The security of symmetric cryptosystem depends upon the cryptographic properties of Boolean function, e.g. balancedness, high nonlinearity, and low autocorrelation used as primitives in their designs. The problem of finding such Boolean functions satisfying multiple cryptographic properties is computationally hard, since the search space consisting of all n variable Boolean functions are 22n. The most common methods used for constructing Boolean functions are the random generation, algebraic construction and evolutionary techniques. In this paper, we use the Genetic algorithm to construct balanced Boolean function with Clark's cost function with high nonlinearity and low autocorrelation. Our main focus is to analyze the Clark's cost function with different values of tuning parameter using Genetic algorithm and compares the results obtained with the nonlinearity as a cost function.

Lizard is a very recently proposed lightweight stream cipher that claims 60 bit security against distinguishing (related to state recovery) and 80 bit security against key recovery attack. This cipher has 121 bit state size. In this paper, we first note that using ψ key stream bits one can recover ψ unknown bits of the state when t state bits are fixed to a specific pattern. This is made possible by guessing the remaining state bits. We present certain values of ψ, t based on the state size that helps in mounting a generic conditional TMDTO attack following the BSW sampling. For Lizard, we obtain the preprocessing complexity as 267, and the maximum of Data, Time and Memory complexity during the online phase as 254. The parameters in the online phase are significantly less than 260.

Two (so-called 𝒞, D) classes of permutation-based bent Boolean functions were introduced by Carlet [4] two decades ago, but without specifying some explicit construction methods for their construction (apart from the subclass 𝒟 0 ). In this article, we look in more detail at the 𝒞 class, and derive some existence and nonexistence results concerning the bent functions in the 𝒞 class for many of the known classes of permutations over 𝔽 2 n . Most importantly, the existence results induce generic methods of constructing bent functions in class 𝒞 which possibly do not belong to the completed Maiorana-McFarland class. The question whether the specific permutations and related subspaces we identify in this article indeed give bent functions outside the completed Maiorana-McFarland class remains open.

In this paper, we consider the spectra of Boolean functions with respect to the action of unitary transforms obtained by taking tensor products of the Hadamard kernel, denoted byH, and the nega-Hadamard kernel, denoted byN. The set of all such transforms is denoted by {H,N}n. A Boolean function is said to be bent4if its spectrum with respect to at least one unitary transform in {H,N}nis flat. We obtain a relationship between bent, semibent, and bent4functions, which is a generalization of the relationship between bent and negabent Boolean functions proved by Parker and Pott [cf., LNCS 4893 (2007), 9-23]. As a corollary to this result, we prove that the maximum possible algebraic degree of a bent4function onnvariables is [n/2] and, hence, solve an open problem posed by Riera and Parker [cf., IEEE-TIT 52:9 (2006), 4142-4159].

In this paper we study the lower bounds of second-order nonlinearities of bent functions in the class D0 constructed by modifying certain cubic Maiorana-McFarland (MMF) type bent functions. We also obtain improvements on existing results on second-or

A novel technique for cryptanalysis of the stream cipher Grain-v1 is given. In a particular setting, the algorithms proposed in this study provide recovery of an internal state of Grain-v1 with the expected time complexity of only 254 table look-up operations employing a memory of dimension ∼270, assuming availability of 234 keystream sequences each of length 238 generated for different initial values, and the pre-processing time complexity of ∼288. These figures appear as significantly better in comparison with the previously reported ones. The proposed approach for cryptanalysis primarily depends on the order of normality of the employed Boolean function in Grain-v1. Accordingly, in addition to the security evaluation insights of Grain-v1, the results of this study are also an evidence of the cryptographic significance of the normality criteria of Boolean functions.

Parkerconsidered a new type of discrete Fourier transform, called nega-Hadamard transform. We prove several results regarding its behavior on combinations of Boolean functions and use this theory to derive several results on negabentness (that is, flat nega-spectrum) of concatenations, and partially symmetric functions. We derive the upper bound$\lceil {{ n}\over { 2}} \rceil $for the algebraic degree of a negabent function on$n$variables. Further, a characterization of bent–negabent functions is obtained within a subclass of the Maiorana–McFarland set. We develop a technique to construct bent–negabent Boolean functions by using complete mapping polynomials. Using this technique, we demonstrate that for each$\ell \geq 2$, there exist bent–negabent functions on$n = 12\ell $variables with algebraic degree$ {{ n}\over { 4}}+1 = 3\ell + 1$. It is also demonstrated that there exist bent–negabent functions on eight variables with algebraic degrees 2, 3, and 4. Simple proofs of several previously known facts are obtained as immediate consequences of our work.

In this paper we find a lower bound of the second-order nonlinearities of Boolean bent functions of the form ${\rm f}({\rm x}) = {\rm Tr}_{1}^{{\rm n}}(\rmalpha_{1}{\rm x}^{{\rm d}_{1}} + \rmalpha_{2}{\rm x}^{{\rm d}_{2}})$, where d 1 and d 2 are Niho exponents. A lower bound of the second-order nonlinearities of these Boolean functions can also be obtained by using a recent result of Li, Hu and Gao (eprint.iacr.org/2010 /009.pdf). It is shown in Section 3, by a direct computation, that for large values of n, the lower bound obtained in this paper are better than the lower bound obtained by Li, Hu and Gao.

A Boolean function is k-normal if it is constant on a k-dimensional flat of its domain. This paper demonstrates that k-normality of a Boolean function can be exploited to mount a dedicated algebraic attack on a stream cipher of the nonlinear filter generator type, which employs a k-normal Boolean function as its filter function. The cryptanalysis is based on the possibility for pre-computing a table of the state-key stream pairs via solving certain system of algebraic equations as a consequence of the employed k-normal Boolean function. This pre-computed table is the main origin for mounting the cryptanalysis and it is independent of a the sample for cryptanalysis and the secret key employed for generating the sample.