Communicating bits over a network is expensive. Therefore, cryptosystems that transmit as little data as possible are valuable. This thesis studies several cryptosystems that require significantly less bandwidth than conventional analogues. The systems we study, called torus-based cryptosystems, were analyzed by Karl Rubin and Alice Silverberg in 2003 [RS03]. They interpreted the XTR [LV00] and LUC [SL93] cryptosystems in terms of quotients of algebraic tori and birational parameterizations, and they also presented CEILIDH, a new torus-based cryptosystem. This thesis introduces the geometry of algebraic tori, uses it to explain the XTR, LUC, and CEILIDH cryptosystems, and presents torus-based extensions of van Dijk, Woodruff, et al. [vDW04, vDGP⁺05] that require even less bandwidth. In addition, a new algorithm of Granger and Vercauteren [GV05] that attacks the security of torus-based cryptosystems is presented. Finally, we list some open research problems.

Communicating bits over a network is expensive. Therefore, cryptosystems that transmit as little data as possible are valuable. This thesis studies several cryptosystems that require significantly less bandwidth than conventional analogues. The systems we study, called torus-based cryptosystems, were analyzed by Karl Rubin and Alice Silverberg in 2003 [RS03]. They interpreted the XTR [LV00] and LUC [SL93] cryptosystems in terms of quotients of algebraic tori and birational parameterizations, and they also presented CEILIDH, a new torus-based cryptosystem. This thesis introduces the geometry of algebraic tori, uses it to explain the XTR, LUC, and CEILIDH cryptosystems, and presents torus-based extensions of van Dijk, Woodruff, et al. [vDW04, vDGP⁺05] that require even less bandwidth. In addition, a new algorithm of Granger and Vercauteren [GV05] that attacks the security of torus-based cryptosystems is presented. Finally, we list some open research problems.

The main objective of this research paper is to find the association between unemployment rate and GDP growth which is presented empirically by Arthur Okun’s in early 1960s. For this purpose I have used annual time series data during the period 1981-2005 of Pakistan. I applied difference version of Okun’s law which is more appropriate to access results directly from empirical data. In order to find long run relation between the variables I used Engle-Granger cointegration technique and Error Correction Mechanism (ECM) to find the short term behavior of GDP growth to its long run value. This paper verifies negative relationship between unemployment rate and GDP growth and both variables have long run relation with each other. Moreover GDP growth will adjust more quickly towards equilibrium in the long run.

Equity risk premium is a financial variable that is surrounded by mystery. Starting from the almost 30 year old equity premium puzzle caused by considerations that equity premium values which are observable in past data imply an implausibly high risk aversion to more recent statements that equity premium does not exist anymore. The purpose of this paper is to find out more about the traits and characteristics of equity risk premium, its current status and interactions of its values across international markets by conducting data analysis on mature equity markets using optimal methods as suggested in academic literature. This paper attempts to clear some of the confusion regarding equity premiums by analyzing equity excess returns in the mature equity markets of France, Germany, Sweden, United Kingdom and USA from 1970 to 2012. It is concluded that equity premium follows a mean reverting process however in short-term and mid-term its values can be volatile and in March 2000 there might have been a structural break. The obtained current equity premium values are significantly higher than zero. At the same time they are lower than popularly used values that are based on longer periods of past data. The paper also finds out that equity premiums in different countries are highly correlated not only due to shared global influence but also due to some direct causality relationships between them, most of which are positive. A panel data analysis is conducted as well to test the explanatory power of some macroeconomic and financial variables on the equity risk premium values and it is concluded that risk-free rate and unemployment rate have some explanatory power for equity risk premium values. This paper manages to clear a part of the mystery that surrounds the equity risk premium.

