Sécurité étendue de la cryptographie fondée sur les réseaux euclidiens

Lattice-based cryptography is considered as a quantum-safe alternative for the replacement of currently deployed schemes based on RSA and discrete logarithm on prime fields or elliptic curves. It offers strong theoretical security guarantees, a large array of achievable primitives, and a competitive level of efficiency. Nowadays, in the context of the NIST post-quantum standardization process, future standards may ultimately be chosen and several new lattice-based schemes are high-profile candidates. The cryptographic research has been encouraged to analyze lattice-based cryptosystems, with a particular focus on practical aspects. This thesis is rooted in this effort.In addition to black-box cryptanalysis with classical computing resources, we investigate the extended security of these new lattice-based cryptosystems, employing a broad spectrum of attack models, e.g. quantum, misuse, timing or physical attacks. Accounting that these models have already been applied to a large variety of pre-quantum asymmetric and symmetric schemes before, we concentrate our efforts on leveraging and addressing the new features introduced by lattice structures. Our contribution is twofold: defensive, i.e. countermeasures for implementations of lattice-based schemes and offensive, i.e. cryptanalysis.On the defensive side, in view of the numerous recent timing and physical attacks, we wear our designer’s hat and investigate algorithmic protections. We introduce some new algorithmic and mathematical tools to construct provable algorithmic countermeasures in order to systematically prevent all timing and physical attacks. We thus participate in the actual provable protection of the GLP, BLISS, qTesla and Falcon lattice-based signatures schemes.On the offensive side, we estimate the applicability and complexity of novel attacks leveraging the lack of perfect correctness introduced in certain lattice-based encryption schemes to improve their performance. We show that such a compromise may enable decryption failures attacks in a misuse or quantum model. We finally introduce an algorithmic cryptanalysis tool that assesses the security of the mathematical problem underlying lattice-based schemes when partial knowledge of the secret is available. The usefulness of this new framework is demonstrated with the improvement and automation of several known classical, decryption-failure, and side-channel attacks.La cryptographie fondée sur les réseaux euclidiens représente une alternative prometteuse à la cryptographie asymétrique utilisée actuellement, en raison de sa résistance présumée à un ordinateur quantique universel. Cette nouvelle famille de schémas asymétriques dispose de plusieurs atouts parmi lesquels de fortes garanties théoriques de sécurité, un large choix de primitives et, pour certains de ses représentants, des performances comparables aux standards actuels. Une campagne de standardisation post-quantique organisée par le NIST est en cours et plusieurs schémas utilisant des réseaux euclidiens font partie des favoris. La communauté scientifique a été encouragée à les analyser car ils pourraient à l’avenir être implantés dans tous nos systèmes. L’objectif de cette thèse est de contribuer à cet effort.Nous étudions la sécurité de ces nouveaux cryptosystèmes non seulement au sens de leur résistance à la cryptanalyse en “boîte noire” à l’aide de moyens de calcul classiques, mais aussi selon un spectre plus large de modèles de sécurité, comme les attaques quantiques, les attaques supposant des failles d’utilisation, ou encore les attaques par canaux auxiliaires. Ces différents types d’attaques ont déjà été largement formalisés et étudiés par le passé pour des schémas asymétriques et symétriques pré-quantiques. Dans ce mémoire, nous analysons leur application aux nouvelles structures induites par les réseaux euclidiens. Notre travail est divisé en deux parties complémentaires : les contremesures et les attaques.La première partie regroupe nos contributions à l’effort actuel de conception de nouvelles protections algorithmiques afin de répondre aux nombreuses publications récentes d’attaques par canaux auxiliaires. Les travaux réalisés en équipe auxquels nous avons pris part on abouti à l’introduction de nouveaux outils mathématiques pour construire des contre-mesures algorithmiques, appuyées sur des preuves formelles, qui permettent de prévenir systématiquement les attaques physiques et par analyse de temps d’exécution. Nous avons ainsi participé à la protection de plusieurs schémas de signature fondés sur les réseaux euclidiens comme GLP, BLISS, qTesla ou encore Falcon.Dans une seconde partie consacrée à la cryptanalyse, nous étudions dans un premier temps de nouvelles attaques qui tirent parti du fait que certains schémas de chiffrement à clé publique ou d’établissement de clé peuvent échouer avec une faible probabilité. Ces échecs sont effectivement faiblement corrélés au secret. Notre travail a permis d’exhiber des attaques dites « par échec de déchiffrement » dans des modèles de failles d’utilisation ou des modèles quantiques. Nous avons d’autre part introduit un outil algorithmique de cryptanalyse permettant d’estimer la sécurité du problème mathématique sous-jacent lorsqu’une information partielle sur le secret est donnée. Cet outil s’est avéré utile pour automatiser et améliorer plusieurs attaques connues comme des attaques par échec de déchiffrement, des attaques classiques ou encore des attaques par canaux auxiliaires

