• 한국해양학회지
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• v.24 no.4
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• pp.194-205
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• 1989

In order to study the biomass of primary producer, phytoplankton is collected monthly September 1985 to August 1986 in Ch$\check{o}$nsu Bay. Phytoplankton carbon contents which are calculated from phytoplankton volume were ranged from $26.7{\mu}gC/l$ to $960.7{\mu}gC/l$, and average carbon contents of each month lie in the range of $58.6-684.7{\mu}gC/l$(annual mean $208.5{\mu}gC/l$). For net plankton analysis with the carbon contents, cell numbers, and chlorophyll concentrations show a close correlation, while for nanoplankton the correlation was low, indicating that nano-fraction includes a significant portion of picoplankton. Also, the multiple regression analysis with carbon content, cell number, and chlorophyll concentration to size fraction well illustrate the prime importance of the net-fraction in phytoplankton group. C/Chl-a ratios ranged from 9.1 to 100.5, average rations of net- and nanoplankton are 111 and 6.4, respectively. The greater net plankton faction is, the higher C/Chl-a ratio is, however in case of high nanoplankton portion C/Chl-a ratio show low level. These results indicate that the difference of C/Chl-a ratio per phytoplankton cell size be main factor for the variation of C/Chl-a ratio in Ch$\check{o}$nsu Bay. As C/Chl-a ratio fluctuates greatly in coastal ecosystem, that use of a direct conversion of convert chlorophyll to organic carbon may lead erronous estimation.

• Journal of the Korea Society of Computer and Information
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• v.19 no.7
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• pp.71-76
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• 2014

There is to be virtually impossible to solve the very large digits of prime number p and q from composite number n=pq using integer factorization in typical public-key cryptosystems, RSA. When the public key e and the composite number n are known but the private key d remains unknown in an asymmetric-key RSA, message decryption is carried out by first obtaining ${\phi}(n)=(p-1)(q-1)=n+1-(p+q)$ and then using a reverse function of $d=e^{-1}(mod{\phi}(n))$. Integer factorization from n to p,q is most widely used to produce ${\phi}(n)$, which has been regarded as mathematically hard. Among various integer factorization methods, the most popularly used is the congruence of squares of $a^2{\equiv}b^2(mod\;n)$, a=(p+q)/2,b=(q-p)/2 which is more commonly used then n/p=q trial division. Despite the availability of a number of congruence of scares methods, however, many of the RSA numbers remain unfactorable. This paper thus proposes an algorithm that directly and immediately obtains ${\phi}(n)$. The proposed algorithm computes $2^k{\beta}_j{\equiv}2^i(mod\;n)$, $0{\leq}i{\leq}{\gamma}-1$, $k=1,2,{\ldots}$ or $2^k{\beta}_j=2{\beta}_j$ for $2^j{\equiv}{\beta}_j(mod\;n)$, $2^{{\gamma}-1}$ < n < $2^{\gamma}$, $j={\gamma}-1,{\gamma},{\gamma}+1$ to obtain the solution. It has been found to be capable of finding an arbitrarily located ${\phi}(n)$ in a range of $n-10{\lfloor}{\sqrt{n}}{\rfloor}$ < ${\phi}(n){\leq}n-2{\lfloor}{\sqrt{n}}{\rfloor}$ much more efficiently than conventional algorithms.

• Journal of Korean Society of Forest Science
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• v.85 no.3
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• pp.539-551
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• 1996

In this study, a number of distance-dependent competition indices on tree-level which incorporate the tree sizes and distances to competitors, and traditional stand-level density measures were estimated from the data compiled with position-dependent survey in a Pinus densiflora stand. The performance of the estimated competition indices was examined by comparing the relationship with the diameter growth, and a dbh growth function, in which the competition index is considered as a one of influence factors, are developed. In the searching method of competing trees, the competition index estimated with $30^{\circ}$ competition interrupting angle showed the highest correlation with the annual dbh growth, while the expanding the competing zone distance had no significant effect on the performance of competition index in estimating annual dbh growth. The most of the examined stand-level competition indices, based on distance-dependent single-tree competition indices, were evaluated to describe similarly the stand competition status. As a result of partial correlation analysis in which the effect of age and site index are eliminated, Alemdag's mean competition index and relative spacing index were determined to have the highest correlation with dbh. The relative spacing index, which can be easily measured in field without measuring the position of individual trees, was considered to be a better suited one for estimating mean dbh of a stand. Among distance-dependent competition indices on tree-level, Hegyi's competition index showed the best performance in their correlation with annual dbh growth, if eliminated the effect of site index and dbh. This enabled to derive the following annual dbh growth function of individual trees which incorporate age, dominant height, dbh and Hegyi's competition index as influence factors : $$dbh^{\prime}=3.975362676{\cdot}age^{-1.099274613}{\cdot}ho^{0.199893990}{\cdot}dbh^{0.269430865}{\cdot}HgCI^{-0.353643587}$$ This function is coincided to the growth principle in which site index has a positive effect on the annual dbh growth, while high age or competition causes to reduce the annual dbh growth, and can be used as a function in single tree growth model.

