Fast Algebraic Attacks and Decomposition of Symmetric Boolean Functions

Algebraic and fast algebraic attacks are power tools to analyze stream ciphers. A class of symmetric Boolean functions with maximum algebraic immunity were found vulnerable to fast algebraic attacks at EUROCRYPT'06. Recently, the notion of AAR (algebraic attack resistant) functions was introduced as a unified measure of protection against both classical algebraic and fast algebraic attacks. In this correspondence, we first give a decomposition of symmetric Boolean functions, then we show that almost all symmetric Boolean functions, including these functions with good algebraic immunity, behave badly against fast algebraic attacks, and we also prove that no symmetric Boolean functions are AAR functions. Besides, we improve the relations between algebraic degree and algebraic immunity of symmetric Boolean functions.Comment: 13 pages, submitted to IEEE Transactions on Information Theor

Algebraic Attack on the Alternating Step(r,s)Generator

The Alternating Step(r,s) Generator, ASG(r,s), is a clock-controlled sequence generator which is recently proposed by A. Kanso. It consists of three registers of length l, m and n bits. The first register controls the clocking of the two others. The two other registers are clocked r times (or not clocked) (resp. s times or not clocked) depending on the clock-control bit in the first register. The special case r=s=1 is the original and well known Alternating Step Generator. Kanso claims there is no efficient attack against the ASG(r,s) since r and s are kept secret. In this paper, we present an Alternating Step Generator, ASG, model for the ASG(r,s) and also we present a new and efficient algebraic attack on ASG(r,s) using 3(m+n) bits of the output sequence to find the secret key with O((m^2+n^2)*2^{l+1}+ (2^{m-1})*m^3 + (2^{n-1})*n^3) computational complexity. We show that this system is no more secure than the original ASG, in contrast to the claim of the ASG(r,s)'s constructor.Comment: 5 pages, 2 figures, 2 tables, 2010 IEEE International Symposium on Information Theory (ISIT2010),June 13-18, 2010, Austin, Texa

New Family of Stream Ciphers as Physically Clone-Resistant VLSI-Structures

A new large class of $2^{100}$ possible stream ciphers as keystream generators KSGs, is presented. The sample cipher-structure-concept is based on randomly selecting a set of 16 maximum-period Nonlinear Feedback Shift Registers (NLFSRs). A non-linear combining function is merging the 16 selected sequences. All resulting stream ciphers with a total state-size of 223 bits are designed to result with the same security level and have a linear complexity exceeding $2^{81}$ and a period exceeding $2^{161}$. A Secret Unknown Cipher (SUC) is created randomly by selecting one cipher from that class of $2^{100}$ ciphers. SUC concept was presented recently as a physical security anchor to overcome the drawbacks of the traditional analog Physically Unclonable Functions (PUFs). Such unknown ciphers may be permanently self-created within System-on-Chip SoC non-volatile FPGA devices to serve as a digital clone-resistant structure. Moreover, a lightweight identification protocol is presented in open networks for physically identifying such SUC structures in FPGA-devices. The proposed new family may serve for lightweight realization of clone-resistant identities in future self-reconfiguring SoC non-volatile FPGAs. Such self-reconfiguring FPGAs are expected to be emerging in the near future smart VLSI systems. The security analysis and hardware complexities of the resulting clone-resistant structures are evaluated and shown to exhibit scalable security levels even for post-quantum cryptography.Comment: 24 pages, 7 Figures, 3 Table

MV3: A new word based stream cipher using rapid mixing and revolving buffers

MV3 is a new word based stream cipher for encrypting long streams of data. A direct adaptation of a byte based cipher such as RC4 into a 32- or 64-bit word version will obviously need vast amounts of memory. This scaling issue necessitates a look for new components and principles, as well as mathematical analysis to justify their use. Our approach, like RC4's, is based on rapidly mixing random walks on directed graphs (that is, walks which reach a random state quickly, from any starting point). We begin with some well understood walks, and then introduce nonlinearity in their steps in order to improve security and show long term statistical correlations are negligible. To minimize the short term correlations, as well as to deter attacks using equations involving successive outputs, we provide a method for sequencing the outputs derived from the walk using three revolving buffers. The cipher is fast -- it runs at a speed of less than 5 cycles per byte on a Pentium IV processor. A word based cipher needs to output more bits per step, which exposes more correlations for attacks. Moreover we seek simplicity of construction and transparent analysis. To meet these requirements, we use a larger state and claim security corresponding to only a fraction of it. Our design is for an adequately secure word-based cipher; our very preliminary estimate puts the security close to exhaustive search for keys of size < 256 bits.Comment: 27 pages, shortened version will appear in "Topics in Cryptology - CT-RSA 2007

On the Design and Analysis of Stream Ciphers

This thesis presents new cryptanalysis results for several different stream cipher constructions. In addition, it also presents two new stream ciphers, both based on the same design principle. The first attack is a general attack targeting a nonlinear combiner. A new class of weak feedback polynomials for linear feedback shift registers is identified. By taking samples corresponding to the linear recurrence relation, it is shown that if the feedback polynomial has taps close together an adversary to take advantage of this by considering the samples in a vector form. Next, the self-shrinking generator and the bit-search generator are analyzed. Both designs are based on irregular decimation. For the self-shrinking generator, it is shown how to recover the internal state knowing only a few keystream bits. The complexity of the attack is similar to the previously best known but uses a negligible amount of memory. An attack requiring a large keystream segment is also presented. It is shown to be asymptotically better than all previously known attacks. For the bit-search generator, an algorithm that recovers the internal state is given as well as a distinguishing attack that can be very efficient if the feedback polynomial is not carefully chosen. Following this, two recently proposed stream cipher designs, Pomaranch and Achterbahn, are analyzed. Both stream ciphers are designed with small hardware complexity in mind. For Pomaranch Version 2, based on an improvement of previous analysis of the design idea, a key recovery attack is given. Also, for all three versions of Pomaranch, a distinguishing attack is given. For Achterbahn, it is shown how to recover the key of the latest version, known as Achterbahn-128/80. The last part of the thesis introduces two new stream cipher designs, namely Grain and Grain-128. The ciphers are designed to be very small in hardware. They also have the distinguishing feature of allowing users to increase the speed of the ciphers by adding extra hardware

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