Important Cryptographic Properties Research Articles

Computational Analysis of Interleaving PN-Sequences with Different Polynomials

Binary PN-sequences generated by LFSRs exhibit good statistical properties; however, due to their intrinsic linearity, they are not suitable for cryptographic applications. In order to break such a linearity, several approaches can be implemented. For example, one can interleave several PN-sequences to increase the linear complexity. In this work, we present a deep randomness study of the resultant sequences of interleaving binary PN-sequences coming from different characteristic polynomials with the same degree. We analyze the period and the linear complexity, as well as many other important cryptographic properties of such sequences.

Interleaving Shifted Versions of a PN-Sequence

The output sequence of the shrinking generator can be considered as an interleaving of determined shifted versions of a single PN -sequence. In this paper, we present a study of the interleaving of a PN-sequence and shifted versions of itself. We analyze some important cryptographic properties as the period and the linear complexity in terms of the shifts. Furthermore, we determine the total number of the interleaving sequences that achieve each possible value of the linear complexity.

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 a Boolean function's resistance 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. Some of the binary LCD codes presented in this paper are optimal. These binary LCD codes 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.

Cryptographic Strength Evaluation of AES S-box Variants

In recent years, researchers have constructed AES s-box variants by customising the values of the parameters in the equation of AES s-box. Strength of these s-box variants is evaluated against the cryptographic properties like avalanche effect, nonlinearity and bit independence criteria, however, there are other important cryptographic properties of s-box, which need to be evaluated before adopting the s-box. In this paper, all types of AES s-box variants are reproduced and evaluated against ten cryptographic properties. The results of five properties, differential and linear probability, nonlinearity, balance and algebraic degree remains the same for any s-box variant due to isomorphic equivalence nature of the variants; whereas, strict avalanche effect, bit independence criteria, correlation immunity, cyclic and fix-point properties showed different results for different s-box variant. Finally, the results are compared with the standard AES s-box and conclusion of overall security of s-box variants with respect to selected properties is conferred.

New Constructions of Binary Interleaved Sequences with Low Autocorrelation

The autocorrelation of a key stream sequence in a stream cipher is an important cryptographic property. This paper proposes two constructions of binary interleaved sequences of period 4N by selecting appropriate shift sequences, subsequences and complement sequences. And the autocorrelation functions of new sequences are given. The results show that these sequences have low autocorrelation under certain conditions.

A Note on 5-bit Quadratic Permutations’ Classification

Classification of vectorial Boolean functions up to affine equivalence is used widely to analyze various cryptographic and implementation properties of symmetric-key algorithms. We show that there exist 75 affine equivalence classes of 5-bit quadratic permutations. Furthermore, we explore important cryptographic properties of these classes, such as linear and differential properties and degrees of their inverses, together with multiplicative complexity and existence of uniform threshold realizations.

DIRECT EXPONENT AND SCALAR MULTIPLICATION TRANSFORMATIONS OF MDS MATRICES: SOME GOOD CRYPTOGRAPHIC RESULTS FOR DYNAMIC DIFFUSION LAYERS OF BLOCK CIPHERS

Abstract: MDS (Maximum Distance Separable) matrices have an important role in the design of block ciphers and hash functions. The methods for transforming an MDS matrix into other ones have been proposed by many authors in the literature. In this paper, some new results about direct exponent and scalar multiplication transformations are given including the preservation of good cryptographic properties (the coefficient of fixed points and involutory property) of MDS matrices and other important cryptographic properties obtained from studying equivalence relations based on these transformations. An estimation of the number of MDS matrices over is also presented. In addition, these results are shown to be an important theoretical basis for building efficient dynamic diffusion layer algorithms for block ciphers.

Cryptographic Boolean functions: One output, many design criteria

Boolean functions represent an important primitive in the design of various cryptographic algorithms. There exist several well-known schemes where a Boolean function is used to add nonlinearity to the cipher. Thus, methods to generate Boolean functions that possess good cryptographic properties present an important research goal. Among other techniques, evolutionary computation has proved to be a well-suited approach for this problem. In this paper, we present three different objective functions, where each inspects important cryptographic properties of Boolean functions, and examine four evolutionary algorithms. Our research confirms previous results, but also sheds new insights on the effectiveness and comparison of different evolutionary algorithms for this problem.

Algebraic immunities of vector-valued functions over finite fields

Algebraic immunity is an important cryptographic property of Boolean functions. The notion of algebraic immunity of Boolean functions has been generalized in several ways to vector-valued functions over arbitrary finite fields. In this paper, the results of Ref. [25] are generalized to arbitrary finite fields. We obtain vector-valued functions over arbitrary finite fields such that their algebraic immunities can reach the upper bounds. Furthermore, all the component functions, together with their some nonzero linear combinations, of vector-valued Boolean functions achieved by this construction have optimal algebraic immunities simultaneously.