• Journal of Venture Innovation
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• v.7 no.1
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• pp.1-15
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• 2024

This study aims to elucidate the characteristics of big tech platform companies' sports content business in an environment of rapid digital transformation. Specifically, this study examines the market structure of big tech platform companies with a focus on Amazon, revealing the role of sports content within this structure through an analysis of Amazon's sports marketing business and provides an outlook on the sports content business of big tech platform companies. Based on two-sided market platform business models, big tech platform companies incorporate sports content as a strategy to enhance the value of their platforms. Therefore, sports content is used as a tool to enhance the value of their platforms and to consolidate their monopoly position by maximizing profits by increasing the synergy of platform ecosystems such as infrastructure. Amazon acquires popular live sports broadcasting rights on a continental or national basis and supplies them to its platforms, which not only increases the number of new customers and purchasing effects, but also provides IT solution services to sports organizations and teams while planning and supplying various promotional contents, thus creates synergy across Amazon's platforms including its advertising business. Amazon also expands its business opportunities and increases its overall value by supplying live sports contents to Amazon Prime Video and Amazon Prime, providing technical services to various stakeholders through Amazon Web Services, and offering Amazon Marketing Cloud services for analyzing and predicting advertisers' advertising and marketing performance. This gives rise to a new paradigm in the sports marketing business in the digital era, stemming from the difference in market structure between big tech companies based on two-sided market platforms and legacy global companies based on one-sided markets. The core of this new model is a business through the development of various contents based on live sports streaming rights, and sports content marketing will become a major field of sports marketing along with traditional broadcasting rights and sponsorship. Big tech platform global companies such as Amazon, Apple, and Google have the potential to become new global sports marketing companies, and the current sports marketing and advertising companies, as well as teams and leagues, are facing both crises and opportunities.

• Journal of National Security and Military Science
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• s.8
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• pp.49-168
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• 2010

