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EP0467239A2
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An encryption system based on Chaos theory
Assignee: Raytheon Co
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Filing: 1991-07-12
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Granted: —
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Expires: 2011-07-12
Abstract
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.
Inventors
- 👤 Mark Bianco
- 👤 Dana Reed
Bibliographic Details
Application Number
—
Jurisdiction
EP
Data Source
google_patents
Last Synchronized
2026-11-05 11:01
CPC Classifications
H; H04; H04L; H04L9/00; H04L9/001; H04L27/00; H04L27/001; H04L9/06; H04L9/065; H04L9/0656; H04L9/0662
Claims Analysis
Total Claims: 38
Claim 1
Independent Claim
96 words
A method of encrypting data comprising the steps of: generating a random value having a selected mathematical precision; generating an initial state of a predetermined chaotic equation by iterating with the random value and a key value having a selected mathematical precision, for a selected number of iterations; iterating the chaotic equation to generate a periodic sequence of encrypting iterates having an extremely long cycle length; performing a domain transformation by converting the encrypting iterates into binary form; and summing the encrypting iterates in binary form with digital data to be encrypted to generate encrypted data.
Claim 2
Independent Claim
96 words
A method of encrypting data comprising the steps of: generating a random value having a selected mathematical precision; generating an initial state of a predetermined chaotic equation by iterating with the random value and a key value having a selected mathematical precision, for a selected number of iterations; iterating the chaotic equation to generate a periodic sequence of encrypting iterates having an extremely long cycle length; performing a domain transformation by converting the encrypting iterates into binary form; and summing the encrypting iterates in binary form with digital data to be encrypted to generate encrypted data.
Claim 3
Dependent Claim
38 words
The method of Claim 1 wherein the step of iterating the chaotic equation further comprises the step of: reiterating the the chaotic equation to generate a periodic sequence of encrypting iterates whose values are within a selected range.
Claim 4
Dependent Claim
34 words
The method of Claim 1 wherein the predetermined chaotic equation comprises the logistic difference equation x n+1 = µx n (1-x n ), where µ is a constant and x is an iterated result.
Claim 5
Dependent Claim
32 words
The method of Claim 1 wherein the step of iterating the chaotic equation further comprises selecting a desired mathematical precision for the iterating process to alter the periodic sequence of encrypting iterates.
Claim 6
Dependent Claim
28 words
The method of Claim 1 wherein the step of iterating the chaotic equation comprises the step of iterating the chaotic equation using a discontinuous set of encrypting iterates.
Claim 7
Dependent Claim
37 words
The method of Claim 1 wherein the step of iterating the chaotic equation comprises the step of periodically perturbing the iterates to add a further discontinuity in the binary encrypting iterates generated by the domain transformation step.
Claim 8
Dependent Claim
74 words
The method of Claim 1 wherein the step of iterating the chaotic equation further comprises the steps of: feeding back the encrypted data; summing the encrypted data with the periodic sequence of encrypting iterates to generate a second set of encrypting iterates; delaying the summed second set of encrypting iterates for a selected time period; and summing the delayed second set of encrypting iterates with digital data to be encrypted to generate encrypted data.
Claim 9
Dependent Claim
40 words
The method of Claim 1 further comprising the steps of: iterating the chaotic equation and performing the domain transformation a selected number of times; and then summing the encrypting iterates with digital data to be encrypted to generate encrypted data.
Claim 10
Dependent Claim
106 words
A method of decrypting data encrypted in accordance with the method of Claim 1, said method comprising the steps of: receiving encrypted data that is to be decrypted; receiving the random value. generating an initial state of the chaotic equation by iterating with the random value and a key value, for the selected number of iterations; iterating the chaotic equation to generate a periodic sequence of decrypting iterates having an extremely long cycle length; performing a domain transformation by converting the decrypting iterates into binary form; and summing the decrypting iterates in binary form with the encrypted digital data to be decrypted to generate decrypted data.
Claim 11
Dependent Claim
38 words
The method of Claim 9 wherein the step of iterating the chaotic equation further comprises the step of: reiterating the the chaotic equation to generate a periodic sequence of decrypting iterates whose values are within a selected range.
Claim 12
Dependent Claim
34 words
The method of Claim 9 wherein the predetermined chaotic equation comprises the logistic difference equation x n+1 = µx n (1-x n ), where 11. is a constant and x is an iterated result.
Claim 13
Dependent Claim
71 words
The method of Claim 9 wherein the step of iterating the chaotic equation further comprises the steps of: summing the encrypted data with the periodic sequence of decrypting iterates in binary form to generate a second set of decrypting iterates; delaying the second set of decrypting iterates for a selected time period; and summing the delayed second set of decrypting iterates with encrypted data to be decrypted to generate decrypted data.