This study presents our attempt to examine the linkages and to investigate the linkage of stock price indexes among Taiwan, China and its major trading countries. Our empirical analysis employs daily data on stock price indexes over the period of January 2, 2000 to May 10, 2010. The total number of observations is about 2500. This study employ a sequence of time-series methodologies, including unit root test, cointegration test, vector error correction model, Granger causality test, Criterion, autocorrelation test, heteroscedasticity test, GARCH and Bi-GARCH. The findings of this study as follows. First, after first difference, every stock price indexes series all became stationary. Second, we found there has no long-run interrelationship among these stock markets. Third, we found that Taiwan¡¦s stock market exits leading role to China¡¦s stock market, but other countries¡¦ stock market lead Taiwan¡¦s stock market. For China, the stock market of United States, Japan, Taiwan and Hong Kong has a leading role to China¡¦s stock market. Only the rela-tionship between South Korea and China¡¦s stock market is independent. Forth, the result of autocorrelation test and ARCH test indicates that the influence of stock price indexes of major trading countries to Taiwan and China¡¦s stock price index has changed over time. Finally, the result of study indicates that every stock market can forecast its future trend by using its past stock data and investor can use the past stock data of stock market of major trading countries to forecast Taiwan and China¡¦s stock market.

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This study investigates the validity of the twin deficits hypothesis for the Turkish quarterly data over the 1988:1-2005:2 periods. To this end, we consider a VAR variable space containing budget deficits, current account deficits, real output, real interest rates and real exchange rates and employ cointegration, equilibrium/error correction mechanism techniques along with Granger-non-causality tests and impulse response analyses. The empirical results from decompositions of the budget and current account deficits into their cyclical and structural components suggest that both CAD and BD are counter-cyclical. The twin deficit hypothesis, consistent with the conventional Mundell-Flemming framework, postulates that current account and budget deficits move together in the long run and the causality runs from the former to the latter. The results from Engle-Granger and Johansen cointegration procedures support either the twin divergence or the Ricardian equivalence postulations but not the twin deficits hypothesis. Current account deficits and budget deficits are also found to be jointly endogenous. The short-run impacts of budget deficits on current account deficits are found to be mainly through the real exchange rate and real interest rate channels.

This study aims to investigate the direction of the relationship between financial deepening and economic growth after the completion of financial liberalization in Turkey. In order to do this, an unbalanced panel data set of 49 OECD and emerging countries for 1953-2005 period is examined with Granger causality and panel data estimation techniques. In the light of panel data analysis results, quarterly Turkish time series data for 1987-2006 period is examined by using Granger causality, cointegration and Vector Error Correction Model (VECM) procedures. Although the unbalanced panel data analysis reveals a relationship that is from financial deepening to economic growth, country specific Granger causality analysis employed with the panel data gives the opposite relationship for Turkey. Moreover, it is observed that quarterly time series data analysis mainly gives a relationship that is from economic growth to financial deepening.

This study is concerned with the lead-lag relationship between Turkish spot equity and derivatives markets. In the study, the spot equity market is represented by the ISE-30 Index. In order to compare the structure of the two markets, the futures contract written on the ISE-30 Index, namely TURKDEX-ISE 30, is chosen to represent the derivatives market. The analysis is performed over the sample period beginning February 4, 2005 and ending on December 10, 2010 which actually covers the entire time span from the establishment of the TURKDEX market until the end of last year. This sample period is examined on the basis of 5-minute intervals during the trading day, enabling a more detailed and accurate evaluation of the lead-lag power of the markets. The main methods applied to examine the structure of information flow between the markets are co-integration and causality analyses. Different approaches of these basic methods are employed as well in order to provide robust results. An additional robustness check is provided through examining the relationship between the markets by using both raw and filtered prices. ARMA filtering is performed on the prices and these findings are compared to those obtained by raw prices in order to avoid the problem of infrequent trading. Outcomes of both raw and filtered price analyses reveal that in 2006, 2007 and 2009 the relationship between the markets is bi-directional, whereas in 2008 and 2010, futures market strictly leads the spot market. Filtered and raw analyses do not have a definitive conclusion regarding the lead-lag relationship in 2005. For this year, while the raw data support a bi-directional relationship, ARMA filtering indicates that the spot market leads the derivatives market.

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