Just before the Korean War, the total number of the North Korean troops was 198,380, while that of the ROK(Republic of Korea) army troops 105,752. That is, the total number of the ROK army troops at that time was 53.3% of the total number of the North Korean army. As of December 2008, the total number of the North Korean troops is estimated to be 1,190,000, while that of the ROK troops is 655,000, so the ROK army maintains 55.04% of the total number of the North Korean troops. If the ROK army continues to reduce its troops according to [Military Reform Plan 2020], the total number of its troops will be 517,000 m 2020. If North Korea maintains the current status(l,190,000 troops), the number of the ROK troops will be 43.4% of the North Korean army. In terms of units, just before the Korean War, the number of the ROK army divisions and regiments was 80% and 44.8% of North Korean army. As of December 2008, North Korea maintains 86 divisions and 69 regiments. Compared to the North Korean army, the ROK army maintains 46 Divisions (53.4% of North Korean army) and 15 regiments (21.3% of North Korean army). If the ROK army continue to reduce the military units according to [Military Reform Plan 2020], the number of ROK army divisions will be 28(13 Active Division, 4 Mobilization Divisions and 11 Local Reserve Divisions), while that of the North Korean army will be 86 in 2020. In that case, the number of divisions of the ROK army will be 32.5% of North Korean army. During the Korean war, North Korea suddenly invaded the Republic of Korea and occupied its capital 3 days after the war began. At that time, the ROK army maintained 80% of army divisions, compared to the North Korean army. The lesson to be learned from this is that, if the ROK army is forced to disperse its divisions because of the simultaneous invasion of North Korea and attack of guerrillas in home front areas, the Republic of Korea can be in a serious military danger, even though it maintains 80% of military divisions of North Korea. If the ROK army promotes the plans in [Military Reform Plan 2020], the number of military units of the ROK army will be 32.5% of that of the North Korean army. This ratio is 2.4 times lower than that of the time when the Korean war began, and in this case, 90% of total military power should be placed in the DMZ area. If 90% of military power is placed in the DMZ area, few troops will be left for the defense of home front. In addition, if the ROK army continues to reduce the troops, it can allow North Korea to have asymmetrical superiority in military force and it will eventually exert negative influence on the stability and peace of the Korean peninsular. On the other hand, it should be reminded that, during the Korean War, the Republic of Korea was attacked by North Korea, though it kept 53.3% of troops, compared to North Korea. It should also be reminded that, as of 2008, the ROK army is defending its territory with the troops 55.04% of North Korea. Moreover, the national defense is assisted by 25,120 troops of the US Forces in Korea. In case the total number of the ROK troops falls below 43.4% of the North Korean army, it may cause social unrest about the national security and may lead North Korea's misjudgement. Besides, according to Lanchester strategy, the party with weaker military power (60% compared to the party with stronger military power) has the 4.1% of winning possibility. Therefore, if we consider the fact that the total number of the ROK army troops is 55.04% of that of the North Korean army, the winning possibility of the ROK army is not higher than 4.1%. If the total number of ROK troops is reduced to 43.4% of that of North Korea, the winning possibility will be lower and the military operations will be in critically difficult situation. [Military Reform Plan 2020] rums at the reduction of troops and units of the ground forces under the policy of 'select few'. However, the problem is that the financial support to achieve this goal is not secured. Therefore, the promotion of [Military Reform Plan 2020] may cause the weakening of military defence power in 2020. Some advanced countries such as Japan, UK, Germany, and France have promoted the policy of 'select few'. However, what is to be noted is that the national security situation of those countries is much different from that of Korea. With the collapse of the Soviet Unions and European communist countries, the military threat of those European advanced countries has almost disappeared. In addition, the threats those advanced countries are facing are not wars in national level, but terrorism in international level. To cope with the threats like terrorism, large scaled army trops would not be necessary. So those advanced European countries can promote the policy of 'select few'. In line with this, those European countries put their focuses on the development of military sections that deal with non-military operations and protection from unspecified enemies. That is, those countries are promoting the policy of 'select few', because they found that the policy is suitable for their national security environment. Moreover, since they are pursuing common interest under the European Union(EU) and they can form an allied force under NATO, it is natural that they are pursing the 'select few' policy. At present, NATO maintains the larger number of troops(2,446,000) than Russia(l,027,000) to prepare for the potential threat of Russia. The situation of japan is also much different from that of Korea. As a country composed of islands, its prime military focus is put on the maritime defense. Accordingly, the development of ground force is given secondary focus. The japanese government promotes the policy to develop technology-concentrated small size navy and air-forces, instead of maintaining large-scaled ground force. In addition, because of the 'Peace Constitution' that was enacted just after the end of World War II, japan cannot maintain troops more than 240,000. With the limited number of troops (240,000), japan has no choice but to promote the policy of 'select few'. However, the situation of Korea is much different from the situations of those countries. The Republic of Korea is facing the threat of the North Korean Army that aims at keeping a large-scale military force. In addition, the countries surrounding Korea are also super powers containing