Algorithm 959: VBF: A Library of C plus plus Classes for Vector Boolean Functions in Cryptography

VBF is a collection of C++ classes designed for analyzing vector Boolean functions (functions that map a Boolean vector to another Boolean vector) from a cryptographic perspective. This implementation uses the NTL library from Victor Shoup, adding new modules that call NTL functions and complement the existing ones, making it better suited to cryptography. The class representing a vector Boolean function can be initialized by several alternative types of data structures such as Truth Table, Trace Representation, and Algebraic Normal Form (ANF), among others. The most relevant cryptographic criteria for both block and stream ciphers as well as for hash functions can be evaluated with VBF: it obtains the nonlinearity, linearity distance, algebraic degree, linear structures, and frequency distribution of the absolute values of the Walsh Spectrum or the Autocorrelation Spectrum, among others. In addition, operations such as equality testing, composition, inversion, sum, direct sum, bricklayering (parallel application of vector Boolean functions as employed in Rijndael cipher), and adding coordinate functions of two vector Boolean functions are presented. Finally, three real applications of the library are described: the first one analyzes the KASUMI block cipher, the second one analyzes the Mini-AES cipher, and the third one finds Boolean functions with very high nonlinearity, a key property for robustness against linear attacks

On lower bounds of second-order nonlinearities of cubic bent functions constructed by concatenating Gold functions

In this paper we consider cubic bent functions obtained by Leander and McGuire (J. Comb. Th. Series A, 116 (2009) 960-970) which are concatenations of quadratic Gold functions. A lower bound of second-order nonlinearities of these functions is obtained. This bound is compared with the lower bounds of second-order nonlinearities obtained for functions belonging to some other classes of functions which are recently studied

Contributions to Confidentiality and Integrity Algorithms for 5G

The confidentiality and integrity algorithms in cellular networks protect the transmission of user and signaling data over the air between users and the network, e.g., the base stations. There are three standardised cryptographic suites for confidentiality and integrity protection in 4G, which are based on the AES, SNOW 3G, and ZUC primitives, respectively. These primitives are used for providing a 128-bit security level and are usually implemented in hardware, e.g., using IP (intellectual property) cores, thus can be quite efficient. When we come to 5G, the innovative network architecture and high-performance demands pose new challenges to security. For the confidentiality and integrity protection, there are some new requirements on the underlying cryptographic algorithms. Specifically, these algorithms should: 1) provide 256 bits of security to protect against attackers equipped with quantum computing capabilities; and 2) provide at least 20 Gbps (Gigabits per second) speed in pure software environments, which is the downlink peak data rate in 5G. The reason for considering software environments is that the encryption in 5G will likely be moved to the cloud and implemented in software. Therefore, it is crucial to investigate existing algorithms in 4G, checking if they can satisfy the 5G requirements in terms of security and speed, and possibly propose new dedicated algorithms targeting these goals. This is the motivation of this thesis, which focuses on the confidentiality and integrity algorithms for 5G. The results can be summarised as follows.1. We investigate the security of SNOW 3G under 256-bit keys and propose two linear attacks against it with complexities 2172 and 2177, respectively. These cryptanalysis results indicate that SNOW 3G cannot provide the full 256-bit security level. 2. We design some spectral tools for linear cryptanalysis and apply these tools to investigate the security of ZUC-256, the 256-bit version of ZUC. We propose a distinguishing attack against ZUC-256 with complexity 2236, which is 220 faster than exhaustive key search. 3. We design a new stream cipher called SNOW-V in response to the new requirements for 5G confidentiality and integrity protection, in terms of security and speed. SNOW-V can provide a 256-bit security level and achieve a speed as high as 58 Gbps in software based on our extensive evaluation. The cipher is currently under evaluation in ETSI SAGE (Security Algorithms Group of Experts) as a promising candidate for 5G confidentiality and integrity algorithms. 4. We perform deeper cryptanalysis of SNOW-V to ensure that two common cryptanalysis techniques, guess-and-determine attacks and linear cryptanalysis, do not apply to SNOW-V faster than exhaustive key search. 5. We introduce two minor modifications in SNOW-V and propose an extreme performance variant, called SNOW-Vi, in response to the feedback about SNOW-V that some use cases are not fully covered. SNOW-Vi covers more use cases, especially some platforms with less capabilities. The speeds in software are increased by 50% in average over SNOW-V and can be up to 92 Gbps.Besides these works on 5G confidentiality and integrity algorithms, the thesis is also devoted to local pseudorandom generators (PRGs). 6. We investigate the security of local PRGs and propose two attacks against some constructions instantiated on the P5 predicate. The attacks improve existing results with a large gap and narrow down the secure parameter regime. We also extend the attacks to other local PRGs instantiated on general XOR-AND and XOR-MAJ predicates and provide some insight in the choice of safe parameters

