Cryptanalysis, Reverse-Engineering and Design of Symmetric Cryptographic Algorithms

In this thesis, I present the research I did with my co-authors on several aspects of symmetric cryptography from May 2013 to December 2016, that is, when I was a PhD student at the university of Luxembourg under the supervision of Alex Biryukov. My research has spanned three different areas of symmetric cryptography. In Part I of this thesis, I present my work on lightweight cryptography. This field of study investigates the cryptographic algorithms that are suitable for very constrained devices with little computing power such as RFID tags and small embedded processors such as those used in sensor networks. Many such algorithms have been proposed recently, as evidenced by the survey I co-authored on this topic. I present this survey along with attacks against three of those algorithms, namely GLUON, PRINCE and TWINE. I also introduce a new lightweight block cipher called SPARX which was designed using a new method to justify its security: the Long Trail Strategy. Part II is devoted to S-Box reverse-engineering, a field of study investigating the methods recovering the hidden structure or the design criteria used to build an S-Box. I co-invented several such methods: a statistical analysis of the differential and linear properties which was applied successfully to the S-Box of the NSA block cipher Skipjack, a structural attack against Feistel networks called the yoyo game and the TU-decomposition. This last technique allowed us to decompose the S-Box of the last Russian standard block cipher and hash function as well as the only known solution to the APN problem, a long-standing open question in mathematics. Finally, Part III presents a unifying view of several fields of symmetric cryptography by interpreting them as purposefully hard. Indeed, several cryptographic algorithms are designed so as to maximize the code size, RAM consumption or time taken by their implementations. By providing a unique framework describing all such design goals, we could design modes of operations for building any symmetric primitive with any form of hardness by combining secure cryptographic building blocks with simple functions with the desired form of hardness called plugs. Alex Biryukov and I also showed that it is possible to build plugs with an asymmetric hardness whereby the knowledge of a secret key allows the privileged user to bypass the hardness of the primitive

State of the Art in Lightweight Symmetric Cryptography

Lightweight cryptography has been one of the ``hot topics'' in symmetric cryptography in the recent years. A huge number of lightweight algorithms have been published, standardized and/or used in commercial products. In this paper, we discuss the different implementation constraints that a ``lightweight'' algorithm is usually designed to satisfy. We also present an extensive survey of all lightweight symmetric primitives we are aware of. It covers designs from the academic community, from government agencies and proprietary algorithms which were reverse-engineered or leaked. Relevant national (\nist{}...) and international (\textsc{iso/iec}...) standards are listed. We then discuss some trends we identified in the design of lightweight algorithms, namely the designers' preference for \arx{}-based and bitsliced-S-Box-based designs and simple key schedules. Finally, we argue that lightweight cryptography is too large a field and that it should be split into two related but distinct areas: \emph{ultra-lightweight} and \emph{IoT} cryptography. The former deals only with the smallest of devices for which a lower security level may be justified by the very harsh design constraints. The latter corresponds to low-power embedded processors for which the \aes{} and modern hash function are costly but which have to provide a high level security due to their greater connectivity

Exponential S-Boxes: a Link Between the S-Boxes of BelT and Kuznyechik/Streebog

The block cipher Kuznyechik and the hash function Streebog were recently standardized by the Russian Federation. These primitives use a common 8-bit S-Box, denoted , which is given only as a look-up table. The rationale behind its design is, for all practical purposes, kept secret by its authors. In a paper presented at Eurocrypt 2016, Biryukov et al. reverse-engineered this S-Box and recovered an unusual Feistel-like structure relying on finite field multiplications. In this paper, we provide a new decomposition of this S-Box and describe how we obtained it. The first step was the analysis of the 8-bit S-Box of the current standard block cipher of Belarus, BelT. This S-Box is a variant of a so-called exponential substitution, a concept we generalize into pseudo-exponential substitution. We derive distinguishers for such permutations based on properties of their linear approximation tables and notice that shares some of them. We then show that indeed has a decomposition based on a pseudo-exponential substitution. More precisely, we obtain a simpler structure based on an 8-bit finite field exponentiation, one 4-bit S-Box, a linear layer and a few modular arithmetic operations. We also make several observations which may help cryptanalysts attempting to reverse-engineer other S-Boxes. For example, the visual pattern used in the previous work as a starting point to decompose is mathematically formalized and the use of differential patterns involving operations other than exclusive-or is explored

Summary of an Open Discussion on IoT and Lightweight Cryptography

This is a summary of the open discussion on IoT security and regulation which took place at the Early Symmetric Crypto (ESC) seminar. Participants have identified that IoT poses critical threat to security and privacy. It was agreed that government regulation and dialogue of security researchers with engineers and manufacturers is necessary in order to find proper control mechanisms

