Computer and network security systems rely on the privacy and authenticity of information, which requires implementation of cryptographic functions. Software implementations of these functions are often desired because of their flexibility and cost effectiveness. In this study, we concentrate on developing high-speed and area-efficient modular multiplication and exponentiation algorithms for number-theoretic cryptosystems. The RSA algorithm, the Diffie-Hellman key exchange scheme and Digital Signature Standard require the computation of modular exponentiation, which is broken into a series of modular multiplications. One of the most interesting advances in modular exponentiation has been the introduction of Montgomery multiplication. We are interested in two aspects of modular multiplication algorithms: development of fast and convenient methods on a given hardware platform, and hardware requirements to achieve high-performance algorithms. Arithmetic operations in the Galois field GF(2[superscript]k) have several applications in coding theory, computer algebra, and cryptography. We are especially interested in cryptographic applications where k is large, such as elliptic curve cryptosystems. / Graduation date: 1998

A public key cryptosystem allows two or more parties to securely communicate over an insecure channel without establishing a physically secure channel for key exchange. The RSA cryptosystem is the most popular public key cryptosystem ever invented. It is based on the difficulty of factoring large composite numbers. Once the RSA system is setup, i.e., the modulus, the private and public exponents are determined, and the public components have been published, the senders as well as the receivers perform a single operation for signing, encryption, decryption, and verification. This operation is the computation of modular exponentiation. In this thesis, we focus on fast implementations of the modular exponentiation operation. Several methods for modular exponentiation are presented, including the binary method and the m-ary method. We give a general algorithm of implementing the m-ary method, and some examples of the quaternary method and the octal method. The standard multiplication and squaring algorithms are also discussed as methods to implement the modular multiplication and squaring operations. Two methods for performing the modular multiplication operation are given: the multiply and reduce method and the Montgomery method. The Montgomery product algorithm is used in the implementation of the modular exponentiation operation. The algorithms presented in this thesis are implemented in C and 16-bit in-line 80486 assembly code. We have performed extensive testing of the code, and obtained timing results which are given in the last chapter of the thesis. / Graduation date: 1995

Thesis (M.S. in Computer Science)--Naval Postgraduate School, December 2009. / Thesis Advisor(s): Dinolt, George. Second Reader: Eagle, Chris. "December 2009." Description based on title screen as viewed on January 27, 2010. Author(s) subject terms: Distributed password cracking, Berkeley Open Infrastructure for Network Computing (BOINC), and John the Ripper. Includes bibliographical references (p. 63-64). Also available in print.

Thesis (Ph. D.)--Florida State University, 2004. / Advisor: Dr. Yvo Desmedt, Florida State University, College of Arts and Sciences, Dept. of Computer Science. Title and description from dissertation home page (June 18, 2004). Includes bibliographical references.

Thesis (Ph. D.)--Hong Kong University of Science and Technology, 2003. / Includes bibliographical references. Also available in electronic version. Access restricted to campus users.

Not available / text

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Thesis (M.S.)--Duquesne University, 2007. / Title from document title page. Abstract included in electronic submission form. Includes bibliographical references (p. 43-47).

Thesis (Ph.D.)--University of Wollongong, 2004. / Typescript. Includes bibliographical references: leaf 109-116.

Thesis (M.S.) -- Rochester Institute of Technology, 2008. / Typescript. Includes bibliographical references (leaves 57-60).