Single-trace Attacks Research Articles

Single trace HQC shared key recovery with SASCA

This paper presents practicable single trace attacks against the Hamming Quasi-Cyclic (HQC) Key Encapsulation Mechanism. These attacks are the first Soft Analytical Side-Channel Attacks (SASCA) against code-based cryptography. We mount SASCA based on Belief Propagation (BP) on several steps of HQC’s decapsulation process. Firstly, we target the Reed-Solomon (RS) decoder involved in the HQC publicly known code. We perform simulated attacks under Hamming weight leakage model, and reach excellent accuracies (superior to 0.9) up to a high noise level (σ = 3), thanks to a re-decoding strategy. In a real case attack scenario, on a STM32F407, this attack leads to a perfect success rate. Secondly, we conduct an analogous attack against the RS encoder used during the re-encryption step required by the Fujisaki-Okamoto-like transform. Both in simulation and practical instances, results are satisfactory and this attack represents a threat to the security of HQC. Finally, we analyze the strength of countermeasures based on masking and shuffling strategies. In line with previous SASCA literature targeting Kyber, we show that masking HQC is a limited countermeasure against BP attacks, as well as shuffling countermeasures adapted from Kyber. We evaluate the “full shuffling” strategy which thwarts our attack by introducing sufficient combinatorial complexity. Eventually, we highlight the difficulty of protecting the current RS encoder with a shuffling strategy. A possible countermeasure would be to consider another encoding algorithm for the scheme to support a full shuffling. Since the encoding subroutine is only a small part of the implementation, it would come at a small cost.

Quantum Circuit Reconstruction from Power Side-Channel Attacks on Quantum Computer Controllers

The interest in quantum computing has grown rapidly in recent years, and with it grows the importance of securing quantum circuits. A novel type of threat to quantum circuits that dedicated attackers could launch are power trace attacks. To address this threat, this paper presents first formalization and demonstration of using power traces to unlock and steal quantum circuit secrets. With access to power traces, attackers can recover information about the control pulses sent to quantum computers. From the control pulses, the gate level description of the circuits, and eventually the secret algorithms can be reverse engineered. This work demonstrates how and what information could be recovered. This work uses algebraic reconstruction from power traces to realize two new types of single trace attacks: per-channel and total power attacks. The former attack relies on per-channel measurements to perform a brute-force attack to reconstruct the quantum circuits. The latter attack performs a single-trace attack using Mixed-Integer Linear Programming optimization. Through the use of algebraic reconstruction, this work demonstrates that quantum circuit secrets can be stolen with high accuracy. Evaluation on 32 real benchmark quantum circuits shows that our technique is highly effective at reconstructing quantum circuits. The findings not only show the veracity of the potential attacks, but also the need to develop new means to protect quantum circuits from power trace attacks. Throughout this work real control pulse information from real quantum computers is used to demonstrate potential attacks based on simulation of collection of power traces.

Advantages of unsupervised learning analysis methods in single-trace SCA attacks

Machine learning techniques are commonly employed in the context of Side Channel Analysis attacks. The clustering algorithms can be successfully used as classifiers in single execution attacks against implementations of Elliptic Curve point multiplication known as kP operation. They can distinguish between the processing of ‘ones’ and ‘zeros’ during secret scalar processing in the binary kP algorithm. The successful SCA performed by designers can aid in recognizing the leakage sources in cryptographic designs and lead to improvement of the cryptographic implementations. In this work we investigate the influence of the hamming weight of scalar k on the success rate of the single-trace attack. We used the clustering method K-means and the statistical method the comparison to the mean. We analysed simulated power traces and power traces of an FPGA implementation to conclude that K-means, unlike the comparison to the mean, was able to deal with extracting the scalar even when it is consisted of less than 30% of ‘ones’ and more than 70% of ‘ones’.

