A different algebraic analysis of the ZUC stream cipher

Existing algebraic analyses of the ZUC cipher indicate that the cipher should be secure against algebraic attacks. In this paper, we present an alternative algebraic analysis method for the ZUC stream cipher, where a combiner is used to represent the nonlinear function and to derive equations representing the cipher. Using this approach, the initial states of ZUC can be recovered from 2^97 observed words of keystream, with a complexity of 2^282 operations. This method is more successful when applied to a modified version of ZUC, where the number of output words per clock is increased. If the cipher outputs 120 bits of keystream per clock, the attack can succeed with 219 observed keystream bits and 2^47 operations. Therefore, the security of ZUC against algebraic attack could be significantly reduced if its throughput was to be increased for efficiency.

Algebraic analysis of the SSS stream cipher

Both the SSS and SOBER-t32 stream cipher designs use a single word-based shift register and a nonlinear filter function to produce keystream. In this paper we show that the algebraic attack method previously applied to SOBER-t32 is prevented from succeeding on SSS by the use of the key dependent substitution box (SBox) in the nonlinear filter of SSS. Additional assumptions and modifications to the SSS cipher in an attempt to enable algebraic analysis result in other difficulties that also render the algebraic attack infeasible. Based on these results, we conclude that a well chosen key-dependent substitution box used in the nonlinear filter of the stream cipher provides resistance against such algebraic attacks.

State cycles, initialization and the Trivium stream cipher

Trivium is a keystream generator for a binary additive synchronous stream cipher. It was selected in the final portfolio for the Profile 2 category of the eSTREAM project. The keystream generator is constructed using bit- based shift registers. In this paper we present an alternate representation of Trivium using word-based shift registers, with a word size of three bits. This representation is useful for determining cycles of internal state values. Under this representation it is clear that the state space can be partitioned into subspaces and that over some of these subspaces the state update function is effectively linear. The role of the initialization process is critical in ensuring the states used for generating keystream are updated nonlinearly at some point, as the state update function alone does not provide this.

Algebraic analysis of Trivium-like ciphers

Trivium is a bit-based stream cipher in the final portfolio of the eSTREAM project. In this paper, we apply the approach of Berbain et al. to Trivium-like ciphers and perform new algebraic analyses on them, namely Trivium and its reduced versions: Trivium-N, Bivium-A and Bivium-B. In doing so, we answer an open question in the literature. We demonstrate a new algebraic attack on Bivium-A. This attack requires less time and memory than previous techniques which use the F4 algorithm to recover Bivium-A's initial state. Though our attacks on Bivium-B, Trivium and Trivium-N are worse than exhaustive keysearch, the systems of equations which are constructed are smaller and less complex compared to previous algebraic analysis. Factors which can affect the complexity of our attack on Trivium-like ciphers are discussed in detail.

Analysis of stream cipher based authenticated encryption schemes

Authenticated Encryption (AE) is the cryptographic process of providing simultaneous confidentiality and integrity protection to messages. This approach is more efficient than applying a two-step process of providing confidentiality for a message by encrypting the message, and in a separate pass providing integrity protection by generating a Message Authentication Code (MAC). AE using symmetric ciphers can be provided by either stream ciphers with built in authentication mechanisms or block ciphers using appropriate modes of operation. However, stream ciphers have the potential for higher performance and smaller footprint in hardware and/or software than block ciphers. This property makes stream ciphers suitable for resource constrained environments, where storage and computational power are limited. There have been several recent stream cipher proposals that claim to provide AE. These ciphers can be analysed using existing techniques that consider confidentiality or integrity separately; however currently there is no existing framework for the analysis of AE stream ciphers that analyses these two properties simultaneously. This thesis introduces a novel framework for the analysis of AE using stream cipher algorithms. This thesis analyzes the mechanisms for providing confidentiality and for providing integrity in AE algorithms using stream ciphers. There is a greater emphasis on the analysis of the integrity mechanisms, as there is little in the public literature on this, in the context of authenticated encryption. The thesis has four main contributions as follows. The first contribution is the design of a framework that can be used to classify AE stream ciphers based on three characteristics. The first classification applies Bellare and Namprempre's work on the the order in which encryption and authentication processes take place. The second classification is based on the method used for accumulating the input message (either directly or indirectly) into the into the internal states of the cipher to generate a MAC. The third classification is based on whether the sequence that is used to provide encryption and authentication is generated using a single key and initial vector, or two keys and two initial vectors. The second contribution is the application of an existing algebraic method to analyse the confidentiality algorithms of two AE stream ciphers; namely SSS and ZUC. The algebraic method is based on considering the nonlinear filter (NLF) of these ciphers as a combiner with memory. This method enables us to construct equations for the NLF that relate the (inputs, outputs and memory of the combiner) to the output keystream. We show that both of these ciphers are secure from this type of algebraic attack. We conclude that using a keydependent SBox in the NLF twice, and using two different SBoxes in the NLF of ZUC, prevents this type of algebraic attack. The third contribution is a new general matrix based model for MAC generation where the input message is injected directly into the internal state. This model describes the accumulation process when the input message is injected directly into the internal state of a nonlinear filter generator. We show that three recently proposed AE stream ciphers can be considered as instances of this model; namely SSS, NLSv2 and SOBER-128. Our model is more general than a previous investigations into direct injection. Possible forgery attacks against this model are investigated. It is shown that using a nonlinear filter in the accumulation process of the input message when either the input message or the initial states of the register is unknown prevents forgery attacks based on collisions. The last contribution is a new general matrix based model for MAC generation where the input message is injected indirectly into the internal state. This model uses the input message as a controller to accumulate a keystream sequence into an accumulation register. We show that three current AE stream ciphers can be considered as instances of this model; namely ZUC, Grain-128a and Sfinks. We establish the conditions under which the model is susceptible to forgery and side-channel attacks.

