• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1305-1320
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• 2018

We define new generalized factorials in several variables over an arbitrary subset ${\underline{S}}{\subseteq}R^n$, where R is a Dedekind domain and n is a positive integer. We then study the properties of the fixed divisor $d(\underline{S},f)$ of a multivariate polynomial $f{\in}R[x_1,x_2,{\ldots},x_n]$. We generalize the results of Polya, Bhargava, Gunji & McQuillan and strengthen that of Evrard, all of which relate the fixed divisor to generalized factorials of ${\underline{S}}$. We also express $d(\underline{S},f)$ in terms of the images $f({\underline{a}})$ of finitely many elements ${\underline{a}}{\in}R^n$, generalizing a result of Hensel, and in terms of the coefficients of f under explicit bases.

• Honam Mathematical Journal
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• v.36 no.2
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• pp.305-338
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• 2014

We investigate the explicit evaluation for the sum $\sum_{(a,b,x,y){\in}\mathbb{N}^4,\\{ax+by=n},\\{C(x,y)}$ ab in terms of various divisor functions (where C(x, y) is the set of residue conditions on x and y) for various fixed C(x, y). We also obtain some identities and congruences as interesting applications.

• The Korean Journal of Applied Statistics
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• v.29 no.2
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• pp.291-299
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• 2016

This paper discusses how to establish estimable functions when there are fixed and random effects in design models. It proves that estimable functions of mixed models are not related to random effects. A fitting constants method is used to obtain sums of squares due to random effects and Hartley's synthesis is used to calculate coefficients of variance components. To test about the fixed effects the degrees of freedom associated with divisor are determined by means of the Satterthwaite approximation.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.233-239
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• 2007

Let $\mathbb{A}=\mathbb{F}_q$[T] be the polynomial ring over a finite field $\mathbb{F}_q$[T] and K=$\mathbb{F}_q$(T) its field of fractions. Let ${\ell}$ be a fixed prime divisor of q-1. Let J be a finite set of monic irreducible polynomials $P{\in}{\mathbb{A}}$ with deg $P{\equiv}0$ (mod ${\ell})$. In this paper we define the group $C_K$ of circular units in K=k$(\{\sqrt[{\ell}]P\;:\;P{\in}J\})$ in the sense of Kucera [4] and compute the index of $C_K$ in the full unit group $O^*_K$.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.24 no.1
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• pp.5-14
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• 2014

Searchable encryption systems provide search on encrypted data while preserving the privacy of the data and the search keywords used in queries. Recently, interest on data outsourcing has increased due to proliferation of cloud computing services. Many researches are on going to minimize the trust put on external servers and searchable encryption is one of them. However, most of previous searchable encryption schemes provide only a single keyword boolean search. Although, there have been proposals to provide conjunctive keyword search, most of these works use a fixed field which limit their application. In this paper, we propose a field-free conjunctive keyword searchable encryption that also provides rank information of search results. Our system uses prime tables and greatest common divisor operation, making our system very efficient. Moreover, our system is practical and can be implemented very easily since it does not require sophisticated cryptographic module.