Single-Trace Side-Channel Attacks on the Toom-Cook: The Case Study of Saber

The Toom-Cook method is a well-known strategy for building algorithms to multiply polynomials efficiently. Along with NTT-based polynomial multiplication, Toom-Cook-based or Karatsuba-based polynomial multiplication algorithms still have regained attention since the start of the NIST’s post-quantum standardization procedure. Compared to the comprehensive analysis done for NTT, the leakage characteristics of Toom-Cook have not been discussed. We analyze the vulnerabilities of Toom-Cook in the reference implementation of Saber, a third round finalist of NIST’s post-quantum standardization process. In this work, we present the first single-trace attack based on the soft-analytical side-channel attack (SASCA) targeting the Toom-Cook. The deep learning-based power analysis is combined with SASCA to decrease the number of templates since there are a large number of similar operations in the Toom-Cook. Moreover, we describe the optimized factor graph and improved belief propagation to make the attack more practical. The feasibility of the attack is verified by evaluation experiments. We also discuss the possible countermeasures to prevent the attack.

Atomicity and Regularity Principles Do Not Ensure Full Resistance of ECC Designs against Single-Trace Attacks.

Elliptic curve cryptography (ECC) is one of the commonly used standard methods for encrypting and signing messages which is especially applicable to resource-constrained devices such as sensor nodes that are networked in the Internet of Things. The same holds true for wearable sensors. In these fields of application, confidentiality and data integrity are of utmost importance as human lives depend on them. In this paper, we discuss the resistance of our fast dual-field ECDSA accelerator against side-channel analysis attacks. We present our implementation of a design supporting four different NIST elliptic curves to allow the reader to understand the discussion of the resistance aspects. For two different target platforms—ASIC and FPGA—we show that the application of atomic patterns, which is considered to ensure resistance against simple side-channel analysis attacks in the literature, is not sufficient to prevent either simple SCA or horizontal address-bit DPA attacks. We also evaluated an approach which is based on the activity of the field multiplier to increase the inherent resistance of the design against attacks performed.

Single-Trace Attack Using One-Shot Learning With Siamese Network in Non-Profiled Setting

Recently, many studies have shown that using deep learning for side-channel attacks offers several advantages, including simplification of the attack phase and target breaking, even in protected implementations, while presenting outstanding attack performance. Power and electromagnetic analysis, which is known as the most robust attack, can be classified into profiling and non-profiling attacks. In the real world, a non-profiling attack is more ideal than a profiling attack. In particular, studies on non-profiling attacks using deep learning for asymmetric cryptosystems are rare and have shortcomings, such as a long analysis time. In this paper, we propose a novel non-profiling attack method for asymmetric cryptosystems that requires only a single trace and a reasonably short attack time to recover a full private key, overcoming the limitations of previous studies. The proposed method applies one-shot learning with a convolutional Siamese network, which is used for the first time in side-channel attacks. Thus, our proposed method can leak private keys used in a protected public-key cryptosystem with up to 100% accuracy with only one single trace in a non-profiled setting.

Horizontal Side-Channel Vulnerabilities of Post-Quantum Key Exchange and Encapsulation Protocols

Key exchange protocols and key encapsulation mechanisms establish secret keys to communicate digital information confidentially over public channels. Lattice-based cryptography variants of these protocols are promising alternatives given their quantum-cryptanalysis resistance and implementation efficiency. Although lattice cryptosystems can be mathematically secure, their implementations have shown side-channel vulnerabilities. But such attacks largely presume collecting multiple measurements under a fixed key, leaving the more dangerous single-trace attacks unexplored. This article demonstrates successful single-trace power side-channel attacks on lattice-based key exchange and encapsulation protocols. Our attack targets both hardware and software implementations of matrix multiplications used in lattice cryptosystems. The crux of our idea is to apply a horizontal attack that makes hypotheses on several intermediate values within a single execution all relating to the same secret, and to combine their correlations for accurately estimating the secret key. We illustrate that the design of protocols combined with the nature of lattice arithmetic enables our attack. Since a straightforward attack suffers from false positives, we demonstrate a novel extend-and-prune procedure to recover the key by following the sequence of intermediate updates during multiplication. We analyzed two protocols, Frodo and FrodoKEM , and reveal that they are vulnerable to our attack. We implement both stand-alone hardware and RISC-V based software realizations and test the effectiveness of the proposed attack by using concrete parameters of these protocols on physical platforms with real measurements. We show that the proposed attack can estimate secret keys from a single power measurement with over 99% success rate.

