• International Journal of Computer Science & Network Security
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• v.21 no.8
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• pp.17-27
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• 2021

Non-abelian group based cryptosystems are a latest research inspiration, since they offer better security due to their non-abelian properties. In this paper, we propose a novel approach to non-abelian group based public-key cryptographic protocols using semidirect products of finite groups. An intractable problem of determining automorphisms and generating elements of a group is introduced as the underlying mathematical problem for the suggested protocols. Then, we show that the difficult problem of determining paths and cycles of Cayley graphs including Hamiltonian paths and cycles could be reduced to this intractable problem. The applicability of Hamiltonian paths, and in fact any random path in Cayley graphs in the above cryptographic schemes and an application of the same concept to two previous cryptographic protocols based on a Generalized Discrete Logarithm Problem is discussed. Moreover, an alternative method of improving the security is also presented.

• International Journal of Computer Science & Network Security
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• v.21 no.4
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• pp.289-300
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• 2021

Non-abelian group based Cryptography is a field which has become a latest trend in research due to increasing vulnerabilities associated with the abelian group based cryptosystems which are in use at present and the interesting algebraic properties associated that can be thought to provide higher security. When developing cryptographic primitives based on non-abelian groups, the researchers have tried to extend the similar layouts associated with the traditional underlying mathematical problems and assumptions by almost mimicking their operations which is fascinating even to observe. This survey contributes in highlighting the different analogous extensions of traditional assumptions presented by various authors and a set of open problems. Further, suggestions to apply the Hamiltonian Cycle/Path Problem in a similar direction is presented.

• Bulletin of the Korean Mathematical Society
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• v.40 no.4
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• pp.565-576
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• 2003

In this paper, we determine the general solution of the quartic equation f(x+2y)+f(x-2y)+6f(x) = 4[f(x+y)+f(x-y)+6f(y)] for all x, $y\;\in\;\mathbb{R}$ without assuming any regularity conditions on the unknown function f. The method used for solving this quartic functional equation is elementary but exploits an important result due to M. Hosszu [3]. The solution of this functional equation is also determined in certain commutative groups using two important results due to L. Szekelyhidi [5].

• Bulletin of the Korean Mathematical Society
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• v.45 no.4
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• pp.729-737
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• 2008

In this paper we characterize multi-Jensen functions f : $V^n\;{\rightarrow}\;W$, where n is a positive integer, V, W are commutative groups and V is uniquely divisible by 2. Moreover, under the assumption that f : $\mathbb{R}\;{\rightarrow}\;\mathbb{R}$ is Borel measurable, we obtain representation of f (respectively, f, g, h : $\mathbb{R}\;{\rightarrow}\;\mathbb{R}$) such that the Jensen difference $$2f\;\(\frac{x\;+\;y}{2}\)\;-\;f(x)\;-\;f(y)$$ (respectively, the Pexider difference $$2f\;\(\frac{x\;+\;y}{2}\)\;-\;g(x)\;-\;h(y))$$ takes values in a countable subgroup of $\mathbb{R}$.

• Korean Journal of Childcare and Education
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• v.12 no.5
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• pp.47-69
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• 2016

The purpose of this study was to examine teaching competency for character education of early childhood teachers and their demands to improve their capacities. 152 kindergarten and child care teachers responded to 30 survey questionnaires, which included 3 sub-factors(commutative, practical, instrumental) of teaching competency for character education of the teachers, as well as 16 detailed components, designed to check their current competency for character education and to investigate the priority elements that they desired to improve. The data were analyzed based on the Borich request formula, the locus for focus model, and the independent sample t-test across the teacher groups. The results were as follows: Firstly, the most highly demanded teaching competency by the teachers was using tools interactively for character education. And the teachers, among the sub-elements, requested (a) recording and evaluating character education systematically, (b) using local or national resources, (c) planning member's participation, and (d) performing character education related activities systematically. Secondly, more new teachers demanded instrumental competency and answered the need of parents' participation among the sub-elements, more than the more experienced teachers, respectively. The study discussed the implications of promoting early childhood teachers' teaching competency for character education.

• Journal of the Korea Organic Resources Recycling Association
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• v.7 no.2
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• pp.65-71
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• 1999

This study was conducted to evaluate the feasibility of food waste as a feed resources by fermentation and fermented food waste as a substitute of rat feed on the performance with measuring the liveweight gain, feed consumption, feed conversion and digestibility Sixty-two grams Sprague-Dawley line 36 rats were allocated three treatments 12 rats of each(3replication ${\times}$ 4 rats). The substitution level of fermented food waste to commercial broiler feed were control, 0: 100: treatment I, 10: 90: treatment II, 20:80. The chemical composition of fermented food waste was appeared to follows : dry matter, 88.47% : crude ash. 12.95: crude protein, 20.82%; crude fiber, 13.62; ether extract, 9.15%. The body weight of treatment I and II at 1 weeks was significantly lower than those of control(p<.05) and weekly weight gain of control at 0-1 weeks was significantly higher than those of treatment I and II(p<.05). Those were higher in treatment I than those of rest groups at 1-2 weeks(p<.05). Total weight gain of treatment II was significantly lower than those of control and treatment I(p<.05) Total feed consumption of treatment II was significantly higher than those of control (p<.05) and weekly feed consumption of control and treatment II at 3-4 weeks was significantly higher than those of treatment II(p<.05). but those were higher in treatment I and II than those of control at 2-3 weeks(p<.05). Commutative feed conversion of treatment II was significantly higher than those of control(p<.05) and weekly feed conversion of treatment II and III at 0-1 weeks was significantly higher than those of control(p<.05) Dry matter digestibility of control and treatment I was significantly higher than those of treatment II(p<.05) and organic matter digestibility was higher in control than those of treatment II(p<.05).