A provably masked implementation of BIKE Key Encapsulation Mechanism

BIKE is a post-quantum key encapsulation mechanism (KEM) selected for the 4th round of the NIST’s standardization campaign. It relies on the hardness of the syndrome decoding problem for quasi-cyclic codes and on the indistinguishability of the public key from a random element, and provides the most competitive performance among round 4 candidates, which makes it relevant for future real-world use cases. Analyzing its side-channel resistance has been highly encouraged by the community and several works have already outlined various side-channel weaknesses and proposed ad-hoc countermeasures. However, in contrast to the well-documented research line on masking lattice-based algorithms, the possibility of generically protecting code-based algorithms by masking has only been marginally studied in a 2016 paper by Cong Chen et al. At this stage of the standardization campaign, it is important to assess the possibility of fully masking BIKE scheme and the resulting cost in terms of performances. In this work, we provide the first high-order masked implementation of a code-based algorithm. We had to tackle many issues such as finding proper ways to handle large sparse polynomials, masking the key-generation algorithm or keeping the benefit of the bitslicing. In this paper, we present all the gadgets necessary to provide a fully masked implementation of BIKE, we discuss our different implementation choices and we propose a full proof of masking in the Ishai Sahai and Wagner (Crypto 2003) model. More practically, we also provide an open C-code masked implementation of the key-generation, encapsulation and decapsulation algorithms with extensive benchmarks. While the obtained performance is slower than existing masked lattice-based algorithms, the scaling in the masking order is still encouraging and no Boolean to Arithmetic conversion has been used. We hope that this work can be a starting point for future analysis and optimization

Mask Compression: High-Order Masking on Memory-Constrained Devices

Masking is a well-studied method for achieving provable security against side-channel attacks. In masking, each sensitive variable is split into $d$ randomized shares, and computations are performed with those shares. In addition to the computational overhead of masked arithmetic, masking also has a storage cost, increasing the requirements for working memory and secret key storage proportionally with $d$. In this work, we introduce mask compression. This conceptually simple technique is based on standard, non-masked symmetric cryptography. Mask compression allows an implementation to dynamically replace individual shares of large arithmetic objects (such as polynomial rings) with $\kappa$-bit cryptographic seeds (or temporary keys) when they are not in computational use. Since $\kappa$ does not need to be larger than the security parameter (e.g., $\kappa=256$ bits) and each polynomial share may be several kilobytes in size, this radically reduces the memory requirement of high-order masking. Overall provable security properties can be maintained by using appropriate gadgets to manage the compressed shares. We describe gadgets with Non-Inteference (NI) and composable Strong-Non Interference (SNI) security arguments. Mask compression can be applied in various settings, including symmetric cryptography, code-based cryptography, and lattice-based cryptography. It is especially useful for cryptographic primitives that allow quasilinear-complexity masking and hence are practically capable of very high masking orders. We illustrate this with a $d=32$ (Order-31) implementation of the recently introduced lattice-based signature scheme Raccoon on an FPGA platform with limited memory resources

On the Algebraic Immunity - Resiliency trade-off, implications for Goldreich\u27s Pseudorandom Generator

