Encryption system based on chaos theory
First Claim
1. A cryptographic system comprising:
- a random number generator;
a memory for storing one or more cryptographic keys;
an arithmetic means coupled to the random number generator and memory for iterating a predetermined logistic difference equation having the form xn+1 =μ
xn (1-xn), where μ
is a cryptographic key, xn is a random number generated by the random number generator, and xn+1 is an iterated result generated by succesively calculating xn+1 in the above equation a selected number of successive times. to thereby generate a sequence of encrypting iterates, and for converting the sequence of encrypting iterates into binary form;
adder means coupled to the arithmetic means for summing the encrypting iterates with digital data to thereby generate encrypted data; and
controller means for controlling the operation of and transfer of data between the random number generator, the memory, the arithmetic means, and the adder means.
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Accused Products
Abstract
An encryption system and method based on the mathematics of Chaos theory, which provides protection of data from unauthorized modification and use during its storage and transmission. At its core are nonlinear equations which exhibits random, noise-like properties, given certain parameter values. When iterated, a periodic sequence is produced with an extremely long cycle length. A domain transformation process is then used to convert the floating-point iterates into binary form for summation with the digital data to be protected. The result is an encrypted message that cannot be modified, replaced, or understood by anyone other than the intended party. The use of Chaos theory in combination with the domain transformation process results in an easily implemented cryptographic system with extremely robust cryptographic properties. The concepts of the present invention also lend themselves well to either hardware or software implementations. The cryptographic system of the present invention may be employed to encrypt and decrypt sensitive information, to authenticate data and video links, or similar applications. It can also be used to provide a simple hash function for the secure storage of passwords in a computer system. Its simplicity, requiring only floating-point operations at its core, allows a lower cost and higher performance product with cryptographic security equivalent to conventional cryptographic systems.
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Citations
14 Claims
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1. A cryptographic system comprising:
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a random number generator; a memory for storing one or more cryptographic keys; an arithmetic means coupled to the random number generator and memory for iterating a predetermined logistic difference equation having the form xn+1 =μ
xn (1-xn), where μ
is a cryptographic key, xn is a random number generated by the random number generator, and xn+1 is an iterated result generated by succesively calculating xn+1 in the above equation a selected number of successive times. to thereby generate a sequence of encrypting iterates, and for converting the sequence of encrypting iterates into binary form;adder means coupled to the arithmetic means for summing the encrypting iterates with digital data to thereby generate encrypted data; and controller means for controlling the operation of and transfer of data between the random number generator, the memory, the arithmetic means, and the adder means. - View Dependent Claims (2, 3)
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4. A method of encrypting data comprising the steps of:
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calculating a value to be used as a random starting point; generating an intitial state of a predetermined logistic difference equation having the form xn+1 =μ
xn (1-xn), where μ
is a cryptographic key, xn is the random starting point, and xn+1 is an iterated result;iterating the logistic differnce equation by using successive xn+1 values to xn and repeating the calculation a selected number of times, the random value xn and the key value μ
having a selected mathematical precision, for a selected number of iterations to thereby generate a sequence of encrypting iterates;converting the encrypting iterates into binary form; and summing the encrypting iterates in binary form with digital data to generate encrypted data. - View Dependent Claims (5, 6, 7, 8, 9, 10)
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11. A cryptographic system comprising:
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random starting point generator means for generating a random starting point; a memory for storing at least one cryptographic key; arithmetic logic unit and arithmetic logic unit controller means coupled to the generator means and memory for iterating a predetermined logistic difference equation having the form xn+1 =μ
xn (1-xn), where μ
is a cryptographic key, xn is the random starting point, and xn+1 is an iterated result, using the random starting point and a cryptographic key, for generating a sequence of iterates, and for converting the sequence of iterates into binary form;adder means coupled to the arithmetic logic unit and arithmetic logic unit controller means for summing the iterates in binary form with digital data to generate encrypted data; and sequencer means for controlling the operation of and transfer of data between the random starting point generator means, the memory, the arithmetic logic unit and arithmetic logic unit controller means. - View Dependent Claims (12, 13, 14)
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Specification