Cryptography – Key management – Having particular key generator
Reexamination Certificate
2000-04-20
2004-08-24
Barrón, Gilberto (Department: 2132)
Cryptography
Key management
Having particular key generator
C380S028000
Reexamination Certificate
active
06782101
ABSTRACT:
STATEMENT OF GOVERNMENT INTEREST
The invention described herein may be manufactured and used by or for the Government of the United States of America for governmental purposes without the payment of any royalties thereon or therefore.
BACKGROUND OF THE INVENTION
(1) Field of the Invention
The present invention relates generally to encryption and decryption, and more particularly to using fractal key generation to encrypt and decrypt two-dimensional data.
(2) Description of the Prior Art
The rapid and parallel development of the telecommunications and computer industries increased requirements for data throughput and analysis. Accordingly, electronic transmission is widely accepted and practiced. Unfortunately, the possibility of electronic mischief, unintentional and intentional, also increases with technological evolution. Parties communicating electronically are therefore increasingly concerned with encrypting transmissions to ensure that an y unintended recipients cannot become privy to transmission contents.
Image data security is of increased importance in the commercial sector with the advent of electronic tax filing, increased fax transmissions, etc. The military similarly has interest in protecting computer screen image transmissions, satellite image transmissions, and other image data communications. In most applications, image data is two-dimensional data; therefore, an image can be considered as two-dimensional memory.
U.S. Pat. No. 5,987,136 to Schipper et al. describes an apparatus for producing a self-authenticating visual image that incorporates positional information with a digital image forming means. The position information is incorporated in the digital image by altering selected pixel bit values for a selected authentication pattern P of pixels in a chosen subset CS of the pixel array; and this selected pattern may be determined using the position information. The position information may be encrypted, using an encryption key based on position information, and may be stored separate from, or as part of, the digital image.
U.S. Pat. No. 5,903,648 to Javidi teaches an image encryption method that multiplies the image by a random phase function. The Fourier transform of the product of the image and the random phase function is then multiplied by another random phase function in the Fourier domain. The inverse Fourier transform is then taken to obtain the encrypted image.
U.S. Pat. No. 5,862,217 to Steinberg et al. provides an in-camera encryption technique for use with digital cameras. Steinberg et al. utilize a password protected encryption generator to encrypt all digital images and ensure that all digital data is stored in encrypted form.
U.S. Pat. No. 5,533,127 to Luther presents two-dimensional data encryption using multiple encryption passes through the data. In each pass through the two-dimensional data having dimensions m rows×n columns, each m
th
row and each nth column of data is encrypted by complementation of the data in the row or column. For each encryption pass, m and n are randomly selected.
In mathematics, fractals describe curves or surfaces created by repeated subdivisions of the curve or surface. Fractals also include geometric shapes that are infinitely ragged, curvy, or otherwise irregular. Fractal analysis applies to weather forecasting, population growth prediction, and to a greater extent, image compression and analysis.
Fractals exploit the self-similarity that exists across scales or sub-bands of images. Fractal image compression algorithms create a series of transformations which, when applied to a set of data, result in that data approaching a “fixed point” that approximates the original data. To regenerate an approximation of the data using fractal techniques, it is only necessary to know the nature and content of the transformations. The transformations can thus be applied to some initial arbitrary data in an iterative process to transform the arbitrary data into an approximation of the original data. With fractal analysis, therefore, the data is represented by its transformations.
Fractal image processing applications include image boundary correction (U.S. Pat. No. 5,982,386), fractal image coding (U.S. Pat. Nos. 5,924,053 and 5,093,678), image compression (U.S. Pat. Nos. 5,862,264, 5,862,263, and 5,857,036), and medical image analysis (U.S. Pat. No. 5,848,198). Because image data is two-dimensional, image data demand large memory segments. The iterative nature of fractal processing is therefore desirable for processing such data.
There is currently no fractal application or method that provides encryption and decryption of two-dimensional data.
What is needed is a fractal method to encrypt and subsequently decrypt, two-dimensional data.
SUMMARY OF THE INVENTION
It is a general purpose and object of the present invention to utilize fractals to generate a fractal key matrix.
It is another object of the present invention to use the generated fractal key to encrypt a matrix of two-dimensional data.
It is yet another object of the present invention to describe a method by which a receiver may obtain the encrypted data with fractal key parameters, reconstruct the fractal key, and decrypt the encrypted data.
Other objects and advantages of the present invention will become more obvious hereinafter in the specification and drawings.
These objects are accomplished with the present invention by a method for encrypting and decrypting two-dimensional data. A fractal and associated fractal computation initialization values are selected, with a square fractal key matrix. The fractal key matrix is computed iteratively, changing fractal parameters as necessary, to obtain a full rank fractal key matrix. Data to be encrypted is buffered in a two-dimensional matrix to allow matrix multiplication between the buffered data matrix and the fractal key matrix. The encrypted data, the encrypted data matrix dimensions, and the fractal parameters necessary to regenerate the fractal key are transmitted to a receiver that recreates the fractal key from the fractal parameters. The receiver additionally generates the fractal key matrix inverse. The data is decrypted by a matrix multiplication of the encrypted data and the fractal key matrix inverse.
REFERENCES:
patent: 4694407 (1987-09-01), Ogden
patent: 5054066 (1991-10-01), Riek et al.
patent: 5253297 (1993-10-01), Press
Schneier, Bruce; Applied Cryptography; 1996; 2ndEdition; pp. 169-187,265-301,397-428.*
Wikipedia: The Free Encyclopedia; http://en2.wikipedia.org/wili/Inverse_matrix.
Barrón Gilberto
Kasischke James M.
Kim Jung Woo
Oglo Michael F.
Stanley Michael P.
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