EM-X-DL: Efficient Cross-device Deep Learning Side-channel Attack With Noisy EM Signatures

This work presents a Cross-device Deep-Learning based Electromagnetic (EM-X-DL) side-channel analysis (SCA) on AES-128, in the presence of a significantly lower signal-to-noise ratio (SNR) compared to previous works. Using a novel algorithm to intelligently select multiple training devices and proper choice of hyperparameters, the proposed 256-class deep neural network (DNN) can be trained efficiently utilizing pre-processing techniques like PCA, LDA, and FFT on measurements from the target encryption engine running on an 8-bit Atmel microcontroller. In this way, EM-X-DL achieves >90% single-trace attack accuracy. Finally, an efficient end-to-end SCA leakage detection and attack framework using EM-X-DL demonstrates high confidence of an attacker with <20 averaged EM traces.

Chosen Ciphertext k-Trace Attacks on Masked CCA2 Secure Kyber

Single-trace attacks are a considerable threat to implementations of classic public-key schemes, and their implications on newer lattice-based schemes are still not well understood. Two recent works have presented successful single-trace attacks targeting the Number Theoretic Transform (NTT), which is at the heart of many lattice-based schemes. However, these attacks either require a quite powerful side-channel adversary or are restricted to specific scenarios such as the encryption of ephemeral secrets. It is still an open question if such attacks can be performed by simpler adversaries while targeting more common public-key scenarios. In this paper, we answer this question positively. First, we present a method for crafting ring/module-LWE ciphertexts that result in sparse polynomials at the input of inverse NTT computations, independent of the used private key. We then demonstrate how this sparseness can be incorporated into a side-channel attack, thereby significantly improving noise resistance of the attack compared to previous works. The effectiveness of our attack is shown on the use-case of CCA2 secure Kyber k-module-LWE, where k ∈ {2, 3, 4}. Our k-trace attack on the long-term secret can handle noise up to a σ ≤ 1.2 in the noisy Hamming weight leakage model, also for masked implementations. A 2k-trace variant for Kyber1024 even allows noise σ ≤ 2.2 also in the masked case, with more traces allowing us to recover keys up to σ ≤ 2.7. Single-trace attack variants have a noise tolerance depending on the Kyber parameter set, ranging from σ ≤ 0.5 to σ ≤ 0.7. As a comparison, similar previous attacks in the masked setting were only successful with σ ≤ 0.5.

Keep it Unsupervised: Horizontal Attacks Meet Deep Learning

To mitigate side-channel attacks, real-world implementations of public-key cryptosystems adopt state-of-the-art countermeasures based on randomization of the private or ephemeral keys. Usually, for each private key operation, a “scalar blinding” is performed using 32 or 64 randomly generated bits. Nevertheless, horizontal attacks based on a single trace still pose serious threats to protected ECC or RSA implementations. If the secrets learned through a single-trace attack contain too many wrong (or noisy) bits, the cryptanalysis methods for recovering remaining bits become impractical due to time and computational constraints. This paper proposes a deep learning-based framework to iteratively correct partially correct private keys resulting from a clustering-based horizontal attack. By testing the trained network on scalar multiplication (or exponentiation) traces, we demonstrate that a deep neural network can significantly reduce the number of wrong bits from randomized scalars (or exponents).When a simple horizontal attack can recover around 52% of attacked multiple private key bits, the proposed iterative framework improves the private key accuracy to above 90% on average and to 100% for at least one of the attacked keys. Our attack model remains fully unsupervised and excludes the need to know where the error or noisy bits are located in each separate randomized private key.

