424 research outputs found

    Fast Algebraic Attacks and Decomposition of Symmetric Boolean Functions

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    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

    Synchronization of spatiotemporal semiconductor lasers and its application in color image encryption

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    Optical chaos is a topic of current research characterized by high-dimensional nonlinearity which is attributed to the delay-induced dynamics, high bandwidth and easy modular implementation of optical feedback. In light of these facts, which adds enough confusion and diffusion properties for secure communications, we explore the synchronization phenomena in spatiotemporal semiconductor laser systems. The novel system is used in a two-phase colored image encryption process. The high-dimensional chaotic attractor generated by the system produces a completely randomized chaotic time series, which is ideal in the secure encoding of messages. The scheme thus illustrated is a two-phase encryption method, which provides sufficiently high confusion and diffusion properties of chaotic cryptosystem employed with unique data sets of processed chaotic sequences. In this novel method of cryptography, the chaotic phase masks are represented as images using the chaotic sequences as the elements of the image. The scheme drastically permutes the positions of the picture elements. The next additional layer of security further alters the statistical information of the original image to a great extent along the three-color planes. The intermediate results during encryption demonstrate the infeasibility for an unauthorized user to decipher the cipher image. Exhaustive statistical tests conducted validate that the scheme is robust against noise and resistant to common attacks due to the double shield of encryption and the infinite dimensionality of the relevant system of partial differential equations.Comment: 20 pages, 11 figures; Article in press, Optics Communications (2011

    Attacks Against Filter Generators Exploiting Monomial Mappings

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    International audienceFilter generators are vulnerable to several attacks which have led to well-known design criteria on the Boolean filtering function. However , Rønjom and Cid have observed that a change of the primitive root defining the LFSR leads to several equivalent generators. They usually offer different security levels since they involve filtering functions of the form F (x k) where k is coprime to (2 n − 1) and n denotes the LFSR length. It is proved here that this monomial equivalence does not affect the resistance of the generator against algebraic attacks, while it usually impacts the resistance to correlation attacks. Most importantly, a more efficient attack can often be mounted by considering non-bijective mono-mial mappings. In this setting, a divide-and-conquer strategy applies based on a search within a multiplicative subgroup of F * 2 n. Moreover, if the LFSR length n is not a prime, a fast correlation involving a shorter LFSR can be performed

    Fast algebraic immunity of Boolean functions and LCD codes

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    Nowadays, the resistance against algebraic attacks and fast algebraic attacks are considered as an important cryptographic property for Boolean functions used in stream ciphers. Both attacks are very powerful analysis concepts and can be applied to symmetric cryptographic algorithms used in stream ciphers. The notion of algebraic immunity has received wide attention since it is a powerful tool to measure the resistance of a Boolean function to standard algebraic attacks. Nevertheless, an algebraic tool to handle the resistance to fast algebraic attacks is not clearly identified in the literature. In the current paper, we propose a new parameter to measure the resistance of a Boolean function to fast algebraic attack. We also introduce the notion of fast immunity profile and show that it informs both on the resistance to standard and fast algebraic attacks. Further, we evaluate our parameter for two secondary constructions of Boolean functions. Moreover, A coding-theory approach to the characterization of perfect algebraic immune functions is presented. Via this characterization, infinite families of binary linear complementary dual codes (or LCD codes for short) are obtained from perfect algebraic immune functions. The binary LCD codes presented in this paper have applications in armoring implementations against so-called side-channel attacks (SCA) and fault non-invasive attacks, in addition to their applications in communication and data storage systems

    Contributions to Confidentiality and Integrity Algorithms for 5G

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    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

    On the Immunity of Rotation Symmetric Boolean Functions Against Fast Algebraic Attacks

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    In this paper, it is shown that an nn-variable rotation symmetric Boolean function ff with nn even but not a power of 2 admits a rotation symmetric function gg of degree at most e≤n/3e\leq n/3 such that the product gfgf has degree at most n−e−1n-e-1

    Design and Analysis of Cryptographic Pseudorandom Number/Sequence Generators with Applications in RFID

