Doctoral Dissertations

Fengi Hwu

Abstract

"The feasibility of implementing the interpolating cubic spline function as encryption and decryption transformations is presented. The encryption method can be viewed as computing a transposed polynomial. The main characteristic of the spline cryptosystem is that the domain and range of encryption are defined over real numbers, instead of the traditional integer numbers. Moreover, the spline cryptosystem can be implemented in terms of inexpensive multiplications and additions.

Using spline functions, a series of discontiguous spline segments can execute the modular arithmetic of the RSA system. The similarity of the RSA and spline functions within the integer domain is demonstrated. Furthermore, we observe that such a reformulation of RSA cryptosystem can be characterized as polynomials with random offsets between ciphertext values and plaintext values. This contrasts with the spline cryptosystems, so that a random spline system has been developed. The random spline cryptosystem is an advanced structure of spline cryptosystem. Its mathematical indeterminacy on computing keys with interpolants no more than 4 and numerical sensitivity to the random offset ti increases its utility.

This article also presents a chaotic public-key cryptosystem employing a one-dimensional difference equation as well as a quadratic difference equation. This system makes use of the El Gamal’s scheme to accomplish the encryption process. We note that breaking this system requires the identical work factor that is needed in solving discrete logarithm with the same size of moduli"--Abstract, page iii.

Advisor(s)

Ho, C. Y. (Chung You), 1933-1988

Committee Member(s)

Zobrist, George W. (George Winston), 1934-
Dekock, Arlan R.
Prater, John Bruce, 1932-2002
Dawson, Darrow Finch, 1931-2007

Department(s)

Computer Science

Degree Name

Ph. D. in Computer Science

Comments

A report which is substantially this dissertation is available here for download.

Publisher

University of Missouri--Rolla

Publication Date

Spring 1993

Pagination

ix, 120 pages

Note about bibliography

Includes bibliographical references (pages 114-119).

Rights

© 1993 Fengi Hwu, All rights reserved.

Document Type

Dissertation - Restricted Access

File Type

text

Language

English

Thesis Number

T 6543

Print OCLC #

29301201

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