Cryptography – Communication system using cryptography – Symmetric key cryptography
Reexamination Certificate
1999-11-09
2002-03-26
Hayes, Gail (Department: 2131)
Cryptography
Communication system using cryptography
Symmetric key cryptography
Reexamination Certificate
active
06363153
ABSTRACT:
FIELD OF THE INVENTION
The present invention relates generally to a method and apparatus for secure digital chaotic communication. More specifically, it relates to a system for encoding and decoding information by controlling a chaotic system.
BACKGROUND OF THE INVENTION
Secure communication is employed for maintaining both the authenticity and the confidentiality of information. There are many different systems for secure communication currently available. However, on the one hand, increases in computing power have raised questions about the security of many of these systems, and, on the other hand, the more secure systems are so complicated that the speed of processing is becoming a limiting factor in transmitting information. Secure communication based on chaotic systems is a rapidly developing field of research. In general, a chaotic system is a dynamical system which has no periodicity and the final state of which depends so sensitively on the system's precise initial state that its time-dependent path is, in effect, long-term unpredictable even though it is deterministic.
One approach to the use of chaotic systems to encode information requires the transmission of a key to decode the information. One such method of secure communication uses a chaotic equation to produce random numbers. Banco U.S. Pat. No. 5,048,086. In summary, this approach converts a sequence of numbers produced by a chaotic equation into digital form, adds the converted numbers to the digital message to be encoded and transmits the combined digital stream to a receiver. The receiver extracts the digital message from the transmitted digital stream by generating the same sequence of digital numbers using the same chaotic equation as the key. See Weiss U.S. Pat. No. 5,479,512. The disadvantage of this approach is the decreased security resulting from the transmission of the key.
Other approaches to the use of chaotic systems for secure communication do not require the transmission of a key. One such approach involves the synchronization of chaotic systems. Carroll U.S. Pat. No. 5,473,694 and Cuomo U.S. Pat. No. 5,291,555. A parameter of a chaotic signal is modulated with an information bearing signal or an information bearing signal is added to a chaotic signal. The resulting chaotic signal is transmitted, using conventional transmission technologies, from a transmitter-encoder to an identical receiver-decoder. The receiver-decoder is driven into synchrony by the original chaotic signal with no key exchange necessary. Comparison of the information bearing chaotic signal is made with the synchronization signal to extract the original information. However, in these systems, if the transmission is intercepted, it is possible to use phase space reconstruction to reconstruct the underlying dynamic of the transmitter-encoder. In some cases, it has been shown that the ability to reconstruct transmitter-encoder dynamics makes it possible to extract the information bearing signal using non-linear dynamic (“NLD”) forecasting or other technologies.
Another approach to secure communication is to “control” a chaotic system by applying very small perturbations to the system. [S. Hayes, C. Grebogi, E. Ott, and A. Mark,
Experimental Control of Chaos for Communication
, Phys. Rev. Lett. 73, 1781 (1994)] To summarize the control approach, a transmitter-encoder encodes a signal by controlling the sequence of output peaks of a chaotic oscillator through the application of small amplitude perturbations to the oscillator. A receiver-decoder extracts the signal by observing the sequence of peaks of the transmitted signal. However, analysis of this communication system through reconstruction of the phase space dynamics or by NLD forecasting detects the imposition of controls. Thus, a chaotic system that transmits a signal that can be used to reconstruct the underlying chaotic system has limited security.
It is an object the present invention to use “control” of a chaotic system for a secure communication system. It is a further object to do so with a transmitted signal that cannot be used for reconstruction of the underlying chaotic system, thereby thwarting attempts to reveal the transmitted message by reconstruction techniques or NLD forecasting. It is also a further object of the present invention to provide a means by which the transmitter-encoder and receiver-decoder of such a secure communication system are synchronized.
SUMMARY OF THE INVENTION
An object of the present invention is to provide a new method and apparatus for secure digital chaotic communication. Another object of the present invention is to provide a faster, more secure method and apparatus for digital communication by controlling a chaotic system.
The present invention may be implemented either in hardware or software. Controls are intermittently applied by a transmitter-encoder to a chaotic system to generate a sequence of bits
0
and
1
corresponding to the plaintext of a digital message. A control
o control bit stream is thereby created in which a 0 indicates that no control was applied and a 1 indicates that a control was applied. The control
o control bit stream and a prepended synchronization bit stream are transmitted, using conventional transmission technologies, from the transmitter-encoder to an identical receiver-decoder. A chaotic system in the receiver-decoder is driven into synchrony and is then subject to intermittent controls based on the control
o control bit stream, thereby causing it to generate the digital message.
The foregoing and other objects, features and advantages of the current invention will be apparent from the following more detailed description of preferred embodiments of the invention as illustrated in the accompanying drawings.
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Carroll et. al. Synchronizing Chaotic System SPIE Chaos in Communications 32-43, 1993.*
Cuomo et. al. Synchronization of Lorenz-Based Chaotic Circuits with Applications to Communications, IEEE Transactions on Circuits and Systems, 626-633, 1993.*
Yang et. al. Secure Communication via Chaotic Parameter Modulation, IEEE Transactions on Circuits and System 817-819, 1996.*
Lai Synchronization of a Chaotic Optical System Using Control SPIE Chaos in Communication 91-102, 1993.*
Shilnikov Mathematical Problems of Nonlinear Dynamics: A Tutorial Journal of Bifurcation and Chaos 7(9) 1953-2001, 1997.*
Kevin Short, “Steps Towards Unmasking Secure Communications,” International Journal of Bifurication and Chaos, vol. 4, No. 4, 1994, pp. 959-977.
Parker Andrew T.
Short Kevin M.
Devine Millimet & Branch PA
Hayes Gail
Remus Paul C.
Seal James
Sullivan Todd A.
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