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

Fast algebraic immunity of Boolean functions and LCD codes

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

Algebraic construction of semi bent function via known power function

The study of semi bent functions (2- plateaued Boolean function) has attracted the attention of many researchers due to their cryptographic and combinatorial properties. In this paper, we have given the algebraic construction of semi bent functions defined over the finite field F₂ⁿ (n even) using the notion of trace function and Gold power exponent. Algebraically constructed semi bent functions have some special cryptographical properties such as high nonlinearity, algebraic immunity, and low correlation immunity as expected to use them effectively in cryptosystems. We have illustrated the existence of these properties with suitable examples.Publisher's Versio

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

Strengthening Crypto-1 Cipher Against Algebraic Attacks

In the last few years, several studies addressed the problem of data security in Mifare Classic. One of its weaknesses is the low random number quality. This causes SAT solver attacks to have lower complexity. In order to strengthen Crypto-1 against SAT solver attacks, a modification of the feedback function with better cryptographic properties is proposed. It applies a primitive polynomial companion matrix. SAT solvers cannot directly attack the feedback shift register that uses the modified Boolean feedback function, the register has to be split into smaller groups. Experimental testing showed that the amount of memory and CPU time needed were highest when attacking the modified Crypto-1 using the modified feedback function and the original filter function. In addition, another modified Crypto-1, using the modified feedback function and a modified filter function, had the lowest percentage of revealed variables. It can be concluded that the security strength and performance of the modified Crypto-1 using the modified feedback function and the modified filter function are better than those of the original Crypto-1

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

Implementing Symmetric Cryptography Using Sequence of Semi-Bent Functions

Symmetric cryptography is a cornerstone of everyday digital security, where two parties must share a common key to communicate. The most common primitives in symmetric cryptography are stream ciphers and block ciphers that guarantee confidentiality of communications and hash functions for integrity. Thus, for securing our everyday life communication, it is necessary to be convinced by the security level provided by all the symmetric-key cryptographic primitives. The most important part of a stream cipher is the key stream generator, which provides the overall security for stream ciphers. Nonlinear Boolean functions were preferred for a long time to construct the key stream generator. In order to resist several known attacks, many requirements have been proposed on the Boolean functions. Attacks against the cryptosystems have forced deep research on Boolean function to allow us a more secure encryption. In this work we describe all main requirements for constructing of cryptographically significant Boolean functions. Moreover, we provide a construction of Boolean functions (semi-bent Boolean functions) which can be used in the construction of orthogonal variable spreading factor codes used in code division multiple access (CDMA) systems as well as in certain cryptographic applications

07021 Abstracts Collection -- Symmetric Cryptography

From .. to .., the Dagstuhl Seminar 07021 ``Symmetric Cryptography\u27\u27 automatically was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available