Algebraic analysis of Trivium-like ciphers

Trivium is a bit-based stream cipher in the final portfolio of the eSTREAM project. In this paper, we apply the algebraic attack approach of Berbain et al. to Trivium-like ciphers and perform new analyses on them. We demonstrate a new algebraic attack on Bivium-A. This attack requires less time and memory than previous techniques to recover Bivium-A's initial state. Though our attacks on Bivium-B, Trivium and Trivium-N are worse than exhaustive keysearch, the systems of equations which are constructed are smaller and less complex compared to previous algebraic analyses. We also answer an open question posed by Berbain et al. on the feasibility of applying their technique on Trivium-like ciphers. Factors which can affect the complexity of our attack on Trivium-like ciphers are discussed in detail. Analysis of Bivium-B and Trivium-N are omitted from this manuscript. The full paper is available on the IACR ePrint Archive.

Secure stream cipher initialisation processes

Stream ciphers are symmetric key cryptosystems that are used commonly to provide confidentiality for a wide range of applications; such as mobile phone, pay TV and Internet data transmissions. This research examines the features and properties of the initialisation processes of existing stream ciphers to identify flaws and weaknesses, then presents recommendations to improve the security of future cipher designs. This research investigates well-known stream ciphers: A5/1, Sfinks and the Common Scrambling Algorithm Stream Cipher (CSA-SC). This research focused on the security of the initialisation process. The recommendations given are based on both the results in the literature and the work in this thesis.

Securing implementations of feedback-shift-register-based ciphers using compiler optimizations and co-processors

