FOX: a new family of block ciphers

In this paper, we describe the design of a new family of block ciphers based on a Lai-Massey scheme, named FOX. The main features of this design, besides a very high security level, are a large implementation flexibility on various platforms as well as high performances. In addition, we propose a new design of strong and efficient key-schedule algorithms. We provide evidence that FOX is immune to linear and differential cryptanalysis, and we discuss its security towards integral cryptanalysis, algebraic attacks, and other attack

Improved Integral Cryptanalysis of FOX Block Cipher

FOX is a new family of block ciphers presented recently, which is based upon some results on proven security and has high performances on various platforms. In this paper, we construct some distinguishers between 3-round FOX and a random permutation of the blocks space. By using integral attack and collision-searching techniques, the distinguishers are used to attack on 4, 5, 6 and 7-round of FOX64, 4 and 5-round FOX128. The attack is more efficient than previous integral attack on FOX. The complexity of improved integral attack is $2^{77.6}$ on 4-round FOX128, $2^{205.6}$ against 5-round FOX128 respectively. For FOX64, the complexity of improved integral attack is $2^{45.4}$ on 4-round FOX64, $2^{109.4}$ against 5-round FOX64, $2^{173.4}$ against 6-round FOX64, $2^{237.4}$ against 7-round FOX64 respectively. Therefore, 4-round FOX64/64, 5-round FOX64/128, 6-round FOX64/192, 7-round FOX64/256 and 5-round FOX128/256 are not immune to the attack in this paper

Dial C for Cipher

We introduce C, a practical provably secure block cipher with a slow key schedule. C is based on the same structure as AES but uses independent random substitution boxes instead of a fixed one. Its key schedule is based on the Blum-Blum-Shub pseudo-random generator, which allows us to prove that all obtained security results are still valid when taking into account the dependencies between the round keys. C is provably secure against several general classes of attacks. Strong evidence is given that it resists an even wider variety of attacks. We also propose a variant of C with simpler substitution boxes which is suitable for most applications, and for which security proofs still hold

Related-Key Differential Attack on Round Reduced RECTANGLE-80

RECTANGLE is a newly proposed lightweight block cipher which allows fast implementations for multiple platforms by using bit-slice techniques. It is an iterative 25-round SPN block cipher with a 64-bit block size and a 80-bit or 128-bit key size. Until now, the results on analyzing the cipher are not too much, which includes an attack on the 18-round reduced version proposed by the designers themselves. In this paper, we find all 15-round differential characteristics with 26--30 active S-boxes for given input, output and round subkey differences, which have a total probability $2^{-60.5}$. Based on these differential characteristics, we extend the corresponding distinguisher to 2 rounds backward and forward respectively, and propose an attack on the 19-round reduced RECTANGLE-80 with data complexity of $2^{62}$ plaintexts, time complexity of about $2^{67.42}$ encryptions and memory complexity of $2^{72}$. TThese data and time complexities are much lower than that of the designers for the 18-round reduced RECTANGLE-80

A Salad of Block Ciphers

This book is a survey on the state of the art in block cipher design and analysis. It is work in progress, and it has been for the good part of the last three years -- sadly, for various reasons no significant change has been made during the last twelve months. However, it is also in a self-contained, useable, and relatively polished state, and for this reason I have decided to release this \textit{snapshot} onto the public as a service to the cryptographic community, both in order to obtain feedback, and also as a means to give something back to the community from which I have learned much. At some point I will produce a final version -- whatever being a ``final version\u27\u27 means in the constantly evolving field of block cipher design -- and I will publish it. In the meantime I hope the material contained here will be useful to other people

FOX Specifications Version 1.2

In this document, we describe the design of a new family of block ciphers, named FOX. The main goals of this design, besides a very high security level, are a large implementation flexibility on various platforms as well as high performances. The high-level structure is based on a Lai-Massey scheme, while the round functions are substitution-permutation networks. In addition, we propose a new design of strong and efficient key-schedule algorithms

Fault Analysis Study of the Block Cipher FOX64

FOX is a family of symmetric block ciphers from MediaCrypt AG that helps to secure digital media, communications, and storage. The high-level structure of FOX is the so-called (extended) Lai-Massey scheme. This paper presents a detailed fault analysis of the block cipher FOX64, the 64-bit version of FOX, based on a differential property of tworound Lai-Massey scheme in a fault model. Previous fault attack on FOX64 shows that each round-key (resp. whole round-keys) could be recovered through 11.45 (resp. 183.20) faults on average. Our proposed fault attack, however, can deduce any round-key (except the first one) through 4.25 faults on average (4 in the best case), and retrieve the whole round-keys through 43.31 faults on average (38 in the best case). This implies that the number of needed faults in the fault attack on FOX64 can be significantly reduced. Furthermore, the technique introduced in this paper can be extended to other series of the block cipher family FOX

