Decorrelation: A Theory for Block Cipher Security

Pseudorandomness is a classical model for the security of block ciphers. In this paper we propose convenient tools in order to study it in connection with the Shannon Theory, the Carter-Wegman universal hash functions paradigm, and the Luby-Rackoff approach. This enables the construction of new ciphers with security proofs under specific models. We show how to ensure security against basic differential and linear cryptanalysis and even more general attacks. We propose practical construction scheme

4-point Attacks with Standard Deviation Analysis on A-Feistel Schemes

A usual way to construct block ciphers is to apply several rounds of a given structure. Many kinds of attacks are mounted against block ciphers. Among them, differential and linear attacks are widely used. In~\cite{V98,V03}, it is shown that ciphers that achieve perfect pairwise decorrelation are secure against linear and differential attacks. It is possible to obtain such schemes by introducing at least one random affine permutation as a round function in the design of the scheme. In this paper, we study attacks on schemes based on classical Feistel schemes where we introduce one or two affine permutations. Since these schemes resist against linear and differential attacks, we will study stronger attacks based on specific equations on 4-tuples of cleartext/ciphertext messages. We give the number of messages needed to distinguish a permutation produced by such schemes from a random permutation, depending on the number of rounds used in the schemes, the number and the position of the random affine permutations introduced in the schemes

Quantitative security of block ciphers:designs and cryptanalysis tools

Block ciphers probably figure in the list of the most important cryptographic primitives. Although they are used for many different purposes, their essential goal is to ensure confidentiality. This thesis is concerned by their quantitative security, that is, by measurable attributes that reflect their ability to guarantee this confidentiality. The first part of this thesis deals with well know results. Starting with Shannon's Theory of Secrecy, we move to practical implications for block ciphers, recall the main schemes on which nowadays block ciphers are based, and introduce the Luby-Rackoff security model. We describe distinguishing attacks and key-recovery attacks against block ciphers and show how to turn the firsts into the seconds. As an illustration, we recall linear cryptanalysis which is a classical example of statistical cryptanalysis. In the second part, we consider the (in)security of block ciphers against statistical cryptanalytic attacks and develop some tools to perform optimal attacks and quantify their efficiency. We start with a simple setting in which the adversary has to distinguish between two sources of randomness and show how an optimal strategy can be derived in certain cases. We proceed with the practical situation where the cardinality of the sample space is too large for the optimal strategy to be implemented and show how this naturally leads to the concept of projection-based distinguishers, which reduce the sample space by compressing the samples. Within this setting, we re-consider the particular case of linear distinguishers and generalize them to sets of arbitrary cardinality. We show how these distinguishers between random sources can be turned into distinguishers between random oracles (or block ciphers) and how, in this setting, one can generalize linear cryptanalysis to Abelian groups. As a proof of concept, we show how to break the block cipher TOY100, introduce the block cipher DEAN which encrypts blocks of decimal digits, and apply the theory to the SAFER block cipher family. In the last part of this thesis, we introduce two new constructions. We start by recalling some essential notions about provable security for block ciphers and about Serge Vaudenay's Decorrelation Theory, and introduce new simple modules for which we prove essential properties that we will later use in our designs. We then present the block cipher C and prove that it is immune against a wide range of cryptanalytic attacks. In particular, we compute the exact advantage of the best distinguisher limited to two plaintext/ciphertext samples between C and the perfect cipher and use it to compute the exact value of the maximum expected linear probability (resp. differential probability) of C which is known to be inversely proportional to the number of samples required by the best possible linear (resp. differential) attack. We then introduce KFC a block cipher which builds upon the same foundations as C but for which we can prove results for higher order adversaries. We conclude both discussions about C and KFC by implementation considerations

Revisiting Iterated Attacks in the Context of Decorrelation Theory

Iterated attacks are comprised of iterating adversaries who can make d plaintext queries, in each iteration to compute a bit, and are trying to distinguish between a random cipher C and the perfect cipher C* based on all bits. Vaudenay showed that a 2d-decorrelated cipher resists to iterated attacks of order d. when iterations have almost no common queries. Then, he first asked what the necessary conditions are for a cipher to resist a non-adaptive iterated attack of order d. I.e., whether decorrelation of order 2d-1 could be sufficient. Secondly, he speculated that repeating a plaintext query in different iterations does not provide any advantage to a non-adaptive distinguisher. We close here these two long-standing open problems negatively. For those questions, we provide two counter-intuitive examples. We also deal with adaptive iterated adversaries who can make both plaintext and ciphertext queries in which the future queries are dependent on the past queries. We show that decorrelation of order 2d protects against these attacks of order d. We also study the generalization of these distinguishers for iterations making non-binary outcomes. Finally, we measure the resistance against two well-known statistical distinguishers, namely, differential-linear and boomerang distinguishers and show that 4-decorrelation degree protects against these attacks

