• Journal of the Chungcheong Mathematical Society
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• v.17 no.1
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• pp.47-56
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• 2004

The nonlinearity of a Boolean function f on $GF(2)^n$ is the minimum hamming distance between f and all affine functions on $GF(2)^n$ and it measures the ability of a cryptographic system using the functions to resist against being expressed as a set of linear equations. Finding out the exact value of the nonlinearity of given Boolean functions is not an easy problem therefore one wants to estimate the nonlinearity using extra information on given functions, or wants to find a lower bound or an upper bound on the nonlinearity. In this paper we extend the notion of auto-correlations of Boolean functions to vector Boolean functions and obtain upper bounds and a lower bound on the nonlinearity of vector Boolean functions in the context of their auto-correlations. Also we can describe avalanche characteristics of vector Boolean functions by examining the extended notion of auto-correlations.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.259-268
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• 1996

The Data Encryption Standard(DES) [3, 8, 9] was developed by an IBM team aroung 1974 and adopted as a national standard in 1977.

• Journal of the Institute of Convergence Signal Processing
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• v.13 no.4
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• pp.194-200
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• 2012

In this paper we analyze the code sequence generating algorism defined on $GF(2^n)$ proposed by S.Bostas and V.Kumar[7] and derive the implementation functions of code sequence generator using Boolean functions which can map the vector space $F_2^n$ of all binary vectors of length n, to the finite field with two elements $F_2$. We find the code sequence generating boolean functions based on two kinds of the primitive polynomials of degree, n=5 and n=7 from trace function. We then design and implement the code sequence generators using these functions, and produce two code sequence groups. The two groups have the period 31 and 127 and the magnitudes of out of phase(${\tau}{\neq}0$) autocorrelation and crosscorrelation functions {-9, -1, 7} and {-17, -1, 15}, satisfying the period $L=2^n-1$ and the correlation functions $R_{ij}({\tau})=\{-2^{(n+1)/2}-1,-1,2^{(n+l)/2}-1\}$ respectively. Through these results, we confirm that the code sequence generators using boolean functions are designed and implemented correctly.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.5 no.1
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• pp.3-16
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• 1995

In this paper, we deal with the cryptographic properties of Boolean functions generated by recursively extended methods from the points of balancedness, nonlinearity and correlation properties. First, we propose a new concept 'Strict Uncorrelated Criterion(SUC)' for two Boolean functions as a necessary condition for constructing Boolean functions of S-box which can be guaranteed to be resistant against Differential cryptanalysis, then we show that the recurively extended Boolean functions with particular form preserve the SUC. We also examine the correlation properties of Boolean functions using Walsh-Hadamard transformations and apply them to discuss nonlinearity, correlation properties and SUC of semi-bent function which is defined over odd dimensional vector space. Finally, we compare semi-bent function with Boolean functions which are generated by other similar recursive methods.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.15 no.6
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• pp.105-110
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• 2005

The linearized polynomial fan be regarded as a generalization of the identity function so that the inverse of the linearized polynomial is a generalization of e inverse function. Since the inverse function has so many good cryptographic properties, the inverse of the linearized polynomial is also a candidate of good Boolean functions. In particular, a construction method of vector resilient functions with high algebraic degree was proposed at Crypto 2001. But the analysis about the algebraic degree of the inverse of the linearized Polynomial. Hence we correct the inexact result and give the exact maximal algebraic degree.

• Journal of the Korean Institute of Telematics and Electronics
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• v.23 no.2
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• pp.197-205
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• 1986

In this paper, we present an efficient test algorithm for data processing function of MC68000 \ulcorner. The test vector for functional testing is determined by stuck-at, coupling and transition fault for data storage and transfer. But for data manipulation it is determined by a boolean function of micro-operation. This test algorithm is composed of 3 parts, choosing optimum test instructions for maximizing fault coverage and minimizing test process time, deciding the test order for minimizing test ambiguity, and processing the actual test.

• Journal of the Korea Convergence Society
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• v.10 no.12
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• pp.29-34
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• 2019

If it takes much time to calculate the fitness of the solution in genetic algorithms, it is essential to create a metamodel. Much research has been completed to improve the performance of metamodels. In this study, we tried to get a better performance of metamotel using discrete Walsh transform in discrete domain. We transforms the basis of the solution and creates a metamodel using the transformed solution. We experimented with NK-landscape, a representative function of the pseudo-boolean function, and provided empirical evidence on the performance of the proposed model. When we performed the genetic algorithm using the proposed model, we confirmed that the genetic algorithm found a better solution. In particular, our metamodel showed better performance than that using the radial basis function network that modified the similarity function for the discrete domain.