• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.6C
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• pp.763-769
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• 2004

It is known that a bent function corresponds to a perfect nonlinear function, which makes it difficult to do the differential cryptanalysis in DES and in many other block ciphers. In this paper, for an odd prime p, quadratic p-ary bent functions defined on finite fields are given from the families of p-ary sequences with optimal correlation properly. And quadratic p-ary bent functions, that is, perfect nonlinear functions from the finite field F $_{p^{m}}$ to its prime field $F_{p}$ are constructed by using the trace functions. trace functions.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.561-574
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• 2023

In this paper, we focus on establishing the MacWilliams-type identities on vectorial Boolean functions with bent component functions. As their applications, we provide a bound for the non-existence of vectorial dual-bent functions with prescribed minimum degree, and several Gleason-type theorems are presented as well.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.6 no.3
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• pp.31-40
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• 1996

In [4, 12], Chee et al. proposed a new class of cryptographic primitive, 'semi-bent functions', which exists on only odd dimensional vector spaces [4]. In this paper, we discuss new notion of generalized semi-bent functions which can be defined on any vector spaces. And we suggest systematic methods for constructing generalized semi-bent functions and analyse their cryptographic properties. In addition, we show that SUC fulfilling Boolean functions can be found on any dimensional vector spaces.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.1 no.1
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• pp.85-90
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• 1991

After we introduce the properties of bent functions satisfying the SAC(Strict Avalanche Criterion), we made cldar the relationship between two functions, i.e., all Boolean functions satisfying the maximum order SAC. Bant function will be useful to implement cryptographic functions like S-boxes of block cipher, nonlinear combiners, etc. But due to thear 0/1 unbalance and their existence for only even number of input bits, bent functions have some restrictions to use as a building block for constructing bijective cryptographic functions.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.9 no.1
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• pp.127-134
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• 1999

Boolean functions have an important role for designing block ciphers and hash functions. In this paper, we propose a method for designing optimum correlation immune functions. We also analyze their cryptographic properties - balancedness, nonlinearity, correlation value to the set of linear functions, correlation immunity, propagation characteristic, and algebraic degree. Such functions are special type of Semi-bent functions [2,5]

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.10C
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• pp.930-935
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• 2003

In this paper, using bent functions defined [n the finite field we generalized the construction method of the family of p-ary bent sequences with balanced and optimal correlation property introduced by Kumar and Moreno for an odd prime p[3], called a generalized p-ary bent sequence. It turns out that the family of balanced p-ary sequences with optimal correlation property introduced by Moriuchi and Imamura [6] is a special case of the generalized p-ary bent sequences.

• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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• 2001.11a
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• pp.121-126
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• 2001

In this paper, for n = 2m and odd prime p, new generalized bent functions from the finite field F$\_$p$^n$/ to the prime field F$\_$p/ are constructed from the partial spreads for F$\_$p$^n$/. Closed form expressions for the proposed generalized bent functions and their trace transform are derived in the form of the trace functions. The trace expressions for the bent functions and their trace transforms defined on F(equation omitted) constructed by using PS- are also derived.

• 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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.27 no.6A
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• pp.549-554
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• 2002

In this paper, for n=2m and odd prime p, new generalized bent functions from the finite field $F_{p^n}$ to the prime field $F_p$ are constructed from the partial spreads for $F_{p^n}$. Closed form expressions for the proposed generalized bent functions and their trace transform are derived in the form of the trace functions.

• Proceedings of the IEEK Conference
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• 2002.07b
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• pp.711-714
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• 2002

This paper presents a method to determine the propagation properties in the junctions between straight and bent waveguides using cylindrical functions of complex order. The proposed method was succeeded by developing the method of numerical calculation of cylindrical functions of complex order. As a result, we numerically calculate the reflection and transmission coefficients in the junctions in various situations, and we compare these results with the results by the perturbation method.