• ETRI Journal
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• v.26 no.3
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• pp.241-251
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• 2004

We propose two improved scalar multiplication methods on elliptic curves over $F_{{q}^{n}}$ $q= 2^{m}$ using Frobenius expansion. The scalar multiplication of elliptic curves defined over subfield $F_q$ can be sped up by Frobenius expansion. Previous methods are restricted to the case of a small m. However, when m is small, it is hard to find curves having good cryptographic properties. Our methods are suitable for curves defined over medium-sized fields, that is, $10{\leq}m{\leq}20$. These methods are variants of the conventional multiple-base binary (MBB) method combined with the window method. One of our methods is for a polynomial basis representation with software implementation, and the other is for a normal basis representation with hardware implementation. Our software experiment shows that it is about 10% faster than the MBB method, which also uses Frobenius expansion, and about 20% faster than the Montgomery method, which is the fastest general method in polynomial basis implementation.

• Proceedings of the KIEE Conference
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• 1999.07d
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• pp.1901-1903
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• 1999

To investigate invar alloy as a core material for increased capacity over-head transmission line which have high strength and low thermal expansion coefficient, hardness and thermal expansion coefficient of Fe-Ni-Co alloy have been studied. It is necessary that invar alloy have low thermal expansion coefficient and high strength for increased capacity over-head transmission line. In this paper. we tried to find out the effect of Ni and Co which has ferromagnetic properties and high saturation magnetization. It was found that Ni decrease thermal expansion coefficient and hardness, Co decrease thermal expansion coefficient but increase hardness in Fe-xNi-Co system. In Fe-(29-x)Ni-Co system, the material has no low thermal expansion properties substituting Co instead of Ni in concentration range of $1\sim7$%Co.

• Journal of Korea Foundry Society
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• v.18 no.5
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• pp.467-473
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• 1998

For enhancing the mechanical properties of LTE (low thermal expansion) cast steel, systematic researches have been carried out. The effects of alloying elements such as vanadium, molybdenum and carbon on the hardness and linear thermal expansion coefficient were investigated. In the range of $0.5{\sim}2.3\;wt%$ carbon, addition of 1.73 wt% carbon caused hardness increase due to the formation of eutectic carbide having high hardness but over the range of 1.73 wt% carbon, hardness was decreased. Thermal expansion coefficient increases with carbon contents. In the LTE cast steel containing 0.6 wt% carbon, hardness increased up to 1.96 wt% vanadium addition. But over the range of 1.96 wt% vanadium hardness was decreased by coarse eutectic carbide. Thermal expansion coefficient of LTE cast steel containing 0.6 wt%carbon moderately increased with increasing vanadium contents. There was no significant variation of hardness and thermal expansion coefficient according to molybdenum content in LTE cast steel.

• International Journal of Highway Engineering
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• v.17 no.2
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• pp.13-20
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• 2015

PURPOSES: This paper describes the expansion caused by the alkali-aggregate reaction (AAR) in concrete pavement currently in service. It also discusses the effects of joints installed to release the stress induced by the AAR expansion. METHODS: The expansion effect on concrete pavement was verified by a visual inspection and long-term measurement of the joint width of a cut-section. The behaviors of 16 newly installed joints were monitored as part of the investigation and long-term monitoring was carried out for three years after cutting. RESULTS: The behavior of a bridge was affected when AAR occurred in the connected pavement. The newly installed joints shrank in the longitudinal direction of the bridge after cutting. The width of the joints decreased over the six months after cutting. A large portion of the joint width (8.5cm) was found to have closed nine months after cutting. It had ultimately shrunk by about 92 percent when the final measurement was taken. CONCLUSIONS : The expansion of the pavement due to AAR was quantitatively described by visual inspection and the long-term monitoring of the newly cut joints. However, the width of the new joints decreased over the six to nine months after cutting. Additional research should be conducted to determine a means of controlling the expansion due to AAR in the pavement.

• International Journal of Automotive Technology
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• v.2 no.1
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• pp.1-7
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• 2001

This paper presents further investigation into the effect of over-expansion cycle in a spark-ignition engine. On the basis of the results obtained in previous studies, several combinations of late-closing (LC) of intake valve and expansion ratio were tested using a single-cylinder production engine. A large volume of intake capacity was inserted into the intake manifold to simulate multi-cylinder engines. With the large capacity volume, LC can decrease the pumping loss and then increase the mechanical efficiency. Increasing the expansion ratio from 11 to 23.9 with LC application can produce about 13% improvement of thermal efficiency which was suggested to be caused by the increased cycle efficiency. The decrease of compression ratio from 11 to 5.5 gives little effect on the thermal efficiency if the expansion ratio could be kept constant. Thus, the expansion ratio is revealed to be a determining factor for cycle efficiency, while compression ratio is no more important, which suggests the usefulness of controlling the intake charge with intake valve closure timing. These were successfully explained by simple thermodynamic calculation and thus the mechanism could be verified by the estimation.