2Deep: Enhancing Side-Channel Attacks on Lattice-Based Key-Exchange via 2-D Deep Learning

Advancements in quantum computing present a security threat to classical cryptography algorithms. Lattice-based key exchange protocols show strong promise due to their resistance to theoretical quantum-cryptanalysis and low implementation overhead. By contrast, their physical implementations have shown vulnerability against side-channel attacks (SCAs) even with a single power measurement. The state-of-the-art SCAs are, however, limited to simple, sequentialized executions of post-quantum key-exchange (PQKE) protocols, leaving the vulnerability of complex, parallelized architectures unknown. This article proposes 2Deep-a deep-learning (DL)-based SCA-targeting parallelized implementations of PQKE protocols, namely, Frodo and NewHope with data augmentation techniques. Specifically, we explore approaches that convert 1-D time-series power measurement data into 2-D images to formulate SCA an image recognition task. The results show our attack's superiority over conventional techniques including horizontal differential power analysis (DPA), template attacks (TAs), and straightforward DL approaches. We demonstrate improvements up to 1.5× to recover a 100% success rate compared to DL with 1-D input data while using fewer data. We furthermore show that machine learning improves the results up to 1.25× compared to TAs. Furthermore, we perform cross-device attacks that obtain profiles from a single device, which has never been explored. Our 2-D approach is especially favored in this setting, improving the success rate of attacking Frodo from 20% to 99% compared to the 1-D approach. Our work thus urges countermeasures even on parallel architectures and single-trace attacks.

Single-Trace Attacks on Keccak

Since its selection as the winner of the SHA-3 competition, Keccak, with all its variants, has found a large number of applications. It is, for instance, a common building block in schemes submitted to NIST’s post-quantum cryptography project. In many of these applications, Keccak processes ephemeral secrets. In such a setting, side-channel adversaries are limited to a single observation, meaning that differential attacks are inherently prevented. If, however, such a single trace of Keccak can already be sufficient for key recovery has so far been unknown. In this paper, we change the above by presenting the first single-trace attack targeting Keccak. Our method is based on soft-analytical side-channel attacks and, thus, combines template matching with message passing in a graphical model of the attacked algorithm. As a straight-forward model of Keccak does not yield satisfactory results, we describe several optimizations for the modeling and the message-passing algorithm. Their combination allows attaining high attack performance in terms of both success rate as well as computational runtime. We evaluate our attack assuming generic software (microcontroller) targets and thus use simulations in the generic noisy Hamming-weight leakage model. Hence, we assume relatively modest profiling capabilities of the adversary. Nonetheless, the attack can reliably recover secrets in a large number of evaluated scenarios at realistic noise levels. Consequently, we demonstrate the need for countermeasures even in settings where DPA is not a threat.

When one vulnerable primitive turns viral: Novel single-trace attacks on ECDSA and RSA

Microarchitecture based side-channel attacks are common threats nowadays. Intel SGX technology provides a strong isolation from an adversarial OS, however, does not guarantee protection against side-channel attacks. In this paper, we analyze the security of the mbedTLS binary GCD algorithm, an implementation that offers interesting challenges when compared for example with OpenSSL, due to the usage of very tight loops in the former. Using practical experiments we demonstrate the mbedTLS binary GCD implementation is vulnerable to side-channel analysis using the SGX-Step framework against mbedTLS based SGX enclaves.We analyze the security of some use cases of this algorithm in this library, resulting in the discovery of a new vulnerability in the ECDSA code path that allows a single-trace attack against this implementation. This vulnerability is three-fold interesting:
 
 It resides in the implementation of a countermeasure which makes it more dangerous due to the false state of security the countermeasure currently offers.
 It reduces mbedTLS ECDSA security to an integer factorization problem.
 An unexpected GCD call inside the ECDSA code path compromises the countermeasure.
 
 We also cover an orthogonal use case, this time inside the mbedTLS RSA code path during the computation of a CRT parameter when loading a private key. The attack also exploits the binary GCD implementation threat, showing how a single vulnerable primitive leads to multiple vulnerabilities. We demonstrate both security threats with end-to-end attacks using 1000 trials each, showing in both cases single-trace attacks can be achieved with success rates very close to 100%.

