Key-Recovery Attacks on Full Kravatte

This paper presents a cryptanalysis of full Kravatte, an instantiation of the Farfalle construction of a pseudorandom function (PRF) with variable input and output length. This new construction, proposed by Bertoni et al., introduces an efficiently parallelizable and extremely versatile building block for the design of symmetric mechanisms, e.g. message authentication codes or stream ciphers. It relies on a set of permutations and on so-called rolling functions: it can be split into a compression layer followed by a two-step expansion layer. The key is expanded and used to mask the inputs and outputs of the construction. Kravatte instantiates Farfalle using linear rolling functions and permutations obtained by iterating the Keccak round function. We develop in this paper several attacks against this PRF, based on three different attack strategies that bypass part of the construction and target a reduced number of permutation rounds. A higher order differential distinguisher exploits the possibility to build an affine space of values in the cipher state after the compression layer. An algebraic meet-in-the-middle attack can be mounted on the second step of the expansion layer. Finally, due to the linearity of the rolling function and the low algebraic degree of the Keccak round function, a linear recurrence distinguisher can be found on intermediate states of the second step of the expansion layer. All the attacks rely on the ability to invert a small number of the final rounds of the construction. In particular, the last two rounds of the construction together with the final masking by the key can be algebraically inverted, which allows to recover the key. The complexities of the devised attacks, applied to the Kravatte specifications published on the IACR ePrint in July 2017, or the strengthened version of Kravatte recently presented at ECC 2017, are far below the security claimed

Cryptanalysis of symmetric encryption algorithms

La sécurité des transmissions et du stockage des données est devenue un enjeu majeur de ces dernières années et la cryptologie, qui traite de la protection algorithmique de l'information, est un sujet de recherche extrêmement actif. Elle englobe la conception d'algorithmes cryptographiques, appelée cryptographie, et l'analyse de leur sécurité, appelée cryptanalyse.Dans cette thèse, nous nous concentrons uniquement sur la cryptanalyse, et en particulier celle des algorithmes de chiffrement symétrique, qui reposent sur le partage d'un même secret entre l'entité qui chiffre l'information et celle qui la déchiffre. Dans ce manuscrit, trois attaques contre des algorithmes de chiffrement symétriques sont présentées. Les deux premières portent sur deux candidats de l'actuelle compétition cryptographique CAESAR, les algorithmes AEZ et NORX, tandis que la dernière porte sur l'algorithme Kravatte, une instance de la construction Farfalle qui utilise la permutation de la fonction de hachage décrite dans le standard SHA-3. Les trois algorithmes étudiés présentent une stratégie de conception similaire, qui consiste à intégrer dans une construction nouvelle une primitive, i.e. une fonction cryptographique élémentaire, déjà existante ou directement inspirée de travaux précédents.La compétition CAESAR, qui a débuté en 2015, a pour but de définir un portefeuille d'algorithmes recommandés pour le chiffrement authentifié. Les deux candidats étudiés, AEZ et NORX, sont deux algorithmes qui ont atteint le troisième tour de cette compétition. Les deux attaques présentées ici ont contribué à l'effort de cryptanalyse nécessaire dans une telle compétition. Cet effort n'a, en l'occurrence, pas permis d'établir une confiance suffisante pour justifier la présence des algorithmes AEZ et NORX parmi les finalistes.AEZ est une construction reposant sur la primitive AES, dont l'un des principaux objectifs est d'offrir une résistance optimale à des scénarios d'attaque plus permissifs que ceux généralement considérés