Fault attacks on RSA and elliptic curve cryptosystems

This thesis answered how a fault attack targeting software used to program EEPROM can threaten hardware devices, for instance IoT devices. The successful fault attacks proposed in this thesis will certainly warn designers of hardware devices of the security risks their devices may face on the programming leve

Formal Analysis of CRT-RSA Vigilant's Countermeasure Against the BellCoRe Attack: A Pledge for Formal Methods in the Field of Implementation Security

In our paper at PROOFS 2013, we formally studied a few known countermeasures to protect CRT-RSA against the BellCoRe fault injection attack. However, we left Vigilant's countermeasure and its alleged repaired version by Coron et al. as future work, because the arithmetical framework of our tool was not sufficiently powerful. In this paper we bridge this gap and then use the same methodology to formally study both versions of the countermeasure. We obtain surprising results, which we believe demonstrate the importance of formal analysis in the field of implementation security. Indeed, the original version of Vigilant's countermeasure is actually broken, but not as much as Coron et al. thought it was. As a consequence, the repaired version they proposed can be simplified. It can actually be simplified even further as two of the nine modular verifications happen to be unnecessary. Fortunately, we could formally prove the simplified repaired version to be resistant to the BellCoRe attack, which was considered a "challenging issue" by the authors of the countermeasure themselves.Comment: arXiv admin note: substantial text overlap with arXiv:1401.817

Secure Cryptographic Algorithm Implementation on Embedded Platforms

Sensitive systems that are based on smart cards use well-studied and well-developed cryptosystems. Generally these cryptosystems have been subject to rigorous mathematical analysis in an effort to uncover cryptographic weaknesses in the system. The cryptosystems used in smart cards are, therefore, not usually vulnerable to these types of attacks. Since smart cards are small objects that can be easily placed in an environment where physical vulnerabilities can be exploited, adversaries have turned to different avenues of attack. This thesis describes the current state-of-the-art in side channel and fault analysis against smart cards, and the countermeasures necessary to provide a secure implementation. Both attack techniques need to be taken into consideration when implementing cryptographic algorithms in smart cards. In the domain of side-channel analysis a new application of using cache accesses to attack an implementation of AES by observing the power consumption is described, including an unpublished extension. Several new fault attacks are proposed based on finding collisions between a correct and a fault-induced execution of a secure secret algorithm. Other new fault attacks include reducing the number of rounds of an algorithm to make a differential cryptanalysis trivial, and fixing portions of the random value used in DSA to allow key recovery. Countermeasures are proposed for all the attacks described. The use of random delays, a simple countermeasure, is improved to render it more secure and less costly to implement. Several new countermeasures are proposed to counteract the particular fault attacks proposed in this thesis. A new method of calculating a modular exponentiation that is secure against side channel analysis is described, based on ideas which have been proposed previously or are known within the smart card industry. A novel method for protecting RSA against fault attacks is also proposed based on securing the underlying Montgomery multiplication. The majority of the fault attacks detailed have been implemented against actual chips to demonstrate the feasibility of these attacks. Details of these experiments are given in appendices. The experiments conducted to optimise the performance of random delays are also described in an appendix

Méthodes logicielles formelles pour la sécurité des implémentations cryptographiques

Implementations of cryptosystems are vulnerable to physical attacks, and thus need to be protected against them.Of course, malfunctioning protections are useless.Formal methods help to develop systems while assessing their conformity to a rigorous specification.The first goal of my thesis, and its innovative aspect, is to show that formal methods can be used to prove not only the principle of the countermeasures according to a model,but also their implementations, as it is where the physical vulnerabilities are exploited.My second goal is the proof and the automation of the protection techniques themselves, because handwritten security code is error-prone.Les implémentations cryptographiques sont vulnérables aux attaques physiques, et ont donc besoin d'en être protégées.Bien sûr, des protections défectueuses sont inutiles.L'utilisation des méthodes formelles permet de développer des systèmes tout en garantissant leur conformité à des spécifications données.Le premier objectif de ma thèse, et son aspect novateur, est de montrer que les méthodes formelles peuvent être utilisées pour prouver non seulement les principes des contre-mesures dans le cadre d'un modèle, mais aussi leurs implémentations, étant donné que c'est là que les vulnérabilités physiques sont exploitées.Mon second objectif est la preuve et l'automatisation des techniques de protection elles-même, car l'écriture manuelle de code est sujette à de nombreuses erreurs, particulièrement lorsqu'il s'agit de code de sécurité

