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Cryptography Project Proposal
Cryptography: Project Proposal
Abstract. The presumed problems of discrete logarithm (DLP) in the finite fields are the basis of many public cryptosystems keys. For instance, the secure identification option of the Sun Network File system uses discrete logarithms with a prime p of 192 bits. Presently, the DLP has become the subject of concern to many cryptographers and mathematicians because of its computational problems. The cryptosystems generally rest its securities on the assumption of mathematical problems that are difficult to solve. The difficulty of DLP in most cases tends to lie in the fact of having a one-way property making its computational complexity measured by algorithm computing time solving the mathematical problems. This paper describes the different steps necessary to solve the problem of discrete logarithm as well as discussing various state-of-the-art results obtained for the solution of Discrete Logarithm Problem (DLP). The paper will also present the Sun Network File System (SNF) while discussing its deficiencies.
Table of Contents
TOC o “1-3” h z u 1.0 Introduction PAGEREF _Toc350791829 h 32.0 The Sun NFS Cryptosystem PAGEREF _Toc350791830 h 32.0.1 Different steps necessary to solve the discrete logarithm problem (DLP) PAGEREF _Toc350791831 h 42.0.2 The state-of-the-art results obtained for the solution of DLP. PAGEREF _Toc350791832 h 42.0.3 SUN NFS cryptosystem deficiencies PAGEREF _Toc350791833 h 5
1.0 IntroductionThe Discrete Logarithm Problem (DLP) shows various mathematical problems that looks simple, however there are computational presumption making it to be difficult. The DLP is significant given that, it has various applications in cryptography field. Nevertheless, DLP study constantly bears a great significance in academics making it the subject of interest for cryptographers. The cryptosystems are secured only under definite computational assumptions. Most organizations today use Diffie-Hellman as a public key algorithm for their exchange for key. This is because it is considered as to be much secured when used with sufficient long keys and generators. However, its security usually relies on the problem of discrete logarithm which is assumed to be very computationally the same to the factoring large integers. The Diffie-Hellman is believed to be sensitive to choices of stronger prime and generators.
2.0 The Sun NFS CryptosystemThe Sun security option for their NFS can be built in the basic of Sun Remote Procedure Call (RPC) along with providing an authentication to both the users using the public key cryptosystem that looks as the modification of Diffie- Hellman key exchange system. In the Sun system, the prime is p while the integer is g which happens to be the same for all the users on every machine across the world using the software. Each machine is identified with a secret key m and p is the public. In this case, p always has 192 bits. The authentication generally requires proving that a person is able to possess the key m, although this does not have any effect on the systems’ security. When someone is breaking the Sun system, this is only necessary when finding the two values of m and p.
2.0.1 Different steps necessary to solve the discrete logarithm problem (DLP)There are different steps to be followed when solving the Discrete Logarithm Problem. First step is to let F = GF (q) while taking µ as a primitive element of letter F, whichever c in F* has a unique representation as c = µm, for 0 <= m <= q-1. C can be computed from µ and m with only 2[log2 q] multiplications. In this case, the binary representation of letter m will definitely give the order of the needed multiplications that consist of only squaring as well as multiplying by µ. The second steps involves sorting the pairs for instance, if m = 171 then 171 = 128 + 32 + 8 + 2 + 1 = (10101011)2. The third and the last steps involves computation, the computation of µ171 is then carried out by starting with 1, then, working from the most significant bit down, we square the current value and if there is a 1 in the binary representation we also multiply by µ. Thus, µ171 = ((((((((1)2µ) 2)2µ) 2)2µ) 2)2µ) 2µ.
2.0.2 The state-of-the-art results obtained for the solution of DLP.The results obtained for the solution of DLP makes an exponentiation in a finite field a state of the art. The results obtained can be used for a public exchange of protocol keys. The public knowledge is q, and µmU for each user U, although each user manages to keep the secret of the value mU. When trying to exchange keys exclusive of the transmission, A has to look up for the B’s public key as well as proponent it with its secret exponent. And likewise, B does the same to the A’s public key. Consequently, each of them will have to calculate the similar key value µmBmA = µmAmB. Solving the discrete logarithm problem for q, the Diffie and Hellman has to use a value of q which is at least 100 bits long to obtain the correct results when using discrete logarithm problem (DLP). In summary, the results obtained for the solution of DLP is that, the computing discrete logarithm module, the prime can be only a little harder compared to the factoring integers having the same size. For instance, with the same amount of the effort used in factoring 110 decimal digits integers can be used in computing the discrete logarithms module primes of up to 100 digits.
