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Publication# Improved Linear Cryptanalysis of Reduced-Round MIBS

Abstract

MIBS is a 32-round lightweight block cipher with 64-bit block size and two different key sizes, namely 64-bit and 80-bit keys. Bay et al. provided the first impossible differential, differential and linear cryptanalyses of MIBS. Their best attack was a linear attack on the 18-round MIBS-80. In this paper, we significantly improve their attack by discovering more approximations and mounting Hermelin et al.'s multidimensional linear cryptanalysis. We also use Nguyen et al.'s technique to have less time complexity. We attack on 19 rounds of MIBS-80 with a time complexity of 2^{74.23} 19-round MIBS-80 encryptions by using 2^{57.87} plaintext-ciphertext pairs. To the best of our knowledge, the result proposed in this paper is the best cryptanalytic result for MIBS, so far.

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Time complexity

In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the

Key size

In cryptography, key size, key length, or key space refer to the number of bits in a key used by a cryptographic algorithm (such as a cipher).
Key length defines the upper-bound on an algorithm's se

Cryptanalysis

Cryptanalysis (from the Greek kryptós, "hidden", and analýein, "to analyze") refers to the process of analyzing information systems in order to understand hidden aspects of the systems. Cryptanalysi

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.

We introduce KFC, a block cipher based on a three round Feistel scheme. Each of the three round functions has an SPN-like structure for which we can either compute or bound the advantage of the best d-limited adaptive distinguisher, for any value of d. Using results from the decorrelation theory, we extend these results to the whole KFC construction. To the best of our knowledge, KFC is the first practical (in the sense that it can be implemented) block cipher to propose tight security proofs of resistance against large classes of attacks, including most classical cryptanalysis (such as linear and differential cryptanalysis, taking hull effect in consideration in both cases, higher order differential cryptanalysis, the boomerang attack, differential-linear cryptanalysis, and others).

2006Block 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.