strong military forces. Therefore, to cope with the actual threat of present and unspecified threat of future, the importance of maintaining a carefully calculated large-scale military force cannot be denied. Furthermore, when considering the fact that Korea is in a peninsular, the Republic of Korea must take it into consideration the tradition of continental countries' to maintain large-scale military powers. Since the Korean War, the ROK army has developed the technology-force combined military system, maintaining proper number of troops and units and pursuing 'select few' policy at the same time. This has been promoted with the consideration of military situation in the Koran peninsular and the cooperation of ROK-US combined forces. This kind of unique military system that cannot be found in other countries can be said to be an insightful one for the preparation for the actual threat of North Korea and the conflicts between continental countries and maritime countries. In addition, this kind of technology-force combined military system has enabled us to keep peace in Korea. Therefore, it would be desirable to maintain this technology-force combined military system until the reunification of the Korean peninsular. Furthermore, it is to be pointed out that blindly following the 'select few' policy of advanced countries is not a good option, because it is ignoring the military strategic situation of the Korean peninsular. If the Republic of Korea pursues the reduction of troops and units radically without consideration of the threat of North Korea and surrounding countries, it could be a significant strategic mistake. In addition, the ROK army should keep an eye on the fact the European advanced countries and Japan that are not facing direct military threats are spending more defense expenditures than Korea. If the ROK army reduces military power without proper alternatives, it would exert a negative effect on the stable economic development of Korea and peaceful reunification of the Korean peninsular. Therefore, the desirable option would be to focus on the development of quality of forces, maintaining proper size and number of troops and units under the technology-force combined military system. The tableau above shows that the advanced countries like the UK, Germany, Italy, and Austria spend more defense expenditure per person than the Republic of Korea, although they do not face actual military threats, and that they keep achieving better economic progress than the countries that spend less defense expenditure. Therefore, it would be necessary to adopt the merits of the defense systems of those advanced countries. As we have examined, it would be desirable to maintain the current size and number of troops and units, to promote 'select few' policy with increased defense expenditure, and to strengthen the technology-force combined military system. On the basis of firm national security, the Republic of Korea can develop efficient policies for reunification and prosperity, and jump into the status of advanced countries. Therefore, the plans to reduce troops and units in [Military Reform Plan 2020] should be reexamined. If it is difficult for the ROK army to maintain its size of 655,000 troops because of low birth rate, the plans to establish the prompt mobilization force or to adopt drafting system should be considered for the maintenance of proper number of troops and units. From now on, the Republic of Korean government should develop plans to keep peace as well as to prepare unexpected changes in the Korean peninsular. For the achievement of these missions, some options can be considered. The first one is to maintain the same size of military troops and units as North Korea. The second one is to maintain the same level of military power as North Korea in terms of military force index. The third one is to maintain the same level of military power as North Korea, with the combination of the prompt mobilization force and the troops in active service under the system of technology-force combined military system. At present, it would be not possible for the ROK army to maintain such a large-size military force as North Korea (1,190,000 troops and 86 units). So it would be rational to maintain almost the same level of military force as North Korea with the combination of the troops on the active list and the prompt mobilization forces. In other words, with the combination of the troops in active service (60%) and the prompt mobilization force (40%), the ROK army should develop the strategies to harmonize technology and forces. The Korean government should also be prepared for the strategic flexibility of USFK, the possibility of American policy change about the location of foreign army, radical unexpected changes in North Korea, the emergence of potential threat, surrounding countries' demand for Korean force for the maintenance of regional stability, and demand for international cooperation against terrorism. For this, it is necessary to develop new approaches toward the proper number and size of troops and units. For instance, to prepare for radical unexpected political or military changes in North Korea, the Republic of Korea should have plans to protect a large number of refugees, to control arms and people, to maintain social security, and to keep orders in North Korea. From the experiences of other countries, it is estimated that 115,000 to 230,000 troops, plus ten thousands of police are required to stabilize the North Korean society, in the case radical unexpected military or political change happens in North Korea. In addition, if the Republic of Korea should perform the release of hostages, control of mass destruction weapons, and suppress the internal wars in North Korea, it should send 460,000 troops to North Korea. Moreover, if the Republic of Korea wants to stop the attack of North Korea and flow of refugees in DMZ area, at least 600,000 troops would be required. In sum, even if the ROK army maintains 600,000 troops, it may need additional 460,000 troops to prepare for unexpected radical changes in North Korea. For this, it is necessary to establish the prompt mobilization force whose size and number are almost the same as the troops in active service. In case the ROK army keeps 650,000 troops, the proper number of the prompt mobilization force would be 460,000 to 500,000.