Effective and Efficient Masking with Low Noise Using Small-Mersenne-Prime Ciphers

Embedded devices used in security applications are natural targets for physical attacks. Thus, enhancing their side-channel resistance is an important research challenge. A standard solution for this purpose is the use of Boolean masking schemes, as they are well adapted to current block ciphers with efficient bitslice representations. Boolean masking guarantees that the security of an implementation grows exponentially in the number of shares under the assumption that leakages are sufficiently noisy (and independent). Unfortunately, it has been shown that this noise assumption is hardly met on low-end devices. In this paper, we therefore investigate techniques to mask cryptographic algorithms in such a way that their resistance can survive an almost complete lack of noise. Building on seed theoretical results of Dziembowski et al., we put forward that arithmetic encodings in prime fields can reach this goal. We first exhibit the gains that such encodings lead to thanks to a simulated information theoretic analysis of their leakage (with up to six shares). We then provide figures showing that on platforms where optimized arithmetic adders and multipliers are readily available (i.e., most MCUs and FPGAs), performing masked operations in small to medium Mersenne-prime fields as opposed to binary extension fields will not lead to notable implementation overheads. We compile these observations into a new AES-like block cipher, called AES-prime, which is well-suited to illustrate the remarkable advantages of masking in prime fields. We also confirm the practical relevance of our findings by evaluating concrete software (ARM Cortex-M3) and hardware (Xilinx Spartan-6) implementations. Our experimental results show that security gains over Boolean masking (and, more generally, binary encodings) can reach orders of magnitude despite the same amount of information being leaked per share

Effective and Efficient Masking with Low Noise using Small-Mersenne-Prime Ciphers

Embedded devices used in security applications are natural targets for physical attacks. Thus, enhancing their side-channel resistance is an important research challenge. A standard solution for this purpose is the use of Boolean masking schemes, as they are well adapted to current block ciphers with efficient bitslice representations. Boolean masking guarantees that the security of an implementation grows exponentially in the number of shares under the assumption that leakages are sufficiently noisy (and independent). Unfortunately, it has been shown that this noise assumption is hardly met on low-end devices. In this paper, we therefore investigate techniques to mask cryptographic algorithms in such a way that their resistance can survive an almost complete lack of noise. Building on seed theoretical results of Dziembowski et al., we put forward that arithmetic encodings in prime fields can reach this goal. We first exhibit the gains that such encodings lead to thanks to a simulated information theoretic analysis of their leakage (with up to six shares). We then provide figures showing that on platforms where optimized arithmetic adders and multipliers are readily available (i.e., most MCUs and FPGAs), performing masked operations in small to medium Mersenne-prime fields as opposed to binary extension fields will not lead to notable implementation overheads. We compile these observations into a new AES-like block cipher, called AES-prime, which is well-suited to illustrate the remarkable advantages of masking in prime fields. We also confirm the practical relevance of our findings by evaluating concrete software (ARM Cortex-M3) and hardware (Xilinx Spartan-6) implementations. Our experimental results show that security gains over Boolean masking (and, more generally, binary encodings) can reach orders of magnitude despite the same amount of information being leaked per share

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