LPN-based Attacks in the White-box Setting

In white-box cryptography, early protection techniques have fallen to the automated Differential Computation Analysis attack (DCA), leading to new countermeasures and attacks. A standard side-channel countermeasure, Ishai-Sahai-Wagner\u27s masking scheme (ISW, CRYPTO 2003) prevents Differential Computation Analysis but was shown to be vulnerable in the white-box context to the Linear Decoding Analysis attack (LDA). However, recent quadratic and cubic masking schemes by Biryukov-Udovenko (ASIACRYPT 2018) and Seker-Eisenbarth-Liskiewicz (CHES 2021) prevent LDA and force to use its higher-degree generalizations with much higher complexity. In this work, we study the relationship between the security of these and related schemes to the Learning Parity with Noise (LPN) problem and propose a new automated attack by applying an LPN-solving algorithm to white-box implementations. The attack effectively exploits strong linear approximations of the masking scheme and thus can be seen as a combination of the DCA and LDA techniques. Different from previous attacks, the complexity of this algorithm depends on the approximation error, henceforth allowing new practical attacks on masking schemes that previously resisted automated analysis. We demonstrate it theoretically and experimentally, exposing multiple cases where the LPN-based method significantly outperforms LDA and DCA methods, including their higher-order variants. This work applies the LPN problem beyond its usual post-quantum cryptography boundary, strengthening its interest in the cryptographic community, while expanding the range of automated attacks by presenting a new direction for breaking masking schemes in the white-box model

LPN-based Attacks in the White-box Setting

peer reviewedIn white-box cryptography, early protection techniques have fallen to the automated Differential Computation Analysis attack (DCA), leading to new countermeasures and attacks. A standard side-channel countermeasure, Ishai-Sahai-Wagner’s masking scheme (ISW, CRYPTO 2003) prevents Differential Computation Analysis but was shown to be vulnerable in the white-box context to the Linear Decoding Analysis attack (LDA). However, recent quadratic and cubic masking schemes by Biryukov-Udovenko (ASIACRYPT 2018) and Seker-Eisenbarth-Liskiewicz (CHES 2021) prevent LDA and force to use its higher-degree generalizations with much higher complexity. In this work, we study the relationship between the security of these and related schemes to the Learning Parity with Noise (LPN) problem and propose a new automated attack by applying an LPN-solving algorithm to white-box implementations. The attack effectively exploits strong linear approximations of the masking scheme and thus can be seen as a combination of the DCA and LDA techniques. Different from previous attacks, the complexity of this algorithm depends on the approximation error, henceforth allowing new practical attacks on masking schemes which previously resisted automated analysis. We demonstrate it theoretically and experimentally, exposing multiple cases where the LPN-based method significantly outperforms LDA and DCA methods, including their higher-order variants. This work applies the LPN problem beyond its usual post-quantum cryptography boundary, strengthening its interest for the cryptographic community, while expanding the range of automated attacks by presenting a new direction for breaking masking schemes in the white-box model.R-AGR-3748 - C19/IS/13641232/APLICA (01/09/2020 - 30/08/2022) - BIRYUKOV Alexe

Higher-Order DCA Attacks on White-Box Implementations with Masking and Shuffling Countermeasures

On white-box implementations, it has been proven that differential computation analysis (DCA) can recover secret keys without time-costly reverse engineering. At CHES 2021, Seker et al. combined linear and non-linear masking protections (SEL masking) to prevent sensitive variables from being predicted by DCA. At Eurocrypt 2021, Biryukov and Udovenko introduced a public dummy shuffling construction (BU shuffling) to protect sensitive functions. In this paper, we extend higher-order DCA (HO-DCA) to higher-degree context for exploiting the vulnerabilities against the state-of-the-art countermeasures. The data-dependency HO-DCA (DDHO-DCA), which is proposed at CHES 2020, is improved to successfully recover the correct key of SEL masking. In specific, our improved DDHO-DCA can also enhance the attack result of #100 which is the third winning challenge in WhibOx 2019. Since the XOR phase plays the same role as linear masking, we prove that a specific BU shuffling is vulnerable to HO-DCA attacks. Furthermore, we demonstrate that the combination of SEL masking and the specific BU shuffling still cannot defeat our higher-degree HO-DCA and improved DDHO-DCA attacks

Resisting Key-Extraction and Code-Compression: a Secure Implementation of the HFE Signature Scheme in the White-Box Model

Cryptography is increasingly deployed in applications running on open devices in which the software is extremely vulnerable to attacks, since the attacker has complete control over the execution platform and the software implementation itself. This creates a challenge for cryptography: design implementations of cryptographic algorithms that are secure, not only in the black-box model, but also in this attack context that is referred to as the white-box adversary model. Moreover, emerging applications such as mobile payment, mobile contract signing or blockchain-based technologies have created a need for white-box implementations of public-key cryptography, and especially of signature algorithms. However, while many attempts were made to construct white-box implementations of block-ciphers, almost no white-box implementations have been published for what concerns asymmetric schemes. We present here a concrete white-box implementation of the well-known HFE signature algorithm for a specific set of internal polynomials. For a security level $2^{80}$, the public key size is approximately 62.5 MB and the white-box implementation of the signature algorithm has a size approximately 256 GB