Goldreich\u27s pseudorandom generator is a well-known building block for many theoretical cryptographic constructions from multi-party computation to indistinguishability obfuscation. Its unique efficiency comes from the use of random local functions: each bit of the output is computed by applying some fixed public $n$-variable Boolean function $f$ to a random public size-$n$ tuple of distinct input bits. The characteristics that a Boolean function $f$ must have to ensure pseudorandomness is a puzzling issue. It has been studied in several works and particularly by Applebaum and Lovett (STOC 2016) who showed that resiliency and algebraic immunity are key parameters in this purpose. In this paper, we propose the first study on Boolean functions that reach together maximal algebraic immunity and high resiliency. 1) We assess the possible consequences of the asymptotic existence of such optimal functions. We show how they allow to build functions reaching all possible algebraic immunity-resiliency trade-offs (respecting the algebraic immunity and Siegenthaler bounds). We provide a new bound on the minimal number of variables~$n$, and thus on the minimal locality, necessary to ensure a secure Goldreich\u27s pseudorandom generator. Our results come with a granularity level depending on the strength of our assumptions, from none to the conjectured asymptotic existence of optimal functions. 2) We extensively analyze the possible existence and the properties of such optimal functions. Our results show two different trends. On the one hand, we were able to show some impossibility results concerning existing families of Boolean functions that are known to be optimal with respect to their algebraic immunity, starting by the promising XOR-MAJ functions. We show that they do not reach optimality and could be beaten by optimal functions if our conjecture is verified. On the other hand, we prove the existence of optimal functions in low number of variables by experimentally exhibiting some of them up to $12$ variables. This directly provides better candidates for Goldreich\u27s pseudorandom generator than the existing XOR-MAJ candidates for polynomial stretches from $2$ to $6$

A Side-Channel Assisted Cryptanalytic Attack Against QcBits

International audienceQcBits is a code-based public key algorithm based on a problem thought to be resistant to quantum computer attacks. It is a constant-time implementation for a quasi-cyclic moderate density parity check (QC-MDPC) Niederreiter encryption scheme, and has excellent performance and small key sizes. In this paper, we present a key recovery attack against QcBits. We first used differential power analysis (DPA) against the syndrome computation of the decoding algorithm to recover partial information about one half of the private key. We then used the recovered information to set up a system of noisy binary linear equations. Solving this system of equations gave us the entire key. Finally, we propose a simple but effective countermeasure against the power analysis used during the syndrome calculation

LWE with Side Information: Attacks and Concrete Security Estimation

We propose a framework for cryptanalysis of lattice-based schemes, when side information---in the form of ``hints\u27\u27--- about the secret and/or error is available. Our framework generalizes the so-called primal lattice reduction attack, and allows the progressive integration of hints before running a final lattice reduction step. Our techniques for integrating hints include sparsifying the lattice, projecting onto and intersecting with hyperplanes, and/or altering the distribution of the secret vector. Our main contribution is to propose a toolbox and a methodology to integrate such hints into lattice reduction attacks and to predict the performance of those lattice attacks with side information. While initially designed for side-channel information, our framework can also be used in other cases: exploiting decryption failures, or simply exploiting constraints imposed by certain schemes (LAC, Round5, NTRU). We implement a Sage 9.0 toolkit to actually mount such attacks with hints when computationally feasible, and to predict their performances on larger instances. We provide several end-to-end application examples, such as an improvement of a single trace attack on Frodo by Bos et al (SAC 2018). In particular, our work can estimates security loss even given very little side information, leading to a smooth measurement/computation trade-off for side-channel attacks

GeT a CAKE: Generic Transformations from Key Encaspulation Mechanisms to Password Authenticated Key Exchanges