pour les algorithmes de chiffrement authentifié. Nous montrons ici que dans de tels scénarios il est possible, avec une probabilité anormalement élevée, de retrouver l'ensemble des secrets utilisés dans l'algorithme.NORX est un algorithme de chiffrement authentifié qui repose sur une variante de la construction dite en éponge employée par exemple dans la fonction de hachage Keccak. Sa permutation interne est inspirée de celles utilisées dans BLAKE et ChaCha. Nous montrons qu'il est possible d'exploiter une propriété structurelle de cette permutation afin de récupérer la clé secrète utilisée. Pour cela, nous tirons parti du choix des concepteurs de réduire les marges de sécurité dans le dimensionnement de la construction en éponge.Enfin, la dernière cryptanalyse remet en cause la robustesse de l'algorithme Kravatte, une fonction pseudo-aléatoire qui autorise des entrées et sorties de taille variable. Dérivée de la permutation Keccak-p de SHA-3 au moyen de la construction Farfalle, Kravatte est efficace et parallélisable. Ici, nous exploitons le faible degré algébrique de la permutation interne pour mettre au jour trois attaques par recouvrement de clé : une attaque différentielle d'ordre supérieur, une attaque algébrique "par le milieu" et une attaque inspirée de la cryptanalyse de certains algorithmes de chiffrement à flot.Nowadays, cryptology is heavily used to protect stored and transmitted data against malicious attacks, by means of security algorithms. Cryptology comprises cryptography, the design of these algorithms, and cryptanalysis, the analysis of their security.In this thesis, we focus on the cryptanalysis of symmetric encryption algorithms, that is cryptographic algorithms that rely on a secret value shared beforehand between two parties to ensure both encryption and decryption. We present three attacks against symmetric encryption algorithms. The first two cryptanalyses target two high profile candidates of the CAESAR cryptographic competition, the AEZ and NORX algorithms, while the last one targets the Kravatte algorithm, an instance of the Farfalle construction based on the Keccak permutation. Farfalle is multipurpose a pseudo-random function (PRF) developed by the same designers' team as the permutation Keccak used in the SHA-3 hash function.The CAESAR competition, that began in 2015, aims at selecting a portfolio of algorithms recommended for authenticated encryption. The two candidates analysed, AEZ and NORX, reached the third round of the CAESAR competition but were not selected to be part of the finalists. These two results contributed to the cryptanalysis effort required in such a competition. This effort did not establish enough confidence to justify that AEZ and NORX accede to the final round of the competition.AEZ is a construction based on the AES primitive, that aims at offering an optimal resistance against more permissive attack scenarios than those usually considered for authenticated encryption algorithms. We show here that one can recover all the secret material used in AEZ with an abnormal success probability.NORX is an authenticated encryption algorithm based on a variant of the so-called sponge construction used for instance in the SHA-3 hash function. The internal permutation is inspired from the one of BLAKE and ChaCha. We show that one can leverage a strong structural property of this permutation to recover the secret key, thanks to the designers' non-conservative choice of reducing the security margin in the sponge construction.Finally, the last cryptanalysis reconsiders the robustness of the Kravatte algorithm. Kravatte is an efficient and parallelizable PRF with input and output of variable length. In this analysis, we exploit the low algebraic degree of the permutation Keccak used in Kravatte to mount three key-recovery attacks targeting different parts of the construction: a higher order differential attack, an algebraic meet-in-the-middle attack and an attack based on a linear recurrence distinguisher