2.0.3 SUN NFS cryptosystem deficienciesIn spite of using SUN NFS cryptosystem as the best machine for solving logarithm problems, there are still several problems of using it as a larger module. The problem can be stopped by using a faster machine that is ready to compute faster. The speeds of a small workstations are generally increasing rapidly. However, using of faster algorithms can be of a great significance at the level of the basic arithmetic using the pre-computed tables.2.0.4 Recommendations for having a secure size for the prime number p
The most recommended way of securing size for the prime number p in the Diffie-Hellman algorithm is to improve the security of the scheme by having different prime for all the users. With the renowned logarithms problems, the problem of pre-computation of discrete logarithms if applied to a 100 decimal digit prime, it might use about 100 computers for computation. However if the prime happened to be used by everyone on the same network, then it will be necessary to obtain individual keys in a minute as compared when the user have different primes that makes it to be obtained more than a year. For this case, Diffie Hellman Scheme may be one of the only one of many methods that can be used for aunthetication.
Ethnic Conflict in Lebanon
Introduction: Ethnic Conflict in Lebanon
Racism did not come naturally from time or from life itself, but it came from the human mind and it causes a lot of divisions and conflict around the world. Racism often happens from the idea that groups of people think that they are, or they believe they are better than other people or groups. Racism often stems from differences in religions, color, language, or some time division within cultures. A lot of people think that ethnic conflict is something natural and occurs everywhere; however once it turns into violence and without understanding, which is not natural.
Lebanon
Lebanon is an Arab country located in Middle East and it shares boarders with Syria, Israel, and Jordan. Lebanon was known as Paris of Middle East because it was so multi-cultural. Its population used to be half Muslim and half Christian and they generally lived peacefully with each other for hundreds of years, sharing everything and even marrying between each other. Lebanon was considered as a secular country. When the civil war started in Lebanon in the year 1975, many people believed that the major reason for this ethnic war in Lebanon was the weakness of their regime, since it was set up based on sectarianism and not based on the interest of the state and the people as a whole. This weakness caused a lot of problems in Lebanon, in which the government could not control the religious organizations such as Hezb Allah (Hezbollah), which is the biggest Islamic Shi’a political organization in Lebanon. They took control of everything there, from education, health, economy, etc., because the government was too weak and divided to provide those services for everyone. Khashan explains, “Hezbollah has indeed gone a long way to achieving its objective of controlling Lebanon since its humble 1985 beginnings” (85-86).
They also worked hard on changing Shi’a thought about other religious groups in Lebanon with strong belief that they alone should rule. They started having children more and more just to raise the number of Muslims in Lebanon, to become the majority of the population over the Christians and Sunni minority. In doing this they could argue that they are the majority and it would be unfair for them to have a leader that is Christian or Sunni. On the other hand, they also succeed in some good things such as forcing the Israeli Army to withdraw from southern Lebanon in year 2000, which was considered a HUGE victory for them. They also funded schools and public projects, fed the poor, and many other social services that the government had been unable to provide in order to gain support of the growing Shi’a Muslim population in Lebanon.
Lebanese Regime
They have form of parliamentary democracy system which is based on sectarianism, which means that they distribute the leadership positions according to the percentage of population per group or sect. Their constitution gives them the right to choose their representatives every 4 years through elections, and then the parliament chooses the president. The president has a six year term.
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The current religious divisions are as follows;
a. President must be Maronite (Christian)
b. Prime Minister must be Sunni
c. Speaker of Parliament must be Shia
d. The confessional composition of parliament is pre-determined
These divisions between the parties and groups continually lead to conflicts between them and rivalries for power. Hezbollah continues to battle for power and legitimacy within the state in order to impose its beliefs in Sharia law, while Christians retain more favorable standing with the West that backs them. According to Khashanm, the Hezbollah said that “we are incapable at the present time of installing the rule of Islam, but this does not mean postponing our ideology and project” (81-82). Conflicts are long standing and both sides have committed atrocities. Political assassinations by both sides are not uncommon. It seems very unlikely that Lebanon will find a stable peace any time soon that will restore its former reputation as the Paris of the Middle East.
WHY it is Religions?
Lebanese youth are dealing with the civil war’s effects, even to this day. These young people are partly divided on the basis of their religion, with their loyalties lying with their religions and families more than with their country. Religious conflict has been the most fundamental cause of political upsets and weak performance of the government in Lebanon throughout the country’s history and continues to be so even today. The people of Lebanon are suffering because they are living confused between their loyalty to their religions and that of their country, which continues to lead to the weakness of nationalism on the part of the Lebanese people. Lebanon dealt with a civil war for a period of more than 16 years.