ECDSA White-Box Implementations: Attacks and Designs from CHES 2021 Challenge

Despite the growing demand for software implementations of ECDSA secure against attackers with full control of the execution environment, scientific literature on ECDSA white-box design is scarce. The CHES 2021 WhibOx contest was thus held to assess the state-of-the-art and encourage relevant practical research, inviting developers to submit ECDSA white-box implementations and attackers to break the corresponding submissions. In this work, attackers (team TheRealIdefix) and designers (team zerokey) join to describe several attack techniques and designs used during this contest. We explain the methods used by the team TheRealIdefix, which broke the most challenges, and we show the efficiency of each of these methods against all the submitted implementations. Moreover, we describe the designs of the two winning challenges submitted by the team zerokey; these designs represent the ECDSA signature algorithm by a sequence of systems of low-degree equations, which are obfuscated with affine encodings and extra random variables and equations. The WhibOx contest has shown that securing ECDSA in the white-box model is an open and challenging problem, as no implementation survived more than two days. In this context, our designs provide a starting methodology for further research, and our attacks highlight the weak points future work should address

Some Notes on Code-Based Cryptography

This thesis presents new cryptanalytic results in several areas of coding-based cryptography. In addition, we also investigate the possibility of using convolutional codes in code-based public-key cryptography. The first algorithm that we present is an information-set decoding algorithm, aiming towards the problem of decoding random linear codes. We apply the generalized birthday technique to information-set decoding, improving the computational complexity over previous approaches. Next, we present a new version of the McEliece public-key cryptosystem based on convolutional codes. The original construction uses Goppa codes, which is an algebraic code family admitting a well-defined code structure. In the two constructions proposed, large parts of randomly generated parity checks are used. By increasing the entropy of the generator matrix, this presumably makes structured attacks more difficult. Following this, we analyze a McEliece variant based on quasi-cylic MDPC codes. We show that when the underlying code construction has an even dimension, the system is susceptible to, what we call, a squaring attack. Our results show that the new squaring attack allows for great complexity improvements over previous attacks on this particular McEliece construction. Then, we introduce two new techniques for finding low-weight polynomial multiples. Firstly, we propose a general technique based on a reduction to the minimum-distance problem in coding, which increases the multiplicity of the low-weight codeword by extending the code. We use this algorithm to break some of the instances used by the TCHo cryptosystem. Secondly, we propose an algorithm for finding weight-4 polynomials. By using the generalized birthday technique in conjunction with increasing the multiplicity of the low-weight polynomial multiple, we obtain a much better complexity than previously known algorithms. Lastly, two new algorithms for the learning parities with noise (LPN) problem are proposed. The first one is a general algorithm, applicable to any instance of LPN. The algorithm performs favorably compared to previously known algorithms, breaking the 80-bit security of the widely used (512,1/8) instance. The second one focuses on LPN instances over a polynomial ring, when the generator polynomial is reducible. Using the algorithm, we break an 80-bit security instance of the Lapin cryptosystem

Entropy in Image Analysis II

Image analysis is a fundamental task for any application where extracting information from images is required. The analysis requires highly sophisticated numerical and analytical methods, particularly for those applications in medicine, security, and other fields where the results of the processing consist of data of vital importance. This fact is evident from all the articles composing the Special Issue "Entropy in Image Analysis II", in which the authors used widely tested methods to verify their results. In the process of reading the present volume, the reader will appreciate the richness of their methods and applications, in particular for medical imaging and image security, and a remarkable cross-fertilization among the proposed research areas

A Network-based Asynchronous Architecture for Cryptographic Devices

Institute for Computing Systems ArchitectureThe traditional model of cryptography examines the security of the cipher as a mathematical function. However, ciphers that are secure when specified as mathematical functions are not necessarily secure in real-world implementations. The physical implementations of ciphers can be extremely difficult to control and often leak socalled side-channel information. Side-channel cryptanalysis attacks have shown to be especially effective as a practical means for attacking implementations of cryptographic algorithms on simple hardware platforms, such as smart-cards. Adversaries can obtain sensitive information from side-channels, such as the timing of operations, power consumption and electromagnetic emissions. Some of the attack techniques require surprisingly little side-channel information to break some of the best known ciphers. In constrained devices, such as smart-cards, straightforward implementations of cryptographic algorithms can be broken with minimal work. Preventing these attacks has become an active and a challenging area of research. Power analysis is a successful cryptanalytic technique that extracts secret information from cryptographic devices by analysing the power consumed during their operation. A particularly dangerous class of power analysis, differential power analysis (DPA), relies on the correlation of power consumption measurements. It has been proposed that adding non-determinism to the execution of the cryptographic device would reduce the danger of these attacks. It has also been demonstrated that asynchronous logic has advantages for security-sensitive applications. This thesis investigates the security and performance advantages of using a network-based asynchronous architecture, in which the functional units of the datapath form a network. Non-deterministic execution is achieved by exploiting concurrent execution of instructions both with and without data-dependencies; and by forwarding register values between instructions with data-dependencies using randomised routing over the network. The executions of cryptographic algorithms on different architectural configurations are simulated, and the obtained power traces are subjected to DPA attacks. The results show that the proposed architecture introduces a level of non-determinism in the execution that significantly raises the threshold for DPA attacks to succeed. In addition, the performance analysis shows that the improved security does not degrade performance

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