Cryptanalyse des algorithmes de chiffrement symétrique

Nowadays, cryptology is heavily used to protect stored and transmitted data against malicious attacks, by means of security algorithms. Cryptology comprises cryptography, the design of these algorithms, and cryptanalysis, the analysis of their security.In this thesis, we focus on the cryptanalysis of symmetric encryption algorithms, that is cryptographic algorithms that rely on a secret value shared beforehand between two parties to ensure both encryption and decryption. We present three attacks against symmetric encryption algorithms. The first two cryptanalyses target two high profile candidates of the CAESAR cryptographic competition, the AEZ and NORX algorithms, while the last one targets the Kravatte algorithm, an instance of the Farfalle construction based on the Keccak permutation. Farfalle is multipurpose a pseudo-random function (PRF) developed by the same designers' team as the permutation Keccak used in the SHA-3 hash function.The CAESAR competition, that began in 2015, aims at selecting a portfolio of algorithms recommended for authenticated encryption. The two candidates analysed, AEZ and NORX, reached the third round of the CAESAR competition but were not selected to be part of the finalists. These two results contributed to the cryptanalysis effort required in such a competition. This effort did not establish enough confidence to justify that AEZ and NORX accede to the final round of the competition.AEZ is a construction based on the AES primitive, that aims at offering an optimal resistance against more permissive attack scenarios than those usually considered for authenticated encryption algorithms. We show here that one can recover all the secret material used in AEZ with an abnormal success probability.NORX is an authenticated encryption algorithm based on a variant of the so-called sponge construction used for instance in the SHA-3 hash function. The internal permutation is inspired from the one of BLAKE and ChaCha. We show that one can leverage a strong structural property of this permutation to recover the secret key, thanks to the designers' non-conservative choice of reducing the security margin in the sponge construction.Finally, the last cryptanalysis reconsiders the robustness of the Kravatte algorithm. Kravatte is an efficient and parallelizable PRF with input and output of variable length. In this analysis, we exploit the low algebraic degree of the permutation Keccak used in Kravatte to mount three key-recovery attacks targeting different parts of the construction: a higher order differential attack, an algebraic meet-in-the-middle attack and an attack based on a linear recurrence distinguisher.La sécurité des transmissions et du stockage des données est devenue un enjeu majeur de ces dernières années et la cryptologie, qui traite de la protection algorithmique de l'information, est un sujet de recherche extrêmement actif. Elle englobe la conception d'algorithmes cryptographiques, appelée cryptographie, et l'analyse de leur sécurité, appelée cryptanalyse.Dans cette thèse, nous nous concentrons uniquement sur la cryptanalyse, et en particulier celle des algorithmes de chiffrement symétrique, qui reposent sur le partage d'un même secret entre l'entité qui chiffre l'information et celle qui la déchiffre. Dans ce manuscrit, trois attaques contre des algorithmes de chiffrement symétriques sont présentées. Les deux premières portent sur deux candidats de l'actuelle compétition cryptographique CAESAR, les algorithmes AEZ et NORX, tandis que la dernière porte sur l'algorithme Kravatte, une instance de la construction Farfalle qui utilise la permutation de la fonction de hachage décrite dans le standard SHA-3. Les trois algorithmes étudiés présentent une stratégie de conception similaire, qui consiste à intégrer dans une construction nouvelle une primitive, i.e. une fonction cryptographique élémentaire, déjà existante ou directement inspirée de travaux précédents.La compétition CAESAR, qui a débuté en 2015, a pour but de définir un portefeuille d'algorithmes recommandés pour le chiffrement authentifié. Les deux candidats étudiés, AEZ et NORX, sont deux algorithmes qui ont atteint le troisième tour de cette compétition. Les deux attaques présentées ici ont contribué à l'effort de cryptanalyse nécessaire dans une telle compétition. Cet effort n'a, en l'occurrence, pas permis d'établir une confiance suffisante pour justifier la présence des algorithmes AEZ et NORX parmi les finalistes.AEZ est une construction reposant sur la primitive AES, dont l'un des principaux objectifs est d'offrir une résistance optimale à des scénarios d'attaque plus permissifs que ceux généralement considérés pour les algorithmes de chiffrement authentifié. Nous montrons ici que dans de tels scénarios il est possible, avec une probabilité anormalement élevée, de retrouver l'ensemble des secrets utilisés dans l'algorithme.NORX est un algorithme de chiffrement authentifié qui repose sur une variante de la construction dite en éponge employée par exemple dans la fonction de hachage Keccak. Sa permutation interne est inspirée de celles utilisées dans BLAKE et ChaCha. Nous montrons qu'il est possible d'exploiter une propriété structurelle de cette permutation afin de récupérer la clé secrète utilisée. Pour cela, nous tirons parti du choix des concepteurs de réduire les marges de sécurité dans le dimensionnement de la construction en éponge.Enfin, la dernière cryptanalyse remet en cause la robustesse de l'algorithme Kravatte, une fonction pseudo-aléatoire qui autorise des entrées et sorties de taille variable. Dérivée de la permutation Keccak-p de SHA-3 au moyen de la construction Farfalle, Kravatte est efficace et parallélisable. Ici, nous exploitons le faible degré algébrique de la permutation interne pour mettre au jour trois attaques par recouvrement de clé : une attaque différentielle d'ordre supérieur, une attaque algébrique "par le milieu" et une attaque inspirée de la cryptanalyse de certains algorithmes de chiffrement à flot

Is AEZ v4.1 Sufficiently Resilient Against Key-Recovery Attacks?

International audienceAEZ is a parallelizable, AES-based authenticated encryption algorithm that is well suited for software implementations on processors equipped with the AES-NI instruction set. It aims at offering exceptionally strong security properties such as nonce and decryption-misuse resistance and optimal security given the selected ciphertext expansion. AEZ was submitted to the authenticated ciphers competition CAESAR and was selected in 2015 for the second round of the competition. In this paper, we analyse the resilience of the latest algorithm version, AEZ v4.1 (October 2015), against key-recovery attacks. While AEZ modifications introduced in 2015 were partly motivated by thwarting a key-recovery attack of birthday complexity against AEZ v3 published at Asiacrypt 2015 by Fuhr, Leurent and Suder, we show that AEZ v4.1 remains vulnerable to a key-recovery attack of similar complexity and security impact. Our attack leverages the use, in AEZ, of an underlying tweakable block cipher based on a 4-round version of AES. Although the presented key-recovery attack does not violate the security claims of AEZ since the designers made no claim for beyond-birthday security, it can be interpreted as an indication that AEZ does not fully meet the objective of being an extremely conservative and misuse-resilient algorithm