• Economic and Environmental Geology
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• v.26 no.3
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• pp.403-420
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• 1993

The Cretaceous Kyongsang Basin is known to be composed of several tectonic blocks (or subbasins) with each distinct stratigraphic succession. The study area represents a major part of one of these blocks, i. e. the $\check{U}is\check{o}ng$ block. The area is charaterized by a suite of WNW-trending sinistral strike-slip faults as well as a number of ring faults. A total of 292 independently oriented core samples were drilled from 23 sites, covering virtually all the formations of the Cretaceous $Ky\check{o}ngsang$ Supergroup. Alternating field and thermal demagnetization experiments were conducted to reveal the primary magnetization. Due to the homoclinal nature of the strata in the area, it was not possible to make use of the conventional fold test It is, however, believed that the primary remanent components have been obtained from the majority of the formations, considering the similarity of the palaeomagnetic pole positions with those of contemporary strata of other blocks and the existence of antiparallel reversed remanence. It was found neither any significant difference in magnetic declination on each side of the strike-slip faults nor systematic change of magnetic declination with distance from the fault-line. This does not support such a block rotation hypothesis associated with the strike-slip faulting in the area as alleged by some authors. The samples from the outcrops on or near the fault-lines were severely overprinted by the recent magnetic fields regardless of age and lithology. Epithermal Au-Ag-Cu-Pb-Zn mineralizations are known along some fault lines in the area. It is interpreted that these two facts are closely related with fluid circulations along the fracture zones caused by fault activities. In regard to the age of the strata as deduced from the magnetostratigraphic consideration, the $Ch\check{o}mgok$ formation and the lower strata should be older than Barremian or 124 Ma. The age of volcanics of the $Yuch^{\prime}\check{o}n$ Group sampled in this study should be younger than Campanian or 83 Ma.

• Journal of the Korean Home Economics Association
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• v.17 no.4
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• pp.117-127
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• 1979

This study attempts to shed additional light on the national diffusion process and interaction of welfare services for children and mothers. The central hypothesis examined is the following : In general, the implant of social welfare system is first considered on the characteristics of their own socio-economics , and diffusion prodess of welfare services tends to occur faster in countries with open sicieties than in countries where entry barriers are high and society ranking rigid. The scope of the study is limited in several ways. Attention is concentrated on the agency of woman in the belief that an in-depth case study of one field can yield more insight than a less detailed investigation embracing a number of social welfare systems. The angency of woman is selected for several reasons. a) It is important the agency of woman alone produce more effective than services affecting both the child welfare and women's libertion bradually. Moreover, these services will form the heart of mother's welfare. b) The services of women's agency is gradually wide spread, since a role of government is still negligible before a full realization of economic income. c) The services of women agency is a prime example of a social welfare. d) statistical data and other information are more readily available. One of major findings of our study is the existence of the barriers inhibiting child welfare form " motherhood cult". Despite all the distinct advantages for mother and child , social attitudes appear to be some resistant on child welfare system among men and women even the agenices of women. What is surprised is the extent of the awareness that strategies of women's agency to liberate woman and to increate activities of women involve the strategies to liberate child. The conviction that solving application problems for child welfare in line with the activities of agency by women offer greater freedom and more advantage to mother are not apparent on the data collected from 18 of multi-functional agencies in our country. there are little sign that such agencies cooperate toward attainment of common goals. The intensive early focus of the movement on consciousness raising is a necessary beginning and such efforts by women's organizations would help both in the continuous evolution of women and child. Some of the agencies offer a variety of services to women and children, others are specialized in that they offer fewer services or even only one. Social welfare agenices giving service to children and their families are identified by various names usually women service and child welfare from govern , mental agency and voluntary public agency to foreign aided. What is totally missing , however, is an integrated synthesis of child welfare program Through women's agency. Social changes to occur, but delineation of appropriate and comprehensive social policy is also necessary at this point at this point since efforts, social changes and polices must be well coordianted and focused, as well as mutually supprotive and reinforcing.

• Korean journal of communication and information
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• v.45
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• pp.463-495
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• 2009

Korea has started to pay attention to civic journalism in recent years while it initially emerged in the United State since late 1980s. Furthermore, albeit some discernable limitations, the Internet has played an important role in fertilizing civic journalism as indicated by the emergence of online news media and the increasing number of civic journalists engaged in the online activities. Whereas there are some patterns of civic journalism practice and the civic influence commonly observed in both countries, there are significant factors that distinguish th1e case of Korea from that of the U.S. The purpose of this study is to compare the two countries in terms of the patterns of civic journalism practice and civic influence. This goal has been achieved by analyzing ‘CNN iReport’ in the U.S. and ‘Ohmynews’ in Korea, both of which are prime civic journalism websites. Those websites have been compared in light of four standards of civic journalism: first, the degree of post-objectivism; second, the search for effective resolutions of social problems; third, civic engagement in the news making process to enhance bottom-up agenda setting; and finally, citizens’ interaction with the news. The results reveal that the American civic journalism website is more likely to shed light on deviating from the principle of objectivity and seeking alternatives and resolutions of social problems. Moreover, it effectively utilizes civic engagement in the news Abstracts 551 making process as indicated by the higher numbers of civic journalists and civic news resources. Also, readers’ interaction with the news was found to be more active in the iReport website than in the Ohmynews.

