Master of Science

<p>Montgomery County, Virginia, is a southern Appalachian county founded in 1776. Throughout the county's antebellum history, as with most other regions of the South, four major population groups were visibly present. There were slaves, free blacks, white slaveowners, and white non-slaveowners. Little research has previously been conducted on the antebellum people of the Appalachian South. This work is a social history consisting of cross tabulations of data found in the county's manuscript census reports for 1850 and 1860. County court records also provide much useful information on the people and their activities before the Civil War. Together they form an invaluable source of information on antebellum mountain life as a forgotten segment of southern society. </p> / Master of Arts

The communication technology is changing rapidly every day, and the internet has played a very important role in our lives. Through specific protocols, people transform the data into 0¡¦s and 1¡¦s as digital signals and transfer them from sender to receiver via the network. Unfortunately, data transfer through the internet is open to the public, and too much exposure of private data may be a serious risk. To avoid this situation, we can encrypt the data before transmission to guarantee data confidentiality and privacy. The RSA encryption system is a simple and highly secure public key cryptosystem, but the encryption and decryption process requires a lot of exponentiation operations and division operations. In order to improve the reliability of the encrypted data, the operands are usually larger than 512 bits. If software is used to perform encryption and decryption, real time application will not be sufficed, since software lacks performance. For this reason, the RSA must be implemented in hardware. Since then, many methods of refining the effectiveness of the RSA encryption and decryption hardware have began to be developed. This research proposes a new Modular Multiplier architecture similar to the original Montgomery Modular Multiplier and the RSA encryption system, which is composed by simple adders, shifting registers and multiplexers. What¡¦s more, we¡¦ve also proposed new concepts including the Quotient Lookahead and the Superfluous Operation Elimination to further enhance the performance. The test results show that our design can reduce the total cycle count by 19%, and also save the overall energy consumption. Due to the features of high performance and energy saving, the proposed design is suitable for portable devices which have low power requirements.

The explosive growth in the data communications industry has positioned the internet to hold very important roles in our lives. Sending or receiving data on an open network is an invitation for unauthorized users to obtain your personal information. In order to avoid compromising sensitive information while transferring data, the data needs to be encrypted before transmission to ensure that the information remains safe and confidential. RSA is the most widely used public-key cryptosystem. An RSA operation is a modular exponentiation, which is usually achieved by repeated modular multiplications. For security reasons, RSA operand sizes need to be 512 bits or greater. It would be difficult to achieve real time transmission on the internet by running software programs on typical processors. For this reason, we believe it is necessary to implement RSA by hardware circuit in order to speed up RSA operations. Modular exponentiation is the only operation in RSA cryptosystem and it can be done through repeated modular multiplications. The Montgomery multiplication algorithm is widely recognized as the most efficient modular multiplication algorithm. In order to improve the speed of RSA operation, many papers have proposed ways to refine the Montgomery Algorithm and its architecture. In this thesis, we focus on further improving the performance and power consumption of RSA cryptosystems. This research presents an improved Montgomery multiplier and RSA cryptosystem architecture using only one carry saver adder to significantly reduce the delays of conventional multipliers. We also proposed a low power shift register to reduce power consumption of shift register in Montgomery multiplier. Experimental results show that the proposed RSA cryptosystem not only runs with higher performance but also consumes less power, leading to this system more competitive and suitable for implementations in portable electronic products.

Thanks to the development of the Internet in recent years, we can see more and more applications on E-commerce in the world. At the same time, we have to prevent our personal information to be leaked out during the transaction. Therefore, topic on researching network security becomes increasingly popular. It is well-known that an encryption system can be applied to consolidate the network security. RSA encryption algorithm is a special kind of asymmetric cryptography, commonly used in public key encryption system on the network, by using two prime numbers as the two keys to encrypt and decrypt. These two keys are called public key and private key, and the key length is at least 512 bits. As a public key encryption, the only way to decrypt is using the private key. As long as the private key is not revealed, it is very difficult to get the private key from the public key even using the reverse engineering. Therefore, RSA encryption algorithm can be regarded as a very safe encryption and decryption algorithm. As the minimum key length has to be greater than 512 bits to ensure information security, using software to execute RSA encryption and decryption will be very slow so that the real time requirement may not be satisfied. Hence we will have to implement RSA encryption system with a hardware circuit to meet the real time requirement on the network. Modular exponentiation (i.e., ME mod N) in RSA cryptosystem is usually achieved by repeated modular multiplications on large integers. A famous approach to implement the modular multiplication into hardware circuits is based on the Montgomery modular multiplication algorithm, which replaces the trial division by modulus with a series of addition and shift operations. However, a large amount of clock cycle is still required to complete a modular multiplication. For example, Montgomery multiplication algorithm will take 512 clock cycles to complete an A․B mod N. As a result, performing one modular exponentiation ME mod N in RSA cryptosystm will need 512․512 clock cycles. To counter the above disadvantage, we employ radix-4 algorithm to reduce 50% of clock cycle number for each A•B mod N. In addition, we also modify the architecture of conventional in order to achieve the radix-4 algorithm to reduce its critical path delay so that the performance can be improved further. Experimental results show that the proposed 1024-bit radix-4 modular multiplier (Our-Booth-Radix-4) before performing as pipeline is 70% faster than the radix-2 multiplier with 24% area overhead. Furthermore, it is 20% faster than traditional radix-4 modular multiplier with 12% area reduction. Therefore, its AT is smaller than the previous architectures.

Spectral methods have been widely used in various fields of engineering and applied mathematics. In the field of computer arithmetic: data compression, polynomial multiplication and the spectral integer multiplication of Sch&uml / onhage and Strassen are among the most important successful utilization. Recent advancements in technology report the spectral methods may also be beneficial for modular operations heavily used in public key cryptosystems. In this study, we evaluate the use of spectral methods in modular multiplication. We carefully compare their timing performances with respect to the full return algorithms. Based on our evaluation, we introduce new approaches for spectral modular multiplication for polynomials and exhibit standard reduction versions of the spectral modular multiplication algorithm for polynomials eliminating the overhead of Montgomery&rsquo / s method. Moreover, merging the bipartite method and standard approach, we introduce the bipartite spectral modular multiplication to improve the hardware performance of spectral modular multiplication for polynomials. Finally, we introduce Karatsuba combined bipartite method for polynomials and its spectral version.

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Thesis (D. Min.)--Harding University Graduate School of Religion, 2002. / Includes bibliographical references (leaves 138-144).

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