Analysis of lightweight stream ciphers

Stream ciphers are fast cryptographic primitives to provide confidentiality of electronically transmitted data. They can be very suitable in environments with restricted resources, such as mobile devices or embedded systems. Practical examples are cell phones, RFID transponders, smart cards or devices in sensor networks. Besides efficiency, security is the most important property of a stream cipher. In this thesis, we address cryptanalysis of modern lightweight stream ciphers. We derive and improve cryptanalytic methods for different building blocks and present dedicated attacks on specific proposals, including some eSTREAM candidates. As a result, we elaborate on the design criteria for the development of secure and efficient stream ciphers. The best-known building block is the linear feedback shift register (LFSR), which can be combined with a nonlinear Boolean output function. A powerful type of attacks against LFSR-based stream ciphers are the recent algebraic attacks, these exploit the specific structure by deriving low degree equations for recovering the secret key. We efficiently determine the immunity of existing and newly constructed Boolean functions against fast algebraic attacks. The concept of algebraic immunity is then generalized by investigating the augmented function of the stream cipher. As an application of this framework, we improve the cryptanalysis of a well-known stream cipher with irregularly clocked LFSR's. Algebraic attacks can be avoided by substituting the LFSR with a suitable nonlinear driving device, such as a feedback shift register with carry (FCSR) or the recently proposed class of T-functions. We investigate both replacement schemes in view of their security, and devise different practical attacks (including linear attacks) on a number of specific proposals based on T-functions. Another efficient method to amplify the nonlinear behavior is to use a round-based filter function, where each round consists of simple nonlinear operations. We use differential methods to break a reduced-round version of eSTREAM candidate Salsa20. Similar methods can be used to break a related compression function with a reduced number of rounds. Finally, we investigate the algebraic structure of the initialization function of stream ciphers and provide a framework for key recovery attacks. As an application, a key recovery attack on simplified versions of eSTREAM candidates Trivium and Grain-128 is given.

Neutrality-Based Symmetric Cryptanalysis

Shahram Khazaei

Cryptographic primitives are the basic components of any cryptographic tool. Block ciphers, stream ciphers and hash functions are the fundamental primitives of symmetric cryptography. In symmetric cryptography, the communicating parties perform essentially the same operation and use the same key, if any. This thesis concerns cryptanalysis of stream ciphers and hash functions. The main contribution of this work is introducing the concept of probabilistic neutrality for the arguments of a function, a generalization of the definition of neutrality. An input argument of a given function is called neutral if it does not affect the output of the function. This simple idea has already been implicitly used in key recovery cryptanalysis of block ciphers and stream ciphers. However, in 2004, Biham and Chen explicitly used the idea of neutrality to speed up collision finding algorithms for hash functions. We call an input argument of a function probabilistic neutral if it does not have a "significant" influence on the output of the function. Simply stated, it means that if the input argument is changed, the output of the function stays the same with a probability "close" to one. We will exploit the idea of probabilistic neutrality to assess the security of several stream ciphers and hash functions. Interestingly, all our cryptanalyses rely on neutrality and/or probabilistic neutrality. In other words, these concepts will appear as a common ingredient in all of our cryptanalytic algorithms. To the best of our knowledge, this is the first time that the probabilistic neutrality has found diverse applications in cryptanalysis.

EPFL2010

Quantitative security of block ciphers

Thomas Baignères

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.

EPFL2008

Algebraic Cryptanalysis of Deterministic Symmetric Encryption

Petr Susil

Deterministic symmetric encryption is widely used in many cryptographic applications. The security of deterministic block and stream ciphers is evaluated using cryptanalysis. Cryptanalysis is divided into two main categories: statistical cryptanalysis and algebraic cryptanalysis. Statistical cryptanalysis is a powerful tool for evaluating the security but it often requires a large number of plaintext/ciphertext pairs which is not always available in real life scenario. Algebraic cryptanalysis requires a smaller number of plaintext/ciphertext pairs but the attacks are often underestimated compared to statistical methods. In algebraic cryptanalysis, we consider a polynomial system representing the cipher and a solution of this system reveals the secret key used in the encryption. The contribution of this thesis is twofold. Firstly, we evaluate the performance of existing algebraic techniques with respect to number of plaintext/ciphertext pairs and their selection. We introduce a new strategy for selection of samples. We build this strategy based on cube attacks, which is a well-known technique in algebraic cryptanalysis. We use cube attacks as a fast heuristic to determine sets of plaintexts for which standard algebraic methods, such as Groebner basis techniques or SAT solvers, are more efficient. Secondly, we develop a~new technique for algebraic cryptanalysis which allows us to speed-up existing Groebner basis techniques. This is achieved by efficient finding special polynomials called mutants. Using these mutants in Groebner basis computations and SAT solvers reduces the computational cost to solve the system. Hence, both our methods are designed as tools for building polynomial system representing a cipher. Both tools can be combined and they lead to a significant speedup, even for very simple algebraic solvers.

EPFL2015

Quantitative security of block ciphers

Thomas Baignères

EPFL2008