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    This thesis is concerned with the design and analysis of strong de Bruijn sequences and span n sequences, and nonlinear feedback shift register (NLFSR) based pseudorandom number generators for radio frequency identification (RFID) tags. We study the generation of span n sequences using structured searching in which an NLFSR with a class of feedback functions is employed to find span n sequences. Some properties of the recurrence relation for the structured search are discovered. We use five classes of functions in this structured search, and present the number of span n sequences for 6 <= n <= 20. The linear span of a new span n sequence lies between near-optimal and optimal. According to our empirical studies, a span n sequence can be found in the structured search with a better probability of success. Newly found span n sequences can be used in the composited construction and in designing lightweight pseudorandom number generators. We first refine the composited construction based on a span n sequence for generating long de Bruijn sequences. A de Bruijn sequence produced by the composited construction is referred to as a composited de Bruijn sequence. The linear complexity of a composited de Bruijn sequence is determined. We analyze the feedback function of the composited construction from an approximation point of view for producing strong de Bruijn sequences. The cycle structure of an approximated feedback function and the linear complexity of a sequence produced by an approximated feedback function are determined. A few examples of strong de Bruijn sequences with the implementation issues of the feedback functions of an (n+16)-stage NLFSR are presented. We propose a new lightweight pseudorandom number generator family, named Warbler family based on NLFSRs for smart devices. Warbler family is comprised of a combination of modified de Bruijn blocks (CMDB) and a nonlinear feedback Welch-Gong (WG) generator. We derive the randomness properties such as period and linear complexity of an output sequence produced by the Warbler family. Two instances, Warbler-I and Warbler-II, of the Warbler family are proposed for passive RFID tags. The CMDBs of both Warbler-I and Warbler-II contain span n sequences that are produced by the structured search. We analyze the security properties of Warbler-I and Warbler-II by considering the statistical tests and several cryptanalytic attacks. Hardware implementations of both instances in VHDL show that Warbler-I and Warbler-II require 46 slices and 58 slices, respectively. Warbler-I can be used to generate 16-bit random numbers in the tag identification protocol of the EPC Class 1 Generation 2 standard, and Warbler-II can be employed as a random number generator in the tag identification as well as an authentication protocol for RFID systems.1 yea

    Design of Stream Ciphers and Cryptographic Properties of Nonlinear Functions

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    Block and stream ciphers are widely used to protect the privacy of digital information. A variety of attacks against block and stream ciphers exist; the most recent being the algebraic attacks. These attacks reduce the cipher to a simple algebraic system which can be solved by known algebraic techniques. These attacks have been very successful against a variety of stream ciphers and major efforts (for example eSTREAM project) are underway to design and analyze new stream ciphers. These attacks have also raised some concerns about the security of popular block ciphers. In this thesis, apart from designing new stream ciphers, we focus on analyzing popular nonlinear transformations (Boolean functions and S-boxes) used in block and stream ciphers for various cryptographic properties, in particular their resistance against algebraic attacks. The main contribution of this work is the design of two new stream ciphers and a thorough analysis of the algebraic immunity of Boolean functions and S-boxes based on power mappings. First we present WG, a family of new stream ciphers designed to obtain a keystream with guaranteed randomness properties. We show how to obtain a mathematical description of a WG stream cipher for the desired randomness properties and security level, and then how to translate this description into a practical hardware design. Next we describe the design of a new RC4-like stream cipher suitable for high speed software applications. The design is compared with original RC4 stream cipher for both security and speed. The second part of this thesis closely examines the algebraic immunity of Boolean functions and S-boxes based on power mappings. We derive meaningful upper bounds on the algebraic immunity of cryptographically significant Boolean power functions and show that for large input sizes these functions have very low algebraic immunity. To analyze the algebraic immunity of S-boxes based on power mappings, we focus on calculating the bi-affine and quadratic equations they satisfy. We present two very efficient algorithms for this purpose and give new S-box constructions that guarantee zero bi-affine and quadratic equations. We also examine these S-boxes for their resistance against linear and differential attacks and provide a list of S-boxes based on power mappings that offer high resistance against linear, differential, and algebraic attacks. Finally we investigate the algebraic structure of S-boxes used in AES and DES by deriving their equivalent algebraic descriptions

    Modified SHARK Cipher and Duffing Map-Based Cryptosystem

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    Recent years have seen a lot of interest in the study of chaotic structures and their accompanying cryptography frameworks. In this research, we came up with a new way to encrypt images that used the chaos and a modified block cipher named the SHARK cipher. The new algorithm looks at the creation of random sequences as a problem that needs to be solved in the best way possible, and then it uses the Duffing chaotic map to get even better random sequences. Chaos has been combined with a revised edition of the SHARK structure to make the algorithm design more robust with increased confusion and diffusion. The offered algorithm includes a complex encryption and decryption structure with minimal time consumption for secure data transmission. The proposed algorithm is verified with the encryption of some standard images of different sizes. Numerous analyses have been performed to see how well the algorithm works against a variety of assaults, and the outcomes show that the cryptosystem has a good level of robustness. The comparative results are also performed in this work, which guarantees the excellent performance of our cryptosystem. The system is also subjected to chosen-plaintext and chosen-ciphertext attacks which implies that it can resist many classical cryptographic attacks. Therefore, our cryptosystem is robust enough to use for image encryption
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