Tamper-Resistant Arithmetic for Public-Key Cryptography

Cryptographic hardware has found many uses in many ubiquitous and pervasive security devices with a small form factor, e.g. SIM cards, smart cards, electronic security tokens, and soon even RFIDs. With applications in banking, telecommunication, healthcare, e-commerce and entertainment, these devices use cryptography to provide security services like authentication, identification and confidentiality to the user. However, the widespread adoption of these devices into the mass market, and the lack of a physical security perimeter have increased the risk of theft, reverse engineering, and cloning. Despite the use of strong cryptographic algorithms, these devices often succumb to powerful side-channel attacks. These attacks provide a motivated third party with access to the inner workings of the device and therefore the opportunity to circumvent the protection of the cryptographic envelope. Apart from passive side-channel analysis, which has been the subject of intense research for over a decade, active tampering attacks like fault analysis have recently gained increased attention from the academic and industrial research community. In this dissertation we address the question of how to protect cryptographic devices against this kind of attacks. More specifically, we focus our attention on public key algorithms like elliptic curve cryptography and their underlying arithmetic structure. In our research we address challenges such as the cost of implementation, the level of protection, and the error model in an adversarial situation. The approaches that we investigated all apply concepts from coding theory, in particular the theory of cyclic codes. This seems intuitive, since both public key cryptography and cyclic codes share finite field arithmetic as a common foundation. The major contributions of our research are (a) a generalization of cyclic codes that allow embedding of finite fields into redundant rings under a ring homomorphism, (b) a new family of non-linear arithmetic residue codes with very high error detection probability, (c) a set of new low-cost arithmetic primitives for optimal extension field arithmetic based on robust codes, and (d) design techniques for tamper resilient finite state machines

Passive SSH Key Compromise via Lattices

We demonstrate that a passive network attacker can opportunistically obtain private RSA host keys from an SSH server that experiences a naturally arising fault during signature computation. In prior work, this was not believed to be possible for the SSH protocol because the signature included information like the shared Diffie-Hellman secret that would not be available to a passive network observer. We show that for the signature parameters commonly in use for SSH, there is an efficient lattice attack to recover the private key in case of a signature fault. We provide a security analysis of the SSH, IKEv1, and IKEv2 protocols in this scenario, and use our attack to discover hundreds of compromised keys in the wild from several independently vulnerable implementations

Fault Attack revealing Secret Keys of Exponentiation Algorithms from Branch Prediction Misses

Performance monitors are provided in modern day computers for observing various features of the underlying microarchitectures. However the combination of underlying micro-architectural features and performance counters lead to side-channels which can be exploited for attacking cipher implementations. In this paper, to the best of our knowledge we study for the first time, the combination of branch-predictor algorithms and performance counters to demonstrate a fault attack on the popular square-and-multiply based exponentiation algorithm, used in the RSA. The attacks exploiting branching event like branch taken can be foiled by Montgomery Ladder based implementation of the exponentiation algorithm, while attacks based on branch miss are more devastating. We demonstrate the power of the attack exploiting branch misses from performance monitors by formalizing a fault attack model, where the adversary is capable of performing a bit flip at a desired bit position of the secret exponent. The paper characterizes the branch predictors using the popular two-bit predictor and formulates the dependence on the number of branch misses on the fault induced. This characterization is exploited to develop an iterative attack algorithm where knowledge of the previously determined key-bits and the difference of branch misses (as gathered from the performance counters) are utilised to determine the next bit. The attack has been validated on several standard Intel platforms, and puts to threat several implementations of exponentiation algorithms ranging from standard square-and-multiply, Montgomery Ladder to RSA-CRT and which are often used as side-channel counter measures. The attacks show that using the fault attack model featuring branch predictors one can attack implementations of exponentiation: both square and multiply, and Montgomery ladder, which forms the central algorithm for several standard public key ciphers