• 한국환경농학회:학술대회논문집
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• 2009.07a
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• pp.3-18
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• 2009

It is difficult for consumers to satisfy high safety request with post-management method such as inspection and surveillance, as various changes in-and-out of the country associated with food safety. In terms of food safety problems related to foods, it is crucial to recognize public health and consumer protection and construct pre-preventive Food Control System. A joint committee, FAO/WHO made the following consultations to the National Food Safety System. ${\circ}$ Approach entirely from farm to table ${\circ}$ Get ready for Risk Analysis System ${\circ}$ Secure transparency ${\circ}$ Establish the optimal policy by evaluating the effect of regulation When it comes to summarizing the consultation, it would be accumulated as two key words; "Efficiency" and "Credibility". Whereas the problem of efficiency focuses on precaution rather than post-management, it requires policy option to maximize consumer's benefit by evaluating the cost for the Food Safety Management and its benefit. Also, analyzing risk's character and amount, demanding an optimal means, and introducing scientific analysis system put much value on the stakeholder's communications are procedure's security which can satisfy both "Efficiency" and "Credibility" simultaneously. Especially, it is emphasized here that Risk Assessment need to be separated from Risk Management. This action is a valid means of credibility security throughout improving transparency. A number of nations and organizations have reformed the method of food management passing through reflection and examination of the prior National Food Safety Management since BSE occurred in Britain, 1996. FSA; Food Standard Agency, AFFSA, EFSA, BfR, and FSC are Risk Assessment Organization functionally separated from Risk Management Organization, JECFA, JMCFA, JMPR, JEMRA in Codex charge Risk Assessment internationally. In case of advanced countries excluding several those such as The U.S. and so forth, though these Risk Assessment Organizations are either separated functionally within Risk Management Organization or operated as apart organ, common factors are in which it has independence as Science Base. While securing independence of Risk Assessment Function, it is a tendency Risk Management should be functionally unified into efficiency as well. Though Germany constructs integral Risk Management System of diverse ways according to social and political conditions of each country such as GFOCP, DVFA, SNFA, CFIS and AQIS, there is a key word in the center, "Securing efficiency of Food Safety Management". However our nation has a representative plural；diversified system with The U.S., we took a step forward for unification as empowering policy's generalization；adjustment and Risk Assessment Function by means of enacting the "Food Safety Fundamental Law" in 2008 and establishing the "Food Safety Policy Commission" with private and governmental sectors in the Prime Minister's office. Even though the unification of Risk Management hereby increased, there is the lack of strengthening function of Risk Assessment and securing independence. It needs to be required for the professional committee in Food Safety Policy Commission to develop as a exclusive office of Risk Assessment by separating from a policy decision. Administrative Branches should reinforce feeble functions such as fundamental investigation；research for carrying out Risk Assessment with securing efficiency throughout reassessment of prior Risk Management Means.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.42 no.9 s.339
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• pp.51-60
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• 2005

The design of efficient cryptosystems is mainly appointed by the efficiency of the underlying finite field arithmetic. Especially, among the basic arithmetic over finite field, the rnultiplicative inversion is the most time consuming operation. In this paper, a fast inversion algerian in finite field $GF(2^m)$ with the standard basis representation is proposed. It is based on the Extended binary gcd algorithm (EBGA). The proposed algorithm executes about $18.8\%\;or\;45.9\%$ less iterations than EBGA or Montgomery inverse algorithm (MIA), respectively. In practical applications where the dimension of the field is large or may vary, systolic array sDucture becomes area-complexity and time-complexity costly or even impractical in previous algorithms. It is not suitable for low-weight and low-power systems, i.e., smartcard, the mobile phone. In this paper, we propose a new hardware architecture to apply an area-efficient and a synchronized inverter on low-complexity systems. It requires the number of addition and reduction operation less than previous architectures for computing the inverses in $GF(2^m)$ furthermore, the proposed inversion is applied over either prime or binary extension fields, more specially $GF(2^m)$ and GF(P) .