Password Authenticated Key Exchange (PAKE) have become a key building block in many security products as they provide interesting efficiency/security trade-offs. Indeed, a PAKE allows to dispense with the heavy public key infrastructures and its efficiency and portability make it well suited for applications such as Internet of Things or e-passports. With the emerging quantum threat and the effervescent development of post-quantum public key algorithms in the last five years, one would wonder how to modify existing password authenticated key exchange protocols that currently rely on Diffie-Hellman problems in order to include newly introduced and soon-to-be-standardized post-quantum key encapsulation mechanisms (KEM). A generic solution is desirable for maintaining modularity and adaptability with the many post-quantum KEM that have been introduced. In this paper, we propose two new generic and natural constructions proven in the Universal Composability (UC) model to transform, in a black-box manner, a KEM into a PAKE with very limited performance overhead: one or two extra symmetric encryptions. Behind the simplicity of the designs, establishing security proofs in the UC model is actually non-trivial and requires some additional properties on the underlying KEM like fuzziness and anonymity. Luckily, post-quantum KEM protocols often enjoy these two extra properties. As a demonstration, we prove that it is possible to apply our transformations to Crystals-Kyber, a lattice-based post-quantum KEM that will soon be standardized by the National Institute of Standards and Technology (NIST). In a nutshell, this work opens up the possibility to securely include post-quantum cryptography in PAKE-based real-world protocols

Masking the GLP Lattice-Based Signature Scheme at Any Order

Recently, numerous physical attacks have been demonstrated against lattice-based schemes, often exploiting their unique properties such as the reliance on Gaussian distributions, rejection sampling and FFT-based polynomial multiplication. As the call for concrete implementations and deployment of postquantum cryptography becomes more pressing, protecting against those attacks is an important problem. However, few countermeasures have been proposed so far. In particular, masking has been applied to the decryption procedure of some lattice-based encryption schemes, but the much more difficult case of signatures (which are highly non-linear and typically involve randomness) has not been considered until now. In this paper, we describe the first masked implementation of a lattice-based signature scheme. Since masking Gaussian sampling and other procedures involving contrived probability distribution would be prohibitively inefficient, we focus on the GLP scheme of Güneysu, Lyubashevsky and Pöppelmann (CHES 2012). We show how to provably mask it in the Ishai--Sahai--Wagner model (CRYPTO 2003) at any order in a relatively efficient manner, using extensions of the techniques of Coron et al for converting between arithmetic and Boolean masking. Our proof relies on a mild generalization of probing security that supports the notion of public outputs. We also provide a proof-of-concept implementation to assess the efficiency of the proposed countermeasure

