Horizontal Clustering Side-Channel Attacks on Embedded ECC Implementations (Extended Version)

Side-channel attacks are a threat to cryptographic algorithms running on embedded devices. Public-key cryptosystems, including elliptic curve cryptography (ECC), are particularly vulnerable because their private keys are usually long-term. Well known countermeasures like regularity, projective coordinates and scalar randomization, among others, are used to harden implementations against common side-channel attacks like DPA. Horizontal clustering attacks can theoretically overcome these countermeasures by attacking individual side-channel traces. In practice horizontal attacks have been applied to overcome protected ECC implementations on FPGAs. However, it has not been known yet whether such attacks can be applied to protected implementations working on embedded devices, especially in a non-profiled setting. In this paper we mount non-profiled horizontal clustering attacks on two protected implementations of the Montgomery Ladder on Curve25519 available in the µNaCl library targeting electromagnetic (EM) emanations. The first implementation performs the conditional swap (cswap) operation through arithmetic of field elements (cswap-arith), while the second does so by swapping the pointers (cswap-pointer). They run on a 32-bit ARM Cortex-M4F core. Our best attack has success rates of 97.64% and 99.60% for cswap-arith and cswap-pointer, respectively. This means that at most 6 and 2 bits are incorrectly recovered, and therefore, a subsequent brute-force can fix them in reasonable time. Furthermore, our horizontal clustering framework used for the aforementioned attacks can be applied against other protected implementations

Single-trace clustering power analysis of the point-swapping procedure in the three point ladder of Cortex-M4 SIKE

In this paper, the recommended implementation of the post-quantum key exchange SIKE for Cortex-M4 is attacked through power analysis with a single trace by clustering with the $k$-means algorithm the power samples of all the invocations of the elliptic curve point swapping function in the constant-time coordinate-randomized three point ladder. Because each sample depends on whether two consecutive bits of the private key are the same or not, a successful clustering (with $k=2$) leads to the recovery of the entire private key. The attack is naturally improved with better strategies, such as clustering the samples in the frequency domain or processing the traces with a wavelet transform, using a simpler clustering algorithm based on thresholding, and using metrics to prioritize certain keys for key validation. The attack and the proposed improvements were experimentally verified using the ChipWhisperer framework. Splitting the swapping mask into multiple shares is suggested as an effective countermeasure

Side-channel Attacks on Blinded Scalar Multiplications Revisited

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

Survey for Performance & Security Problems of Passive Side-channel Attacks Countermeasures in ECC

The main objective of the Internet of Things is to interconnect everything around us to obtain information which was unavailable to us before, thus enabling us to make better decisions. This interconnection of things involves security issues for any Internet of Things key technology. Here we focus on elliptic curve cryptography (ECC) for embedded devices, which offers a high degree of security, compared to other encryption mechanisms. However, ECC also has security issues, such as Side-Channel Attacks (SCA), which are a growing threat in the implementation of cryptographic devices. This paper analyze the state-of-the-art of several proposals of algorithmic countermeasures to prevent passive SCA on ECC defined over prime fields. This work evaluates the trade-offs between security and the performance of side-channel attack countermeasures for scalar multiplication algorithms without pre-computation, i.e. for variable base point. Although a number of results are required to study the state-of-the-art of side-channel attack in elliptic curve cryptosystems, the interest of this work is to present explicit solutions that may be used for the future implementation of security mechanisms suitable for embedded devices applied to Internet of Things. In addition security problems for the countermeasures are also analyzed

