-channel attacks, have led to the design of several countermeasures to protect cryptographic secrets. This raises the need for sound methods to assess their security. However, this is a challenging task and the difficulty resides in the fact that unsuccessful attacks do not prove security. We must expand our scope to more powerful adversaries to reach higher security guarantees. In this thesis, we investigate such worst-case evaluations in the context of both symmetric and asymmetric cryptography. In the first part of the thesis, we speed up evaluations of elliptic curve cryptography implementations against horizontal attacks using shortcut formulas. In the second part, we study worst-case analytical belief-propagation-based attacks and compare them to simpler divide-and-conquer attacks to evaluate the elliptic curve point randomization countermeasure. The third part of the thesis relates to the masking and shuffling countermeasures. In this respect, we first improve tools for their evaluations, then we analyze and enhance the security impact of their combination.(FSA - Sciences de l'ingénieur) -- UCL, 202

Blind Side-Channel SIFA

Statistical Ineffective Fault Attacks (SIFA) have been recently proposed as very powerful key-recovery strategies on symmetric cryptographic primitives' implementations. Specifically, they have been shown to bypass many common countermeasures against faults such as redundancy or infection, and to remain applicable even when side-channel countermeasures are deployed. In this work, we investigate combined side-channel and fault attacks and show that a profiled, SIFA-like attack can be applied despite not having any direct ciphertext knowledge. The proposed attack exploits the ciphertext's side-channel and fault characteristics to mount successful key recoveries, even in the presence of masking and duplication countermeasures. We analyze the attack using simulations, discuss its requirements, strengths and limitations, and compare different approaches to distinguish the correct key. Finally, we demonstrate its applicability on an ARM Cortex-M4 device, utilizing a combination of laser-based fault injection and microprobe-based EM side-channel analysis