Sécurité étendue de la cryptographie fondée sur les réseaux euclidiens

Lattice-based cryptography is considered as a quantum-safe alternative for the replacement of currently deployed schemes based on RSA and discrete logarithm on prime fields or elliptic curves. It offers strong theoretical security guarantees, a large array of achievable primitives, and a competitive level of efficiency. Nowadays, in the context of the NIST post-quantum standardization process, future standards may ultimately be chosen and several new lattice-based schemes are high-profile candidates. The cryptographic research has been encouraged to analyze lattice-based cryptosystems, with a particular focus on practical aspects. This thesis is rooted in this effort.In addition to black-box cryptanalysis with classical computing resources, we investigate the extended security of these new lattice-based cryptosystems, employing a broad spectrum of attack models, e.g. quantum, misuse, timing or physical attacks. Accounting that these models have already been applied to a large variety of pre-quantum asymmetric and symmetric schemes before, we concentrate our efforts on leveraging and addressing the new features introduced by lattice structures. Our contribution is twofold: defensive, i.e. countermeasures for implementations of lattice-based schemes and offensive, i.e. cryptanalysis.On the defensive side, in view of the numerous recent timing and physical attacks, we wear our designer’s hat and investigate algorithmic protections. We introduce some new algorithmic and mathematical tools to construct provable algorithmic countermeasures in order to systematically prevent all timing and physical attacks. We thus participate in the actual provable protection of the GLP, BLISS, qTesla and Falcon lattice-based signatures schemes.On the offensive side, we estimate the applicability and complexity of novel attacks leveraging the lack of perfect correctness introduced in certain lattice-based encryption schemes to improve their performance. We show that such a compromise may enable decryption failures attacks in a misuse or quantum model. We finally introduce an algorithmic cryptanalysis tool that assesses the security of the mathematical problem underlying lattice-based schemes when partial knowledge of the secret is available. The usefulness of this new framework is demonstrated with the improvement and automation of several known classical, decryption-failure, and side-channel attacks.La cryptographie fondée sur les réseaux euclidiens représente une alternative prometteuse à la cryptographie asymétrique utilisée actuellement, en raison de sa résistance présumée à un ordinateur quantique universel. Cette nouvelle famille de schémas asymétriques dispose de plusieurs atouts parmi lesquels de fortes garanties théoriques de sécurité, un large choix de primitives et, pour certains de ses représentants, des performances comparables aux standards actuels. Une campagne de standardisation post-quantique organisée par le NIST est en cours et plusieurs schémas utilisant des réseaux euclidiens font partie des favoris. La communauté scientifique a été encouragée à les analyser car ils pourraient à l’avenir être implantés dans tous nos systèmes. L’objectif de cette thèse est de contribuer à cet effort.Nous étudions la sécurité de ces nouveaux cryptosystèmes non seulement au sens de leur résistance à la cryptanalyse en “boîte noire” à l’aide de moyens de calcul classiques, mais aussi selon un spectre plus large de modèles de sécurité, comme les attaques quantiques, les attaques supposant des failles d’utilisation, ou encore les attaques par canaux auxiliaires. Ces différents types d’attaques ont déjà été largement formalisés et étudiés par le passé pour des schémas asymétriques et symétriques pré-quantiques. Dans ce mémoire, nous analysons leur application aux nouvelles structures induites par les réseaux euclidiens. Notre travail est divisé en deux parties complémentaires : les contremesures et les attaques.La première partie regroupe nos contributions à l’effort actuel de conception de nouvelles protections algorithmiques afin de répondre aux nombreuses publications récentes d’attaques par canaux auxiliaires. Les travaux réalisés en équipe auxquels nous avons pris part on abouti à l’introduction de nouveaux outils mathématiques pour construire des contre-mesures algorithmiques, appuyées sur des preuves formelles, qui permettent de prévenir systématiquement les attaques physiques et par analyse de temps d’exécution. Nous avons ainsi participé à la protection de plusieurs schémas de signature fondés sur les réseaux euclidiens comme GLP, BLISS, qTesla ou encore Falcon.Dans une seconde partie consacrée à la cryptanalyse, nous étudions dans un premier temps de nouvelles attaques qui tirent parti du fait que certains schémas de chiffrement à clé publique ou d’établissement de clé peuvent échouer avec une faible probabilité. Ces échecs sont effectivement faiblement corrélés au secret. Notre travail a permis d’exhiber des attaques dites « par échec de déchiffrement » dans des modèles de failles d’utilisation ou des modèles quantiques. Nous avons d’autre part introduit un outil algorithmique de cryptanalyse permettant d’estimer la sécurité du problème mathématique sous-jacent lorsqu’une information partielle sur le secret est donnée. Cet outil s’est avéré utile pour automatiser et améliorer plusieurs attaques connues comme des attaques par échec de déchiffrement, des attaques classiques ou encore des attaques par canaux auxiliaires