Towards a Theory of Symmetric Encryption

Motivée par le commerce et l'industrie, la recherche publique dans le domaine du chiffrement symétrique s'est considérablement développée depuis vingt cinq ans si bien qu'il est maintenant possible d'en faire le bilan. La recherche a tout d'abord progressé de manière empirique. De nombreux algorithmes de chiffrement fondés sur la notion de réseau de substitutions et de permutations ont été proposés, suivis d'attaques dédiées contre eux. Cela a permis de définir des stratégies générales: les méthodes d'attaques différentielles, linéaires et statistiques, et les méthodes génériques fondées sur la notion de boîte noire. En modélisant ces attaques on a trouvé en retour des règles utiles dans la conception d'algorithmes sûrs: la notion combinatoire de multipermutation pour les fonctions élémentaires, le contrôle de la diffusion par des critères géométriques de réseau de calcul, l'étude algébrique de la non-linéarité, ... Enfin, on montre que la sécurité face à un grand nombre de classes d'attaques classiques est assurée grâce à la notion de décorrélation par une preuve formelle. Ces principes sont à l'origine de deux algorithmes particuliers: la fonction CS-Cipher qui permet un chiffrement à haut débit et une sécurité heuristique, et le candidat DFC au processus de standardisation AES, prototype d'algorithme fondé sur la notion de décorrélation

The related-key analysis of feistel constructions

Lecture Notes in Computer Science, Volume 8540, 2015.It is well known that the classical three- and four-round Feistel constructions are provably secure under chosen-plaintext and chosen-ciphertext attacks, respectively. However, irrespective of the number of rounds, no Feistel construction can resist related-key attacks where the keys can be offset by a constant. In this paper we show that, under suitable reuse of round keys, security under related-key attacks can be provably attained. Our modification is substantially simpler and more efficient than alternatives obtained using generic transforms, namely the PRG transform of Bellare and Cash (CRYPTO 2010) and its random-oracle analogue outlined by Lucks (FSE 2004). Additionally we formalize Luck’s transform and show that it does not always work if related keys are derived in an oracle-dependent way, and then prove it sound under appropriate restrictions

Statistical cryptanalysis of block ciphers

Since the development of cryptology in the industrial and academic worlds in the seventies, public knowledge and expertise have grown in a tremendous way, notably because of the increasing, nowadays almost ubiquitous, presence of electronic communication means in our lives. Block ciphers are inevitable building blocks of the security of various electronic systems. Recently, many advances have been published in the field of public-key cryptography, being in the understanding of involved security models or in the mathematical security proofs applied to precise cryptosystems. Unfortunately, this is still not the case in the world of symmetric-key cryptography and the current state of knowledge is far from reaching such a goal. However, block and stream ciphers tend to counterbalance this lack of "provable security" by other advantages, like high data throughput and ease of implementation. In the first part of this thesis, we would like to add a (small) stone to the wall of provable security of block ciphers with the (theoretical and experimental) statistical analysis of the mechanisms behind Matsui's linear cryptanalysis as well as more abstract models of attacks. For this purpose, we consider the underlying problem as a statistical hypothesis testing problem and we make a heavy use of the Neyman-Pearson paradigm. Then, we generalize the concept of linear distinguisher and we discuss the power of such a generalization. Furthermore, we introduce the concept of sequential distinguisher, based on sequential sampling, and of aggregate distinguishers, which allows to build sub-optimal but efficient distinguishers. Finally, we propose new attacks against reduced-round version of the block cipher IDEA. In the second part, we propose the design of a new family of block ciphers named FOX. First, we study the efficiency of optimal diffusive components when implemented on low-cost architectures, and we present several new constructions of MDS matrices; then, we precisely describe FOX and we discuss its security regarding linear and differential cryptanalysis, integral attacks, and algebraic attacks. Finally, various implementation issues are considered