Los algoritmos basados en registros de desplazamiento con realimentación (en inglés FSR) se han utilizado como generadores de flujos pseudoaleatorios en aplicaciones con recursos limitados como los sistemas de apertura sin llave. Se considera canal primario a aquel que se utiliza para realizar una transmisión de información. La aparición de los ataques de canal auxiliar (en inglés SCA), que explotan información filtrada inintencionadamente a través de canales laterales como el consumo, las emisiones electromagnéticas o el tiempo empleado, supone una grave amenaza para estas aplicaciones, dado que los dispositivos son accesibles por un atacante. El objetivo de esta tesis es proporcionar un conjunto de protecciones que se puedan aplicar de forma automática y que utilicen recursos ya disponibles, evitando un incremento sustancial en los costes y alargando la vida útil de aplicaciones que puedan estar desplegadas. Explotamos el paralelismo existente en algoritmos FSR, ya que sólo hay 1 bit de diferencia entre estados de rondas consecutivas. Realizamos aportaciones en tres niveles: a nivel de sistema, utilizando un coprocesador reconfigurable, a través del compilador y a nivel de bit, aprovechando los recursos disponibles en el procesador. Proponemos un marco de trabajo que nos permite evaluar implementaciones de un algoritmo incluyendo los efectos introducidos por el compilador considerando que el atacante es experto. En el campo de los ataques, hemos propuesto un nuevo ataque diferencial que se adapta mejor a las condiciones de las implementaciones software de FSR, en las que el consumo entre rondas es muy similar. SORU2 es un co-procesador vectorial reconfigurable propuesto para reducir el consumo energético en aplicaciones con paralelismo y basadas en el uso de bucles. Proponemos el uso de SORU2, además, para ejecutar algoritmos basados en FSR de forma segura. Al ser reconfigurable, no supone un sobrecoste en recursos, ya que no está dedicado en exclusiva al algoritmo de cifrado. Proponemos una configuración que ejecuta múltiples algoritmos de cifrado similares de forma simultánea, con distintas implementaciones y claves. A partir de una implementación sin protecciones, que demostramos que es completamente vulnerable ante SCA, obtenemos una implementación segura a los ataques que hemos realizado. A nivel de compilador, proponemos un mecanismo para evaluar los efectos de las secuencias de optimización del compilador sobre una implementación. El número de posibles secuencias de optimizaciones de compilador es extremadamente alto. El marco de trabajo propuesto incluye un algoritmo para la selección de las secuencias de optimización a considerar. Debido a que las optimizaciones del compilador transforman las implementaciones, se pueden generar automáticamente implementaciones diferentes combinamos para incrementar la seguridad ante SCA. Proponemos 2 mecanismos de aplicación de estas contramedidas, que aumentan la seguridad de la implementación original sin poder considerarse seguras. Finalmente hemos propuesto la ejecución paralela a nivel de bit del algoritmo en un procesador. Utilizamos la forma algebraica normal del algoritmo, que automáticamente se paraleliza. La implementación sobre el algoritmo evaluado mejora en rendimiento y evita que se filtre información por una ejecución dependiente de datos. Sin embargo, es más vulnerable ante ataques diferenciales que la implementación original. Proponemos una modificación del algoritmo para obtener una implementación segura, descartando parcialmente ejecuciones del algoritmo, de forma aleatoria. Esta implementación no introduce una sobrecarga en rendimiento comparada con las implementaciones originales. En definitiva, hemos propuesto varios mecanismos originales a distintos niveles para introducir aleatoridad en implementaciones de algoritmos FSR sin incrementar sustancialmente los recursos necesarios. ABSTRACT Feedback Shift Registers (FSR) have been traditionally used to implement pseudorandom sequence generators. These generators are used in Stream ciphers in systems with tight resource constraints, such as Remote Keyless Entry. When communicating electronic devices, the primary channel is the one used to transmit the information. Side-Channel Attack (SCA) use additional information leaking from the actual implementation, including power consumption, electromagnetic emissions or timing information. Side-Channel Attacks (SCA) are a serious threat to FSR-based applications, as an attacker usually has physical access to the devices. The main objective of this Ph.D. thesis is to provide a set of countermeasures that can be applied automatically using the available resources, avoiding a significant cost overhead and extending the useful life of deployed systems. If possible, we propose to take advantage of the inherent parallelism of FSR-based algorithms, as the state of a FSR differs from previous values only in 1-bit. We have contributed in three different levels: architecture (using a reconfigurable co-processor), using compiler optimizations, and at bit level, making the most of the resources available at the processor. We have developed a framework to evaluate implementations of an algorithm including the effects introduced by the compiler. We consider the presence of an expert attacker with great knowledge on the application and the device. Regarding SCA, we have presented a new differential SCA that performs better than traditional SCA on software FSR-based algorithms, where the leaked values are similar between rounds. SORU2 is a reconfigurable vector co-processor. It has been developed to reduce energy consumption in loop-based applications with parallelism. In addition, we propose its use for secure implementations of FSR-based algorithms. The cost overhead is discarded as the co-processor is not exclusively dedicated to the encryption algorithm. We present a co-processor configuration that executes multiple simultaneous encryptions, using different implementations and keys. From a basic implementation, which is proved to be vulnerable to SCA, we obtain an implementation where the SCA applied were unsuccessful. At compiler level, we use the framework to evaluate the effect of sequences of compiler optimization passes on a software implementation. There are many optimization passes available. The optimization sequences are combinations of the available passes. The amount of sequences is extremely high. The framework includes an algorithm for the selection of interesting sequences that require detailed evaluation. As existing compiler optimizations transform the software implementation, using different optimization sequences we can automatically generate different implementations. We propose to randomly switch between the generated implementations to increase the resistance against SCA.We propose two countermeasures. The results show that, although they increase the resistance against SCA, the resulting implementations are not secure. At bit level, we propose to exploit bit level parallelism of FSR-based implementations using pseudo bitslice implementation in a wireless node processor. The bitslice implementation is automatically obtained from the Algebraic Normal Form of the algorithm. The results show a performance improvement, avoiding timing information leakage, but increasing the vulnerability against differential SCA.We provide a secure version of the algorithm by randomly discarding part of the data obtained. The overhead in performance is negligible when compared to the original implementations. To summarize, we have proposed a set of original countermeasures at different levels that introduce randomness in FSR-based algorithms avoiding a heavy overhead on the resources required.

