Nonlinear Approximations in Cryptanalysis Revisited

This work studies deterministic and non-deterministic nonlinear approximations for cryptanalysis of block ciphers and cryptographic permutations and embeds it into the well-understood framework of linear cryptanalysis. For a deterministic (i.e., with correlation ±1) nonlinear approximation we show that in many cases, such a nonlinear approximation implies the existence of a highly-biased linear approximation. For non-deterministic nonlinear approximations, by transforming the cipher under consideration by conjugating each keyed instance with a fixed permutation, we are able to transfer many methods from linear cryptanalysis to the nonlinear case. Using this framework we in particular show that there exist ciphers for which some transformed versions are significantly weaker with regard to linear cryptanalysis than their original counterparts

Nonlinear Approximations in Cryptanalysis Revisited

International audienceThis work studies deterministic and non-deterministic nonlinear approximations for cryptanalysis of block ciphers and cryptographic permutations and embeds it into the well-understood framework of linear cryptanalysis. For a deterministic (i.e., with correlation ±1) nonlinear approximation we show that in many cases, such a nonlinear approximation implies the existence of a highly-biased linear approximation. For non-deterministic nonlinear approximations, by transforming the cipher under consideration by conjugating each keyed instance with a fixed permutation, we are able to transfer many methods from linear cryptanalysis to the nonlinear case. Using this framework we in particular show that there exist ciphers for which some transformed versions are significantly weaker with regard to linear cryptanalysis than their original counterparts

On Some Symmetric Lightweight Cryptographic Designs

This dissertation presents cryptanalysis of several symmetric lightweight primitives, both stream ciphers and block ciphers. Further, some aspects of authentication in combination with a keystream generator is investigated, and a new member of the Grain family of stream ciphers, Grain-128a, with built-in support for authentication is presented. The first contribution is an investigation of how authentication can be provided at a low additional cost, assuming a synchronous stream cipher is already implemented and used for encryption. These findings are then used when presenting the latest addition to the Grain family of stream ciphers, Grain-128a. It uses a 128-bit key and a 96-bit initialization vector to generate keystream, and to possibly also authenticate the plaintext. Next, the stream cipher BEAN, superficially similar to Grain, but notably using a weak output function and two feedback with carry shift registers (FCSRs) rather than linear and (non-FCSR) nonlinear feedback shift registers, is cryptanalyzed. An efficient distinguisher and a state-recovery attack is given. It is shown how knowledge of the state can be used to recover the key in a straightforward way. The remainder of this dissertation then focuses on block ciphers. First, a related-key attack on KTANTAN is presented. The attack notably uses only a few related keys, runs in less than half a minute on a current computer, and directly contradicts the designers' claims. It is discussed why this is, and what can be learned from this. Next, PRINTcipher is subjected to linear cryptanalysis. Several weak key classes are identified and it is shown how several observations of the same statistical property can be made for each plaintext--ciphertext pair. Finally, the invariant subspace property, first observed for certain key classes in PRINTcipher, is investigated. In particular, its connection to large linear biases is studied through an eigenvector which arises inside the cipher and leads to trail clustering in the linear hull which, under reasonable assumptions, causes a significant number of large linear biases. Simulations on several versions of PRINTcipher are compared to the theoretical findings

A Basic Framework for the Cryptanalysis of Digital Chaos-Based Cryptography

Chaotic cryptography is based on the properties of chaos as source of entropy. Many different schemes have been proposed to take advantage of those properties and to design new strategies to encrypt information. However, the right and efficient use of chaos in the context of cryptography requires a thorough knowledge about the dynamics of the selected chaotic system. Indeed, if the final encryption system reveals enough information about the underlying chaotic system it could be possible for a cryptanalyst to get the key, part of the key or some information somehow equivalent to the key just analyzing those dynamical properties leaked by the cryptosystem. This paper shows what those dynamical properties are and how a cryptanalyst can use them to prove the inadequacy of an encryption system for the secure exchange of information. This study is performed through the introduction of a series of mathematical tools which should be the basic framework of cryptanalysis in the context of digital chaos-based cryptography.Comment: 6 pages, 5 figure

Nonlinear cryptanalysis of reduced-round Serpent and metaheuristic search for S-box approximations.

We utilise a simulated annealing algorithm to find several nonlinear approximations to various S-boxes which can be used to replace the linear approximations in the outer rounds of existing attacks. We propose three variants of a new nonlinear cryptanalytic algorithm which overcomes the main issues that prevented the use of nonlinear approximations in previous research, and we present the statistical frameworks for calculating the complexity of each version. We present new attacks on 11-round Serpent with better data complexity than any other known-plaintext or chosen-plaintext attack, and with the best overall time complexity for a 256-bit key

Some Words on Cryptanalysis of Stream Ciphers

In the world of cryptography, stream ciphers are known as primitives used to ensure privacy over a communication channel. One common way to build a stream cipher is to use a keystream generator to produce a pseudo-random sequence of symbols. In such algorithms, the ciphertext is the sum of the keystream and the plaintext, resembling the one-time pad principal. Although the idea behind stream ciphers is simple, serious investigation of these primitives has started only in the late 20th century. Therefore, cryptanalysis and design of stream ciphers are important. In recent years, many designs of stream ciphers have been proposed in an effort to find a proper candidate to be chosen as a world standard for data encryption. That potential candidate should be proven good by time and by the results of cryptanalysis. Different methods of analysis, in fact, explain how a stream cipher should be constructed. Thus, techniques for cryptanalysis are also important. This thesis starts with an overview of cryptography in general, and introduces the reader to modern cryptography. Later, we focus on basic principles of design and analysis of stream ciphers. Since statistical methods are the most important cryptanalysis techniques, they will be described in detail. The practice of statistical methods reveals several bottlenecks when implementing various analysis algorithms. For example, a common property of a cipher to produce n-bit words instead of just bits makes it more natural to perform a multidimensional analysis of such a design. However, in practice, one often has to truncate the words simply because the tools needed for analysis are missing. We propose a set of algorithms and data structures for multidimensional cryptanalysis when distributions over a large probability space have to be constructed. This thesis also includes results of cryptanalysis for various cryptographic primitives, such as A5/1, Grain, SNOW 2.0, Scream, Dragon, VMPC, RC4, and RC4A. Most of these results were achieved with the help of intensive use of the proposed tools for cryptanalysis

A Geometric Approach to Linear Cryptanalysis

A new interpretation of linear cryptanalysis is proposed. This \u27geometric approach\u27 unifies all common variants of linear cryptanalysis, reveals links between various properties, and suggests additional generalizations. For example, new insights into invariants corresponding to non-real eigenvalues of correlation matrices and a generalization of the link between zero-correlation and integral attacks are obtained. Geometric intuition leads to a fixed-key motivation for the piling-up principle, which is illustrated by explaining and generalizing previous results relating invariants and linear approximations. Rank-one approximations are proposed to analyze cell-oriented ciphers, and used to resolve an open problem posed by Beierle, Canteaut and Leander at FSE 2019. In particular, it is shown how such approximations can be analyzed automatically using Riemannian optimization

Generalization of Statistical Criteria for Sboxes

Linear and differential cryptanalysis and their generalizations are the most important tools in ststistical analysis of symmetric ciphers. These attacks make use of linear and differential properties of Sboxes and component functions of symmetric ciphers. In this article, we investigate generalized statistical properties for Sboxes. We justify the application of linear, differential and differential-linear cryptanalysis from the mathematical viewpoint. We verify some well-known Sboxes and vectotial Boolean functions by the proposed criteria and show that these functions have larger biases compared with previous criteria presentesd up to now