Sécurité étendue de la cryptographie fondée sur les réseaux Euclidiens

Lattice-based cryptography is considered as a quantum-safe alternative for the replacement of currently deployed schemes based on RSA and discrete logarithm on prime fields or elliptic curves. It offers strong theoretical security guarantees, a large array of achievable primitives, and a competitive level of efficiency. Nowadays, in the context of the NIST post-quantum standardization process, future standards may ultimately be chosen and several new lattice-based schemes are high-profile candidates. The cryptographic research has been encouraged to analyze lattice-based cryptosystems, with a particular focus on practical aspects. This thesis is rooted in this effort. In addition to black-box cryptanalysis with classical computing resources, we investigate the extended security of these new lattice-based cryptosystems, employing a broad spectrum of attack models e.g. quantum, misuse, timing or physical attacks. Accounting that these models have already been applied to a large variety of pre-quantum asymmetric and symmetric schemes before, we concentrate our efforts on leveraging and addressing the new features introduced by lattice structures. Our contribution is twofold: defensive, i.e. countermeasures for implementations of lattice-based schemes and offensive, i.e. cryptanalysis. On the defensive side, in view of the numerous recent timing and physical attacks, we wear our designer's hat and investigate algorithmic protections. We introduce some new algorithmic and mathematical tools to construct provable algorithmic countermeasures in order to systematically prevent all timing and physical attacks. We thus participate in the actual provable protection of the GLP, BLISS, qTesla and Falcon lattice-based signatures schemes. On the offensive side, we estimate the applicability and complexity of novel attacks leveraging the lack of perfect correctness introduced in certain lattice-based encryption schemes to improve their performance. We show that such a compromise may enable decryption failures attacks in a misuse or quantum model. We finally introduce an algorithmic cryptanalysis tool that assesses the security of the mathematical problem underlying lattice-based schemes when partial knowledge of the secret is available. The usefulness of this new framework is demonstrated with the improvement and automation of several known classical, decryption-failure, and side-channel attacks.La cryptographie fondée sur les réseaux euclidiens représente une alternative prometteuse à la cryptographie asymétrique utilisée actuellement, en raison de sa résistance présumée à un ordinateur quantique universel. Cette nouvelle famille de schémas asymétriques dispose de plusieurs atouts parmi lesquels de fortes garanties théoriques de sécurité, un large choix de primitives et, pour certains de ses représentants, des performances comparables aux standards actuels. Une campagne de standardisation post-quantique organisée par le NIST est en cours et plusieurs schémas utilisant des réseaux euclidiens font partie des favoris. La communauté scientifique a été encouragée à les analyser car ils pourraient à l'avenir être implantés dans tous nos systèmes. L'objectif de cette thèse est de contribuer à cet effort. Nous étudions la sécurité de ces nouveaux cryptosystèmes non seulement au sens de leur résistance à la cryptanalyse en ''boîte noire'' à l'aide de moyens de calcul classiques, mais aussi selon un spectre plus large de modèles de sécurité, comme les attaques quantiques, les attaques supposant des failles d'utilisation, ou encore les attaques par canaux auxiliaires. Ces différents types d’attaques ont déjà été largement formalisés et étudiés par le passé pour des schémas asymétriques et symétriques pré-quantiques. Dans ce mémoire, nous analysons leur application aux nouvelles structures induites par les réseaux euclidiens. Notre travail est divisé en deux parties complémentaires : les contremesures et les attaques. La première partie regroupe nos contributions à l'effort actuel de conception de nouvelles protections algorithmiques afin de répondre aux nombreuses publications récentes d’attaques par canaux auxiliaires. Les travaux réalisés en équipe auxquels nous avons pris part on abouti à l'introduction de nouveaux outils mathématiques pour construire des contre-mesures algorithmiques, appuyées sur des preuves formelles, qui permettent de prévenir systématiquement les attaques physiques et par analyse de temps d'exécution. Nous avons ainsi participé à la protection de plusieurs schémas de signature fondés sur les réseaux euclidiens comme GLP, BLISS, qTesla ou encore Falcon. Dans une seconde partie consacrée à la cryptanalyse, nous étudions dans un premier temps de nouvelles attaques qui tirent parti du fait que certains schémas de chiffrement à clé publique ou d'établissement de clé peuvent échouer avec une faible probabilité. Ces échecs sont effectivement faiblement corrélés au secret. Notre travail a permis d’exhiber des attaques dites « par échec de déchiffrement » dans des modèles de failles d'utilisation ou des modèles quantiques. Nous avons d'autre part introduit un outil algorithmique de cryptanalyse permettant d’estimer la sécurité du problème mathématique sous-jacent lorsqu’une information partielle sur le secret est donnée. Cet outil s’est avéré utile pour automatiser et améliorer plusieurs attaques connues comme des attaques par échec de déchiffrement, des attaques classiques ou encore des attaques par canaux auxiliaires