Algebraic analysis of small scale LEX-BES

This paper examines the algebraic cryptanalysis of small scale variants of the LEX-BES. LEX-BES is a stream cipher based on the Advanced Encryption Standard (AES) block cipher. LEX is a generic method proposed for constructing a stream cipher from a block cipher, initially introduced by Biryukov at eSTREAM, the ECRYPT Stream Cipher project in 2005. The Big Encryption System (BES) is a block cipher introduced at CRYPTO 2002 which facilitates the algebraic analysis of the AES block cipher. In this paper, experiments were conducted to find solution of the equation system describing small scale LEX-BES using Gröbner Basis computations. This follows a similar approach to the work by Cid, Murphy and Robshaw at FSE 2005 that investigated algebraic cryptanalysis on small scale variants of the BES. The difference between LEX-BES and BES is that due to the way the keystream is extracted, the number of unknowns in LEX-BES equations is fewer than the number in BES. As far as the author knows, this attempt is the first at creating solvable equation systems for stream ciphers based on the LEX method using Gröbner Basis computations.

Improved algebraic cryptanalysis of QUAD, Bivium and Trivium via graph partitioning on equation systems

We present a novel approach for preprocessing systems of polynomial equations via graph partitioning. The variable-sharing graph of a system of polynomial equations is defined. If such graph is disconnected, then the corresponding system of equations can be split into smaller ones that can be solved individually. This can provide a tremendous speed-up in computing the solution to the system, but is unlikely to occur either randomly or in applications. However, by deleting certain vertices on the graph, the variable-sharing graph could be disconnected in a balanced fashion, and in turn the system of polynomial equations would be separated into smaller systems of near-equal sizes. In graph theory terms, this process is equivalent to finding balanced vertex partitions with minimum-weight vertex separators. The techniques of finding these vertex partitions are discussed, and experiments are performed to evaluate its practicality for general graphs and systems of polynomial equations. Applications of this approach in algebraic cryptanalysis on symmetric ciphers are presented: For the QUAD family of stream ciphers, we show how a malicious party can manufacture conforming systems that can be easily broken. For the stream ciphers Bivium and Trivium, we nachieve significant speedups in algebraic attacks against them, mainly in a partial key guess scenario. In each of these cases, the systems of polynomial equations involved are well-suited to our graph partitioning method. These results may open a new avenue for evaluating the security of symmetric ciphers against algebraic attacks.

Bias in the nonlinear filter generator output sequence

Nonlinear filter generators are common components used in the keystream generators for stream ciphers and more recently for authentication mechanisms. They consist of a Linear Feedback Shift Register (LFSR) and a nonlinear Boolean function to mask the linearity of the LFSR output. Properties of the output of a nonlinear filter are not well studied. Anderson noted that the m-tuple output of a nonlinear filter with consecutive taps to the filter function is unevenly distributed. Current designs use taps which are not consecutive. We examine m-tuple outputs from nonlinear filter generators constructed using various LFSRs and Boolean functions for both consecutive and uneven (full positive difference sets where possible) tap positions. The investigation reveals that in both cases, the m-tuple output is not uniform. However, consecutive tap positions result in a more biased distribution than uneven tap positions, with some m-tuples not occurring at all. These biased distributions indicate a potential flaw that could be exploited for cryptanalysis.

Bias in the nonlinear filter generator output sequence

Nonlinear filter generators are common components used in the keystream generators for stream ciphers and more recently for authentication mechanisms. They consist of a Linear Feedback Shift Register (LFSR) and a nonlinear Boolean function to mask the linearity of the LFSR output. Properties of the output of a nonlinear filter are not well studied. Anderson noted that the m-tuple output of a nonlinear filter with consecutive taps to the filter function is unevenly distributed. Current designs use taps which are not consecutive. We examine m-tuple outputs from nonlinear filter generators constructed using various LFSRs and Boolean functions for both consecutive and uneven (full positive difference sets where possible) tap positions. The investigation reveals that in both cases, the m-tuple output is not uniform. However, consecutive tap positions result in a more biased distribution than uneven tap positions, with some m-tuples not occurring at all. These biased distributions indicate a potential flaw that could be exploited for cryptanalysis

Algebraic analysis of small Scale LEX-BES

This work examines the algebraic cryptanalysis of small scale variants of the LEX-BES. LEX-BES is a stream cipher based on the Advanced Encryption Standard (AES) block cipher. LEX is a generic method proposed for constructing a stream cipher from a block cipher, initially introduced by Biryukov at eSTREAM, the ECRYPT Stream Cipher project in 2005. The Big Encryption System (BES) is a block cipher introduced at CRYPTO 2002 which facilitates the algebraic analysis of the AES block cipher. In this article, experiments were conducted to find solutions of equation systems describing small scale LEX-BES using Gröbner Basis computations. This follows a similar approach to the work by Cid, Murphy and Robshaw at FSE 2005 that investigated algebraic cryptanalysis on small scale variants of the BES. The difference between LEX-BES and BES is that due to the way the keystream is extracted, the number of unknowns in LEX-BES equations is fewer than the number in BES. As far as the authors know, this attempt is the first at creating solvable equation systems for stream ciphers based on the LEX method using Gröbner Basis computations.