When one vulnerable primitive turns viral: Novel single-trace attacks on ECDSA and RSA

When one vulnerable primitive turns viral: Novel single-trace attacks on ECDSA and RSA

A Combined Single Trace Attack on Global Shuffling Long Integer Multiplication and its Novel Countermeasure

Advanced collision-based single trace attacks which can be applied on simple power analysis resistant scalar multiplications become virtual threat on elliptic curve cryptosystems recently as their practical experimental results are increasingly reported in the literature. Since such attacks are based on detecting collisions of data dependent leakage caused by underlying long integer multiplications, so-called global shuffling countermeasure which breaks such collision correlation by independently randomizing the execution order of unit operations such as single precision multiplication and carry propagation, is considered as promising countermeasure if theoretical randomness of shuffling order is guaranteed. In this paper, we firstly analyze the practical security of the global shuffling long integer multiplications by exhibiting a combined single trace attack on software implementations on an ARM Cortex-M4 microcontroller. Our combined attack consists of a simple power analysis for revealing random permutation vectors which enables later collision-based single trace attack. First we demonstrate how to reveal random permutation vectors for carry propagation process of whole global shuffling long integer multiplications within a single power trace by simple power analysis accompanied with straightforward substitution of power consumption samples. Then we perform collision-based single trace attacks after rearranging the order of subtraces for unit carry propagations based on revealed permutation vectors. Since the vulnerability to simple power analysis is originated from the if-statement for selection of proper entries of the permutation vectors, we propose a novel countermeasure which eliminates such selection with simple addition and modulus operation and also demonstrate practical result achieving regularity in power trace patterns.

Single-Trace Attacks on Message Encoding in Lattice-Based KEMs

In this article, we propose single-trace side-channel attacks against lattice-based key encapsulation mechanisms (KEMs) that are the third-round candidates of the national institute of standards and technology (NIST) standardization project. Specifically, we analyze the message encoding operation in the encapsulation phase of lattice-based KEMs to obtain an ephemeral session key. We conclude that a single-trace leakage implies a whole key recovery: the experimental results realized on a ChipWhisperer UFO STM32F3 target board achieve a success rate of 100% for $\mathsf {CRYSTALS-KYBER}$ and $\mathsf {SABER}$ regardless of an optimization level and those greater than 79% for $\mathsf {FrodoKEM}$ . We further demonstrate that the proposed attack methodologies are not restricted to the above algorithms but are widely applicable to other NIST post-quantum cryptography (PQC) candidates, including $\mathsf {NTRU Prime}$ and $\mathsf {NTRU}$ .

Novel Side-Channel Attacks on Quasi-Cyclic Code-Based Cryptography

Chou suggested a constant-time implementation for quasi-cyclic moderatedensity parity-check (QC-MDPC) code-based cryptography to mitigate timing attacks at CHES 2016. This countermeasure was later found to become vulnerable to a differential power analysis (DPA) in private syndrome computation, as described by Rossi et al. at CHES 2017. The proposed DPA, however, still could not completely recover accurate secret indices, requiring further solving linear equations to obtain entire secret information. In this paper, we propose a multiple-trace attack which enables to completely recover accurate secret indices. We further propose a singletrace attack which can even work when using ephemeral keys or applying Rossi et al.’s DPA countermeasures. Our experiments show that the BIKE and LEDAcrypt may become vulnerable to our proposed attacks. The experiments are conducted using power consumption traces measured from ChipWhisperer-Lite XMEGA (8-bit processor) and ChipWhisperer UFO STM32F3 (32-bit processor) target boards.

Single Trace Side Channel Analysis on NTRU Implementation

As researches on the quantum computer have progressed immensely, interests in post-quantum cryptography have greatly increased. NTRU is one of the well-known algorithms due to its practical key sizes and fast performance along with the resistance against the quantum adversary. Although NTRU has withstood various algebraic attacks, its side-channel resistance must also be considered for secure implementation. In this paper, we proposed the first single trace attack on NTRU. Previous side-channel attacks on NTRU used numerous power traces, which increase the attack complexity and limit the target algorithm. There are two versions of NTRU implementation published in succession. We demonstrated our attack on both implementations using a single power consumption trace obtained in the decryption phase. Furthermore, we propose a countermeasure to prevent the proposed attacks. Our countermeasure does not degrade in terms of performance.