• ETRI Journal
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• v.27 no.5
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• pp.617-627
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• 2005

This paper proposes an efficient scalar multiplication algorithm for hyperelliptic curves, which is based on the idea that efficient endomorphisms can be used to speed up scalar multiplication. We first present a new Frobenius expansion method for special hyperelliptic curves that have Gallant-Lambert-Vanstone (GLV) endomorphisms. To compute kD for an integer k and a divisor D, we expand the integer k by the Frobenius endomorphism and the GLV endomorphism. We also present improved scalar multiplication algorithms that use the new expansion method. By our new expansion method, the number of divisor doublings in a scalar multiplication is reduced to a quarter, while the number of divisor additions is almost the same. Our experiments show that the overall throughputs of scalar multiplications are increased by 15.6 to 28.3 % over the previous algorithms when the algorithms are implemented over finite fields of odd characteristics.

• The korean journal of orthodontics
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• v.21 no.3
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• pp.657-670
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• 1991

It was said that early rapid palatal expansion was the treatment of choice in case of maxillary constriction with posterior crossbite. The author tried to assess dimensional changes of nasal and oral cavity before rapid palatal expansion and over 4 months of retention by use of three coronal tomograms through the incisal, molar, and maxillary tuberosity areas. The subjects of this study were consisted of 9 boys and 11 girls ranging from 11 to 13 years old. The results were as follows: 1. A mean change in maxillary first molar width was 3.68mm and a mean change in nasal cavity width was 2.26mm after 6.70mm expansion by Hyrax-type screw and over 4 months of retention tomographically in molar cut. 2. A change in nasal cavity width tomographically showed in order of molar cut, incisal cut, maxillary tuberosity cut respectively. 3. There was no correlation between changes in oral cavity width and nasal cavity width.

• Proceedings of the KIEE Conference
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• 2000.07c
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• pp.1599-1601
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• 2000

To study invar alloy as a core material for large ampacity over-head transmission line which have high strength and low thermal expansion coefficient simultaneously, thermal expansion coefficient, physical properties and hardness of Fe-Ni-Co-xC alloy have been studied. It is necessary that invar alloy possess low thermal expansion coefficient and high strength for increased capacity over-head transmission line. In this paper we tried to find out the effect of carbon addition related with mechanical and physical properties. It was found that the thermal expansion coefficient and hardness were increased with carbon addition for whole composition range but the saturation magnetization was decreased except for the range of 0.1$\sim$0.4%C.

• Computers and Concrete
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• v.18 no.5
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• pp.937-950
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• 2016

This study applied autoclave expansion and heat curing to accelerate the hydration of concrete and investigated how these methods affect the expansion rate, crack pattern, aggregate size effect, and expansion of electric arc furnace oxidizing slag (EOS)-containing concrete. An expansion prediction model was simulated to estimate the expansion behavior over a long period and to establish usage guidelines for EOS aggregates. The results showed that the EOS content in concrete should range between 20% and 30% depending on the construction conditions, and that coarse aggregates with a diameter of ${\geq}4.75-mm$ are not applicable to construction engineering. By comparison, aggregates with a size of 1.18-0.03 mm resulted in higher expansion rates; these aggregates can be used depending on the construction conditions. On Day 21, the prediction model attained a coefficient of determination ($R^2$) of at least 0.9.

• Journal of Ocean Engineering and Technology
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• v.22 no.2
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• pp.13-19
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• 2008

A camprehensive review of the expansion behavior of marine pipelines due to thermal and pressure change is presented based on research work over the last 10 years. The review is organized into five main sections, namely free expansion with uniform temperature, free expansion with temperature gradient, expansion with end restraints, expansion of pipe-in-pipe system, and lateral deviation (snaking). Based on the accumulated knowledge of the interactions between the soil and pipeline behavior, a whole pipeline system can be modeled by an accurate finite element method (FEM). This methodology requires a comprehensive understanding and engineering verification of the expansion behavior of marine pipelines.