On the construction of odd-variable boolean functions with optimal algebraic immunity

Algebraic immunity is an important cryptographic property of Boolean functions. In this paper, odd-variable balanced Boolean functions with optimal algebraic immunity are obtained by m-sequence and consequently, we get bases with special constructions of vector space. Furthermore, through swapping some vectors of these two bases, we establish all kinds of odd-variable balanced Boolean functions with optimal algebraic immunity.

Analysis of Algebraic Immunity for Balanced Boolean Function On 4-Variable

Algebraic immunity and balancedness have been widely investigated as important cryptographic properties .Boolean functions with high algebraic immunity can resist algebraic attacks. So, Boolean functions which achieve maximum algebraic immunity and balancedness are our research objects. In this paper, we present a method to study the algebraic immunity of balanced Boolean functions on 4-variable from the rank of matrix, and indicate that all 4-variable balanced Boolean functions with algebraic degree not less than 2 have maximum algebraic immunity. Finally, we introduce two classes balanced functions on even variables which don't achieve maximum algebraic immunity.

Algebraic construction of cryptographically good binary linear transformations

Maximum Distance Separable MDS and Maximum Distance Binary Linear MDBL codes are used as diffusion layers in the design of the well-known block ciphers like the Advanced Encryption Standard, Khazad, Camellia, and ARIA. The reason for the use of these codes in the design of block ciphers is that they provide optimal diffusion effect to meet security of a round function of a block cipher. On the other hand, the constructions of these diffusion layers are various. For example, whereas the Advanced Encryption Standard uses a 4×4 MDS matrix over GF28, ARIA uses a 16×16 involutory binary matrix over GF28. The most important cryptographic property of a diffusion layer is the branch number of that diffusion layer, which represents the diffusion rate and measures security against linear and differential cryptanalysis. Therefore, MDS and Maximum Distance Binary Linear codes, which provide maximum branch number for a diffusion layer, are preferred in the design of block ciphers as diffusion layers. In this paper, we present a new algebraic construction method based on MDS codes for 8×8 and 16×16 involutory and non-involutory binary matrices of branch numbers 5 and 8, respectively. By using this construction method, we also show some examples of these diffusion layers. Copyright © 2012 John Wiley & Sons, Ltd.

Rotation symmetric Boolean functions—Count and cryptographic properties

Rotation symmetric ( RotS) Boolean functions have been used as components of different cryptosystems. This class of Boolean functions are invariant under circular translation of indices. Using Burnside's lemma it can be seen that the number of n-variable rotation symmetric Boolean functions is 2 g n , where g n = ( 1 / n ) ∑ t | n φ ( t ) 2 n / t , and φ ( . ) is the Euler phi-function. In this paper, we find the number of short and long cycles of elements in F 2 n having fixed weight, under the RotS action. As a consequence we obtain the number of homogeneous RotS functions having algebraic degree w . Our results make the search space of RotS functions much reduced and we successfully analyzed important cryptographic properties of such functions by executing computer programs. We study RotS bent functions up to 10 variables and observe (experimentally) that there is no homogeneous rotation symmetric bent function having degree > 2 . Further, we studied the RotS functions on 5 , 6 , 7 variables by computer search for correlation immunity and propagation characteristics and found some functions with very good cryptographic properties which were not known earlier.

Rotation Symmetric Boolean Functions –; Count and Cryptographic Properties

Abstract In 1999, Pieprzyk and Qu presented rotation symmetric (RotS) functions as components in the rounds of hashing algorithm. Later, in 2002, Cusick and Stǎnicǎ presented further advancement in this area. This class of Boolean functions are invariant under circular translation of indices. In this paper, using Burnside's lemma, we prove that the number of n-variable rotation symmetric Boolean functions is 2gn, where gn and φ is the Euler phi-function. Moreover, we find the number of short and long cycles of elements in Zn2 having fixed weight, under the RotS action. As a consequence we obtain the number of homogeneous RotS functions having algebraic degree w. Our results make the search space of RotS functions much reduced and we successfully analyzed important cryptographic properties of such functions by executing computer programs. We found that there are exactly 8, 48, and 15104, RotS bent functions on 4, 6, and 8 variables respectively. Experimental results up to 10 variables show that there is no homogeneous rotation symmetric bent function with degree > 2. Further, we studied the RotS functions on 5, 6, 7 variables for correlation immunity and propagation characteristics and found some functions with very good cryptographic properties which were not known earlier.