Information Leakage Attacks and Countermeasures

The scientific community has been consistently working on the pervasive problem of information leakage, uncovering numerous attack vectors, and proposing various countermeasures. Despite these efforts, leakage incidents remain prevalent, as the complexity of systems and protocols increases, and sophisticated modeling methods become more accessible to adversaries. This work studies how information leakages manifest in and impact interconnected systems and their users. We first focus on online communications and investigate leakages in the Transport Layer Security protocol (TLS). Using modern machine learning models, we show that an eavesdropping adversary can efficiently exploit meta-information (e.g., packet size) not protected by the TLS’ encryption to launch fingerprinting attacks at an unprecedented scale even under non-optimal conditions. We then turn our attention to ultrasonic communications, and discuss their security shortcomings and how adversaries could exploit them to compromise anonymity network users (even though they aim to offer a greater level of privacy compared to TLS). Following up on these, we delve into physical layer leakages that concern a wide array of (networked) systems such as servers, embedded nodes, Tor relays, and hardware cryptocurrency wallets. We revisit location-based side-channel attacks and develop an exploitation neural network. Our model demonstrates the capabilities of a modern adversary but also presents an inexpensive tool to be used by auditors for detecting such leakages early on during the development cycle. Subsequently, we investigate techniques that further minimize the impact of leakages found in production components. Our proposed system design distributes both the custody of secrets and the cryptographic operation execution across several components, thus making the exploitation of leaks difficult

Profiling side-channel attacks on cryptographic algorithms

Traditionally, attacks on cryptographic algorithms looked for mathematical weaknesses in the underlying structure of a cipher. Side-channel attacks, however, look to extract secret key information based on the leakage from the device on which the cipher is implemented, be it smart-card, microprocessor, dedicated hardware or personal computer. Attacks based on the power consumption, electromagnetic emanations and execution time have all been practically demonstrated on a range of devices to reveal partial secret-key information from which the full key can be reconstructed. The focus of this thesis is power analysis, more specifically a class of attacks known as profiling attacks. These attacks assume a potential attacker has access to, or can control, an identical device to that which is under attack, which allows him to profile the power consumption of operations or data flow during encryption. This assumes a stronger adversary than traditional non-profiling attacks such as differential or correlation power analysis, however the ability to model a device allows templates to be used post-profiling to extract key information from many different target devices using the power consumption of very few encryptions. This allows an adversary to overcome protocols intended to prevent secret key recovery by restricting the number of available traces. In this thesis a detailed investigation of template attacks is conducted, along with how the selection of various attack parameters practically affect the efficiency of the secret key recovery, as well as examining the underlying assumption of profiling attacks in that the power consumption of one device can be used to extract secret keys from another. Trace only attacks, where the corresponding plaintext or ciphertext data is unavailable, are then investigated against both symmetric and asymmetric algorithms with the goal of key recovery from a single trace. This allows an adversary to bypass many of the currently proposed countermeasures, particularly in the asymmetric domain. An investigation into machine-learning methods for side-channel analysis as an alternative to template or stochastic methods is also conducted, with support vector machines, logistic regression and neural networks investigated from a side-channel viewpoint. Both binary and multi-class classification attack scenarios are examined in order to explore the relative strengths of each algorithm. Finally these machine-learning based alternatives are empirically compared with template attacks, with their respective merits examined with regards to attack efficiency

Security of Ubiquitous Computing Systems

The chapters in this open access book arise out of the EU Cost Action project Cryptacus, the objective of which was to improve and adapt existent cryptanalysis methodologies and tools to the ubiquitous computing framework. The cryptanalysis implemented lies along four axes: cryptographic models, cryptanalysis of building blocks, hardware and software security engineering, and security assessment of real-world systems. The authors are top-class researchers in security and cryptography, and the contributions are of value to researchers and practitioners in these domains. This book is open access under a CC BY license

Security of Ubiquitous Computing Systems

The chapters in this open access book arise out of the EU Cost Action project Cryptacus, the objective of which was to improve and adapt existent cryptanalysis methodologies and tools to the ubiquitous computing framework. The cryptanalysis implemented lies along four axes: cryptographic models, cryptanalysis of building blocks, hardware and software security engineering, and security assessment of real-world systems. The authors are top-class researchers in security and cryptography, and the contributions are of value to researchers and practitioners in these domains. This book is open access under a CC BY license