Automatic Search of Truncated Impossible Differentials for Word-Oriented Block Ciphers (Full Version)

Impossible differential cryptanalysis is a powerful technique to recover the secret key of block ciphers by exploiting the fact that in block ciphers specific input and output differences are not compatible. This paper introduces a novel tool to search truncated impossible differentials for word-oriented block ciphers with bijective Sboxes. Our tool generalizes the earlier $\mathcal{U}$-method and the UID-method. It allows to reduce the gap between the best impossible differentials found by these methods and the best known differentials found by ad hoc methods that rely on cryptanalytic insights. The time and space complexities of our tool in judging an $r$-round truncated impossible differential are about $O(c\cdot l^4\cdot r^4)$ and $O(c\u27\cdot l^2\cdot r^2)$ respectively, where $l$ is the number of words in the plaintext and $c$, $c\u27$ are constants depending on the machine and the block cipher. In order to demonstrate the strength of our tool, we show that it does not only allow to automatically rediscover the longest truncated impossible differentials of many word-oriented block ciphers, but also finds new results. It independently rediscovers all 72 known truncated impossible differentials on 9-round CLEFIA. In addition, finds new truncated impossible differentials for AES, ARIA, Camellia without FL and FL$^{-1}$ layers, E2, LBlock, MIBS and Piccolo. Although our tool does not improve the lengths of impossible differentials for existing block ciphers, it helps to close the gap between the best known results of previous tools and those of manual cryptanalysis