Multiset-Algebraic Cryptanalysis of Reduced Kuznyechik, Khazad, and secret SPNs

We devise the first closed formula for the number of rounds of a blockcipher with secret components so that these components can be revealed using multiset, algebraic-degree, or division-integral properties, which in this case are equivalent. Using the new result, we attack 7 (out of 9) rounds of Kuznyechik, the recent Russian blockcipher standard, thus halving its security margin. With the same technique we attack 6 (out of 8) rounds of Khazad, the legacy 64-bit blockcipher. Finally, we show how to cryptanalyze and find a decomposition of generic SPN construction for which the inner-components are secret. All the attacks are the best to date

Triathlon of Lightweight Block Ciphers for the Internet of Things

In this paper, we introduce a framework for the benchmarking of lightweight block ciphers on a multitude of embedded platforms. Our framework is able to evaluate the execution time, RAM footprint, as well as binary code size, and allows one to define a custom "figure of merit" according to which all evaluated candidates can be ranked. We used the framework to benchmark implementations of 19 lightweight ciphers, namely AES, Chaskey, Fantomas, HIGHT, LBlock, LEA, LED, Piccolo, PRESENT, PRIDE, PRINCE, RC5, RECTANGLE, RoadRunneR, Robin, Simon, SPARX, Speck, and TWINE, on three microcontroller platforms: 8-bit AVR, 16-bit MSP430, and 32-bit ARM. Our results bring some new insights into the question of how well these lightweight ciphers are suited to secure the Internet of things. The benchmarking framework provides cipher designers with an easy-to-use tool to compare new algorithms with the state of the art and allows standardization organizations to conduct a fair and consistent evaluation of a large number of candidates

On the Properties of S-boxes : A Study of Differentially 6-Uniform Monomials over Finite Fields of Characteristic 2

S-boxes are key components of many symmetric cryptographic primitives. Among them, some block ciphers and hash functions are vulnerable to attacks based on differential cryptanalysis, a technique introduced by Biham and Shamir in the early 90’s. Resistance against attacks from this family depends on the so-called differential properties of the S-boxes used. When we consider S-boxes as functions over finite fields of characteristic 2, monomials turn out to be good candidates. In this Master’s Thesis, we study the differential properties of a particular family of monomials, namely those with exponent 2ͭᵗ-1 In particular, conjectures from Blondeau’s PhD Thesis are proved. More specifically, we derive the differential spectrum of monomials with exponent 2ͭᵗ-1 for several values of t using a method similar to the proof Blondeau et al. made of the spectrum of x - x⁷. The first two chapters of this Thesis provide the mathematical and cryptographic background necessary while the third and fourth chapters contain the proofs of the spectra we extracted and some observations which, among other things, connect this problem with the study of particular Dickson polynomials

On Reverse-Engineering S-Boxes with Hidden Design Criteria or Structure

S-Boxes are the key components of many cryptographic primitives and designing them to improve resilience to attacks such as linear or differential cryptanalysis is well understood. In this paper, we investigate techniques that can be used to reverse-engineer S-box design and illustrate those by studying the S-Box $F$ of the Skipjack block cipher whose design process so far remained secret. We first show that the linear properties of $F$ are far from random and propose a design criteria, along with an algorithm which generates S-Boxes very similar to that of Skipjack. Then we consider more general S-box decomposition problems and propose new methods for decomposing S-Boxes built from arithmetic operations or as a Feistel Network of up to 5 rounds. Finally, we develop an S-box generating algorithm which can fix a large number of DDT entries to the values chosen by the designer. We demonstrate this algorithm by embedding images into the visual representation of S-box's DDT

Meet-in-the-Middle Attacks and Structural Analysis of Round-Reduced PRINCE

NXP Semiconductors and its academic partners challenged the cryptographic community with finding practical attacks on the block cipher they designed, PRINCE. Instead of trying to attack as many rounds as possible using attacks which are usually impractical despite being faster than brute-force, the challenge invites cryptographers to find practical attacks and encourages them to actually implement them. In this paper, we present new attacks on round-reduced PRINCE including the ones which won the challenge in the 6 and 8-round categories --- the highest for which winners were identified. Our first attacks rely on a meet-in-the-middle approach and break up to 10 rounds of the cipher. We also describe heuristic methods we used to find practical SAT-based and differential attacks. Finally, we also present an analysis of the cycle structure of the internal rounds of PRINCE leading both to a low complexity distinguisher for 4-round PRINCE-core and an alternative representation of the cipher valid in particular contexts and which highlights, in this cases, a poor diffusion