Cryptanalysis of NORX v2.0

International audienceNORX is an authenticated encryption scheme with associated data that was selected, along with 14 other primitives, for the third phase of the ongoing CAESAR competition. It is based on the sponge construction and relies on a simple permutation that allows efficient and versatile implementations. Thanks to research on the security of the sponge construction, the design of NORX, whose permutation is inspired from the permutations used in BLAKE and ChaCha, has evolved throughout three main versions (v1.0, v2.0 and v3.0). The main result of this paper is a cryptanalysis of the full NORX v2.0 that successfully passed, in 2016, the second round of the CAESAR competition. We exhibit a strong symmetry preservation property of the underlying sponge permutation and show that this property can be turned into an attack on the full primitive. This attack yields a ciphertext-only forgery with time and data complexity (Formula presented.) (resp. (Formula presented.)) for the variant of NORX v2.0 using 128-bit (resp. 256-bit) keys and breaks the designers’ claim of a 128-bit (resp. 256-bit) security. We further show that this forgery attack can be extended to a key-recovery attack on the full NORX v2.0 with the same time and data complexities. We have implemented and experimentally verified the correctness of the attacks on a toy version of NORX v2.0. We also investigate the security of the NORX v3.0, a tweaked version of NORX v2.0 introduced at the beginning of the third round of the CAESAR competition. The introduction in NORX v3.0 of an extra initial and final key addition thwarts the former forgery and key-recovery attacks. We exhibit, however, a long-message forgery attack on both NORX v2.0 and NORX v3.0 that, given the ciphertext of a (Formula presented.)-block message, allows to forge another (Formula presented.)-block ciphertext with a success probability of about (Formula presented.) (resp. (Formula presented.)) instead of (Formula presented.) (resp. (Formula presented.)) as one would ideally expect. We further show that since the symmetry preservation of the NORX v2.0 permutation persists in NORX v3.0, the former long-message forgery attack can be extended in both versions to a state-recovery attack. This high-complexity attack does not threaten the practical security of NORX v3.0, but show that the security loss once a successful forgery has been issued is larger than one would expect. © 2018 International Association for Cryptologic Researc

Key-Recovery Attacks on Full Kravatte

This paper presents a cryptanalysis of full Kravatte, an instantiation of the Farfalle construction of a pseudorandom function (PRF) with variable input and output length. This new construction, proposed by Bertoni et al., introduces an efficiently parallelizable and extremely versatile building block for the design of symmetric mechanisms, e.g. message authentication codes or stream ciphers. It relies on a set of permutations and on so-called rolling functions: it can be split into a compression layer followed by a two-step expansion layer. The key is expanded and used to mask the inputs and outputs of the construction. Kravatte instantiates Farfalle using linear rolling functions and permutations obtained by iterating the Keccak round function.We develop in this paper several attacks against this PRF, based on three different attack strategies that bypass part of the construction and target a reduced number of permutation rounds. A higher order differential distinguisher exploits the possibility to build an affine space of values in the cipher state after the compression layer. An algebraic meet-in-the-middle attack can be mounted on the second step of the expansion layer. Finally, due to the linearity of the rolling function and the low algebraic degree of the Keccak round function, a linear recurrence distinguisher can be found on intermediate states of the second step of the expansion layer. All the attacks rely on the ability to invert a small number of the final rounds of the construction. In particular, the last two rounds of the construction together with the final masking by the key can be algebraically inverted, which allows to recover the key.The complexities of the devised attacks, applied to the Kravatte specifications published on the IACR ePrint in July 2017, or the strengthened version of Kravatte recently presented at ECC 2017, are far below the security claimed

Reconciling well-being and resilience for sustainable development

Securing well-being and building resilience in response to shocks are often viewed as key goals of sustainable development. Here, we present an overview of the latest published evidence, as well as the consensus of a diverse group of scientists and practitioners drawn from a structured analytical review and deliberative workshop process. We argue that resilience and well-being are related in complex ways, but in their applications in practice they are often assumed to be synergistic. Although theoretically compatible, evidence we present here shows that they may in fact work against each other. This has important implications for policy