Cross-core Microarchitectural Attacks and Countermeasures

In the last decade, multi-threaded systems and resource sharing have brought a number of technologies that facilitate our daily tasks in a way we never imagined. Among others, cloud computing has emerged to offer us powerful computational resources without having to physically acquire and install them, while smartphones have almost acquired the same importance desktop computers had a decade ago. This has only been possible thanks to the ever evolving performance optimization improvements made to modern microarchitectures that efficiently manage concurrent usage of hardware resources. One of the aforementioned optimizations is the usage of shared Last Level Caches (LLCs) to balance different CPU core loads and to maintain coherency between shared memory blocks utilized by different cores. The latter for instance has enabled concurrent execution of several processes in low RAM devices such as smartphones. Although efficient hardware resource sharing has become the de-facto model for several modern technologies, it also poses a major concern with respect to security. Some of the concurrently executed co-resident processes might in fact be malicious and try to take advantage of hardware proximity. New technologies usually claim to be secure by implementing sandboxing techniques and executing processes in isolated software environments, called Virtual Machines (VMs). However, the design of these isolated environments aims at preventing pure software- based attacks and usually does not consider hardware leakages. In fact, the malicious utilization of hardware resources as covert channels might have severe consequences to the privacy of the customers. Our work demonstrates that malicious customers of such technologies can utilize the LLC as the covert channel to obtain sensitive information from a co-resident victim. We show that the LLC is an attractive resource to be targeted by attackers, as it offers high resolution and, unlike previous microarchitectural attacks, does not require core-colocation. Particularly concerning are the cases in which cryptography is compromised, as it is the main component of every security solution. In this sense, the presented work does not only introduce three attack variants that can be applicable in different scenarios, but also demonstrates the ability to recover cryptographic keys (e.g. AES and RSA) and TLS session messages across VMs, bypassing sandboxing techniques. Finally, two countermeasures to prevent microarchitectural attacks in general and LLC attacks in particular from retrieving fine- grain information are presented. Unlike previously proposed countermeasures, ours do not add permanent overheads in the system but can be utilized as preemptive defenses. The first identifies leakages in cryptographic software that can potentially lead to key extraction, and thus, can be utilized by cryptographic code designers to ensure the sanity of their libraries before deployment. The second detects microarchitectural attacks embedded into innocent-looking binaries, preventing them from being posted in official application repositories that usually have the full trust of the customer

Sécurité physique de la cryptographie sur courbes elliptiques

Elliptic Curve Cryptography (ECC) has gained much importance in smart cards because of its higher speed and lower memory needs compared with other asymmetric cryptosystems such as RSA. ECC is believed to be unbreakable in the black box model, where the cryptanalyst has access to inputs and outputs only. However, it is not enough if the cryptosystem is embedded on a device that is physically accessible to potential attackers. In addition to inputs and outputs, the attacker can study the physical behaviour of the device. This new kind of cryptanalysis is called Physical Cryptanalysis. This thesis focuses on physical cryptanalysis of ECC. The first part gives the background on ECC. From the lowest to the highest level, ECC involves a hierarchy of tools: Finite Field Arithmetic, Elliptic Curve Arithmetic, Elliptic Curve Scalar Multiplication and Cryptographie Protocol. The second part exhibits a state-of-the-art of the different physical attacks and countermeasures on ECC.For each attack, the context on which it can be applied is given while, for each countermeasure, we estimate the lime and memory cost. We propose new attacks and new countermeasures. We then give a clear synthesis of the attacks depending on the context. This is useful during the task of selecting the countermeasures. Finally, we give a clear synthesis of the efficiency of each countermeasure against the attacks.La Cryptographie sur les Courbes Elliptiques (abréviée ECC de l'anglais Elliptic Curve Cryptography) est devenue très importante dans les cartes à puces car elle présente de meilleures performances en temps et en mémoire comparée à d'autres cryptosystèmes asymétriques comme RSA. ECC est présumé incassable dans le modèle dit « Boite Noire », où le cryptanalyste a uniquement accès aux entrées et aux sorties. Cependant, ce n'est pas suffisant si le cryptosystème est embarqué dans un appareil qui est physiquement accessible à de potentiels attaquants. En plus des entrés et des sorties, l'attaquant peut étudier le comportement physique de l'appareil. Ce nouveau type de cryptanalyse est appelé cryptanalyse physique. Cette thèse porte sur les attaques physiques sur ECC. La première partie fournit les pré-requis sur ECC. Du niveau le plus bas au plus élevé, ECC nécessite les outils suivants : l'arithmétique sur les corps finis, l'arithmétique sur courbes elliptiques, la multiplication scalaire sur courbes elliptiques et enfin les protocoles cryptographiques. La deuxième partie expose un état de l'art des différentes attaques physiques et contremesures sur ECC. Pour chaque attaque, nous donnons le contexte dans lequel elle est applicable. Pour chaque contremesure, nous estimons son coût en temps et en mémoire. Nous proposons de nouvelles attaques et de nouvelles contremesures. Ensuite, nous donnons une synthèse claire des attaques suivant le contexte. Cette synthèse est utile pendant la tâche du choix des contremesures. Enfin, une synthèse claire de l'efficacité de chaque contremesure sur les attaques est donnée