With the escalation of the civil war in Lebanon, Lebanese militias became strong enough to surpass the army. The government’s ability to maintain peace was sapped by the Lebanese army’s divided nature. Trust among the Muslims for the army and other central institutions were low because of the domination by the Christians of the government. They could not trust each other just because of their different religious beliefs. Muslims eventually deserted the Lebanese Army, declaring their decision of not following the commands of the Maronite generals any more. Although civil war in Lebanon ended in 1990, its side effects can still be observed to this day, as the Lebanese National Army evidences it and the Shi’a Muslim backed Hezbollah. (“Testimonies >> Lebanon”). Khashan asserts that the Hezbollah said, “We must work hard to achieve our goal, and the most important means of doing so is to transform Lebanon into a society of war” (81).
Since the establishment of authority over the Lebanese Armed Forces in the year 1945, the government of Lebanon has been purposefully keeping its armed forces weak and small because of the unique internal politics of the country. Christian politicians were afraid that Muslims might seize power in a military coup using their majority in the armed forces and use the power to control the military for themselves. Christian Lebanese also feared that Lebanon might be forced into a conflict between the frequent confrontations between Arabs and Israel, if they kept a large national army. So the government seemed unwilling to spend a large cost to develop the army. However, Muslim and Christian politicians also felt the need for developing a strong army as Lebanon might needed it against other countries, especially Israel and Syria, but they could not do it because of the ethnic and religious differences that made having a strong and unified military impossible.
Military division within the state of Lebanon is made even worse by outside lateral pressure by the neighboring Syria regime that often backs the illegitimate forces of Hezbollah. This too is an example of religious differences that are being promoted by outside foreign powers. One goal of the Syrian government is to create a more powerful military force within Lebanon that is run by Shi’a Muslim ideology (Hezbollah) in hopes of someday controlling the country and would be a strong ally to Syria. According to Khashan, “Hezbollah has striven during the past few years to overcome its limitations and promote its ultimate goal of transforming Lebanon into an Islamic state modeled after Iran’s wilayat al-faqih (the guardianship of the jurist)” (82-83).
Conflict of religions has served as the most important factor in hindering the effectiveness and sapping the power of the government to control the situation of law and order in Lebanon. Starting from the civil war through to Arab-Israel conflict to the outbreak of conflict in Syria recently, government has not been able to control effectively because of the conflict of religions. The conflict between the Christians and Muslims cannot be assumed. It does not seem to end anytime soon and the fat that there is calmness does not mean that there is peace. According to Hajjar, “the status of Christian–Muslim relations (CMR), which are difficult to assess, has been ambiguous in contemporary Lebanon” (n.p).Why it is not the Economy or the Politics?
The instability created by religious differences in Lebanon continues to create economic instability, which will cause the deterioration of the situation in Lebanon and the Lebanese people, who will not be able to unify enough to use the huge amount of resources that could be very essential for the stability of the country. It is well known that in every country where the lack of economic stability contributes to the conflicts because the people are dis-satisfied with the government. The people or groups within the country believe that the government is not doing a good job.
However, Lebanon is different case then the other countries since the religious conflicts are responsible for the weakness of government and the economy, because it is like an equation; if you have many religions conflicts that create an instable government and weak army, then of course, you will have a broken economy with little ability to fix it. There are still contradicting comments from experts regarding the Christian Muslims relations showing that there is no peace even in the contemporary Lebanon. According to Hajjar, “analysts, as well as individuals within Lebanese communities in Lebanon and within the diaspora have made conflicting claims” (n.p).
The ethnic and religious conflicts are the cause of what Lebanon went through and continues to be a growing crisis within the state. This caused an economic crisis, which hurt the ordinary citizens most particularly, and because the country is politically unstable, there is little or no chance that the regime will find a solution to fix this and bring peace between the religious
groups. In every unstable country you rarely find corporations that are willing to risk themselves and their investment because the dangers are too high. Without foreign investments economies remain weak. So again it is back to religious differences.
Opinion & Recommendations
Annotated Bibliographies
Khashan, H. “Hezbollah’s Plans for Lebanon.” Middle East Quarterly 20.2 (2013): 81-86. Print.
This article addresses Hezbollah’s intention of converting Lebanon into an Islamic state by controlling the political system with military component. However, the author indicates that the Hezbollah, which has premier military force in Lebanon, cannot transform itself into the genuine local political system because it does not want to be equated to the ordinary political groups that conform to the rules of accommodation.