Analysis and Design of Symmetric Cryptographic Algorithms

This doctoral thesis is dedicated to the analysis and the design of symmetric cryptographic algorithms. In the first part of the dissertation, we deal with fault-based attacks on cryptographic circuits which belong to the field of active implementation attacks and aim to retrieve secret keys stored on such chips. Our main focus lies on the cryptanalytic aspects of those attacks. In particular, we target block ciphers with a lightweight and (often) non-bijective key schedule where the derived subkeys are (almost) independent from each other. An attacker who is able to reconstruct one of the subkeys is thus not necessarily able to directly retrieve other subkeys or even the secret master key by simply reversing the key schedule. We introduce a framework based on differential fault analysis that allows to attack block ciphers with an arbitrary number of independent subkeys and which rely on a substitution-permutation network. These methods are then applied to the lightweight block ciphers LED and PRINCE and we show in both cases how to recover the secret master key requiring only a small number of fault injections. Moreover, we investigate approaches that utilize algebraic instead of differential techniques for the fault analysis and discuss advantages and drawbacks. At the end of the first part of the dissertation, we explore fault-based attacks on the block cipher Bel-T which also has a lightweight key schedule but is not based on a substitution-permutation network but instead on the so-called Lai-Massey scheme. The framework mentioned above is thus not usable against Bel-T. Nevertheless, we also present techniques for the case of Bel-T that enable full recovery of the secret key in a very efficient way using differential fault analysis. In the second part of the thesis, we focus on authenticated encryption schemes. While regular ciphers only protect privacy of processed data, authenticated encryption schemes also secure its authenticity and integrity. Many of these ciphers are additionally able to protect authenticity and integrity of so-called associated data. This type of data is transmitted unencrypted but nevertheless must be protected from being tampered with during transmission. Authenticated encryption is nowadays the standard technique to protect in-transit data. However, most of the currently deployed schemes have deficits and there are many leverage points for improvements. With NORX we introduce a novel authenticated encryption scheme supporting associated data. This algorithm was designed with high security, efficiency in both hardware and software, simplicity, and robustness against side-channel attacks in mind. Next to its specification, we present special features, security goals, implementation details, extensive performance measurements and discuss advantages over currently deployed standards. Finally, we describe our preliminary security analysis where we investigate differential and rotational properties of NORX. Noteworthy are in particular the newly developed techniques for differential cryptanalysis of NORX which exploit the power of SAT- and SMT-solvers and have the potential to be easily adaptable to other encryption schemes as well.Diese Doktorarbeit beschäftigt sich mit der Analyse und dem Entwurf von symmetrischen kryptographischen Algorithmen. Im ersten Teil der Dissertation befassen wir uns mit fehlerbasierten Angriffen auf kryptographische Schaltungen, welche dem Gebiet der aktiven Seitenkanalangriffe zugeordnet werden und auf die Rekonstruktion geheimer Schlüssel abzielen, die auf diesen Chips gespeichert sind. Unser Hauptaugenmerk liegt dabei auf den kryptoanalytischen Aspekten dieser Angriffe. Insbesondere beschäftigen wir uns dabei mit Blockchiffren, die leichtgewichtige und eine (oft) nicht-bijektive Schlüsselexpansion besitzen, bei denen die erzeugten Teilschlüssel voneinander (nahezu) unabhängig sind. Ein Angreifer, dem es gelingt einen Teilschlüssel zu rekonstruieren, ist dadurch nicht in der Lage direkt weitere Teilschlüssel oder sogar den Hauptschlüssel abzuleiten indem er einfach die Schlüsselexpansion umkehrt. Wir stellen Techniken basierend auf differenzieller Fehleranalyse vor, die es ermöglichen Blockchiffren zu analysieren, welche eine beliebige Anzahl unabhängiger Teilschlüssel einsetzen und auf Substitutions-Permutations Netzwerken basieren. Diese Methoden werden im Anschluss auf die leichtgewichtigen Blockchiffren LED und PRINCE angewandt und wir zeigen in beiden Fällen wie der komplette geheime Schlüssel mit einigen wenigen Fehlerinjektionen rekonstruiert werden kann. Darüber hinaus untersuchen wir Methoden, die algebraische statt differenzielle Techniken der Fehleranalyse einsetzen und diskutieren deren Vor- und Nachteile. Am Ende des ersten Teils der Dissertation befassen wir uns mit fehlerbasierten Angriffen auf die Blockchiffre Bel-T, welche ebenfalls eine leichtgewichtige Schlüsselexpansion besitzt jedoch nicht auf einem Substitutions-Permutations Netzwerk sondern auf dem sogenannten Lai-Massey Schema basiert. Die oben genannten Techniken können daher bei Bel-T nicht angewandt werden. Nichtsdestotrotz werden wir auch für den Fall von Bel-T Verfahren vorstellen, die in der Lage sind den vollständigen geheimen Schlüssel sehr effizient mit Hilfe von differenzieller Fehleranalyse zu rekonstruieren. Im zweiten Teil der Doktorarbeit beschäftigen wir uns mit authentifizierenden Verschlüsselungsverfahren. Während gewöhnliche Chiffren nur die Vertraulichkeit der verarbeiteten Daten sicherstellen, gewährleisten authentifizierende Verschlüsselungsverfahren auch deren Authentizität und Integrität. Viele dieser Chiffren sind darüber hinaus in der Lage auch die Authentizität und Integrität von sogenannten assoziierten Daten zu gewährleisten. Daten dieses Typs werden in nicht-verschlüsselter Form übertragen, müssen aber dennoch gegen unbefugte Veränderungen auf dem Transportweg geschützt sein. Authentifizierende Verschlüsselungsverfahren bilden heutzutage die Standardtechnologie um Daten während der Übertragung zu beschützen. Aktuell eingesetzte Verfahren weisen jedoch oftmals Defizite auf und es existieren vielfältige Ansatzpunkte für Verbesserungen. Mit NORX stellen wir ein neuartiges authentifizierendes Verschlüsselungsverfahren vor, welches assoziierte Daten unterstützt. Dieser Algorithmus wurde vor allem im Hinblick auf Einsatzgebiete mit hohen Sicherheitsanforderungen, Effizienz in Hardware und Software, Einfachheit, und Robustheit gegenüber Seitenkanalangriffen entwickelt. Neben der Spezifikation präsentieren wir besondere Eigenschaften, angestrebte Sicherheitsziele, Details zur Implementierung, umfassende Performanz-Messungen und diskutieren Vorteile gegenüber aktuellen Standards. Schließlich stellen wir Ergebnisse unserer vorläufigen Sicherheitsanalyse vor, bei der wir uns vor allem auf differenzielle Merkmale und Rotationseigenschaften von NORX konzentrieren. Erwähnenswert sind dabei vor allem die für die differenzielle Kryptoanalyse von NORX entwickelten Techniken, die auf die Effizienz von SAT- und SMT-Solvern zurückgreifen und das Potential besitzen relativ einfach auch auf andere Verschlüsselungsverfahren übertragen werden zu können