Hezbollah has actually made great steps and goal of controlling Lebanon since its initiation in 1985 such as dominating both the domestic and foreign policies as well as having a more superior army compared to the national army. Although it controls major arms of the government such as instituting government and making judicial appointments, it does not intend to integrate with the Lebanese political practices. The author indicates that there is a need of eliminating the Hezbollah to build a viable state. This article relates to other articles because it addresses Lebanon concerns. It gives significant details of the topic of research, which is based on Lebanon political systems. The article explains some of the atrocities done in Lebanon since the beginning of the Hezbollah.
Hajjar, G. Voices and Visions of Christian-Muslim Relations In Post-Civil War Lebanon : An Overview of Causes, Effects and The Question Of Identity 2000-2008 2012: Print.
Christian Muslim status in Lebanon has been very shaky and ambiguous of late due to the religious conflicts between the Christians and the Muslims. According to the author Hajjar, various analysts and voices both internationally and within the Lebanon community have voiced their concern, which appear to be conflicting regarding the Christian-Muslim relations. Some of the assertions according to Hajjar are that the relations between the two religions have largely improved after the 1991 Lebanese Civil War. The proponents believe that if there would be any tension then there would perhaps been another civil war amongst the two groups.
They claim that Lebanon has been better than before the war because of the possible good relationship between the Muslims and the Christians. The proponents’ further claim that the Taif agreement played a huge role in bringing peace between the two groups particularly after the post-civil war. Major communities were involved in signing the document in 1991 thus prompting unity in Lebanon. Nevertheless, Hajjar has explored legitimacy of this proposal through the comprehensive quantitative and qualitative research. The author has exposed the tension and poor state of the Christian Muslim relations in the modern Lebanon through exhaustive research.
He highlighted through the interviews he conducted with various stakeholders, some of the weaker parts of the relations as well as giving detailed reasons that support the weaknesses. He conducted the research with the university students who were asked about their feelings and attitude regarding the relations’ challenges and factors affecting the problems. He further researched on the role that identity played in the Christian Muslim relation and finally compared his results with understanding of the relations. The author finally gave recommendations concerning further and better study as well as the future relations between the Christian Muslims.
This paper is very relevant to the research as it addresses some of the challenges facing Lebanon. Christians being part of the larger population in Lebanon have faced opposition from the Muslims including the Hezbollah group who wanted to turn Lebanon into a Muslim country. The rise of conflict during the Civil war remains integral in the history of Lebanon. It is also worth noting that the tension between the Christians and Muslims in Lebanon is very significant has it affects several issues such as political decisions. The article relates with the other article in that it considers some important aspects of Lebanon.
Ethics
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Ethics
If I was given an opportunity to either send 800 dollars to an area that is suffering from famine and save the lives of a dozen people from starvation or give the money to my sibling to purchase books she needs for college, I would go with the first option of donating the money to the starving people. There are many reasons why I would make this decision, and they have to do with my belief in the greater good of my actions and the values I hold about what is morally wrong and morally wrong. I would decide to donate the money to the less fortunate and later find a way to find money to purchase books about my sister. At every opportunity, I get, I believe that my actions should be an indication of who I am as a person. I feel that by choosing to give the money to my sister, I would be doing an injustice to the people who are starting. This is because when you compare both situations, the people who are in starvation are in more dire need than my sister, and giving the money to my sister rather than them would be like signing their death certificate. Further, although both victims need basic needs, I feel that the problem of hunger is more severe than education hence there is a need to address the needs of the people who are affected by this problem more. The fact that they are a dozen means that I will be helping more people by donating as opposed to my sister who is alone.
My decision-making process aligns more with the moral theory of utilitarianism, one of the most influential theories of morality in history. The theory holds that the right action is one that directly produces a balance of happiness over unhappiness for the parties concerned. In this regard, happiness is the only intrinsic good and what matters the most is the amount of happiness that is derived from performing an action. To determine the correct action one only needs to calculate the amount of happiness derived from all actions and select the one that generates the most happiness. In this case, the act of donating the 800 dollars to the starving lot will bring a lot of happiness and satisfaction than giving the money to my sister. Although my sister will also be happy that she will purchase the books, the people who were rescued from starvation would be happier. In this theory, the moral thing to do is to select an action that brings more benefits to society and in this scenario, donating the 800 dollars to people who are on the brink of starvation is the right thing to do.