Claim 14
Dependent Claim
37 words
The method of Claim 9 further comprising the steps of: iterating the chaotic equation and performing the domain transformation a selected number of times; and then summing the decrypted iterates with encrypted data to generate decrypted data.
Claim 15
Independent Claim
98 words
A method of encrypting data comprising the steps of: generating a random value having a selected mathematical precision; generating an initial state of a predetermined logistic difference equation by iterating with the random value and a key value having a selected mathematical precision, for a selected number of iterations; iterating the logistic difference equation to generate a periodic sequence of encrypting iterates having an extremely long cycle length; performing a domain transformation by converting the encrypting iterates into binary form; and summing the encrypting iterates in binary form with digital data to he encrypted to generate encrypted data.
Claim 16
Independent Claim
98 words
A method of encrypting data comprising the steps of: generating a random value having a selected mathematical precision; generating an initial state of a predetermined logistic difference equation by iterating with the random value and a key value having a selected mathematical precision, for a selected number of iterations; iterating the logistic difference equation to generate a periodic sequence of encrypting iterates having an extremely long cycle length; performing a domain transformation by converting the encrypting iterates into binary form; and summing the encrypting iterates in binary form with digital data to he encrypted to generate encrypted data.
Claim 17
Dependent Claim
39 words
The method of Claim 14 wherein the step of iterating the logistic difference equation further comprises the step of: reiterating the the chaotic equation to generate a periodic sequence of encrypting iterates whose values are within a selected range.
Claim 18
Dependent Claim
32 words
The method of Claim 14 wherein the logistic difference equation comprises the equation x n+1 = µx n (1-x n ), where 11. is a constant and x is an iterated result.
Claim 19
Dependent Claim
39 words
The method of Claim 14 wherein the step of iterating the logistic difference equation further comprises adjusting the mathematical precision of the random value and key value to adjust the cycle length of the periodic sequence of encrypting iterates.
Claim 20
Dependent Claim
30 words
The method of Claim 14 wherein the step of iterating the logistic difference equation comprises the step of iterating the logistic difference equation using a discontinuous set of encrypting iterates.
Claim 21
Dependent Claim
38 words
The method of Claim 14 wherein the step of iterating the logistic difference equation comprises the step of periodically perturbing the iterates to add a further discontinuity in the binary encrypting iterates generated by the domain transformation step.
Claim 22
Dependent Claim
74 words
The method of Claim 14 wherein the step of iterating the logistic difference equation further comprises the steps of: feeding back the encrypted data; summing the encrypted data with the periodic sequence of encrypting iterates to generate a second set of encrypting iterates; delaying the summed second set of encrypting iterates for a selected time period; summing the delayed second set of encrypting iterates with digital data to be encrypted to generate encrypted data.
Claim 23
Dependent Claim
41 words
The method of Claim 14 further comprising the steps of: iterating the logistic difference equation and performing the domain transformation a selected number of times; and then summing the encrypting iterates with digital data to be encrypted to generate encrypted data.
Claim 24
Dependent Claim
108 words
A method of decrypting data encrypted in accordance with the method of Claim 14, said method comprising the steps of: receiving encrypted data that is to be decrypted; receiving the random value. generating an initial state of the logistic difference equation by iterating with the random value and a key value, for the selected number of iterations; iterating the logistic difference equation to generate a periodic sequence of decrypting iterates having an extremely long cycle length; performing a domain transformation by converting the decrypting iterates into binary form; and summing the decrypting iterates in binary form with the encrypted digital data to be decrypted to generate decrypted data.
Claim 25
Dependent Claim
40 words
The method of Claim 22 wherein the step of iterating the logistic difference equation further comprises the step of: reiterating the the logistic difference equation to generate a periodic sequence of decrypting iterates whose values are within a selected range.
Claim 26
Dependent Claim
32 words
The method of Claim 22 wherein the logistic difference equation comprises the equation x n+1 = µx n (1-x n ), where 11. is a constant and x is an iterated result.
Claim 27
Dependent Claim
19 words
The method of Claim 22 wherein the step of iterating the logistic difference equation further comprises the steps of:
Claim 28
Dependent Claim
53 words
summing the encrypted data with the periodic sequence of decrypting iterates in binary form to generate a second set of decrypting iterates; delaying the second set of decrypting iterates for a selected time period; and summing the delayed second set of decrypting iterates with encrypted data to be decrypted to generate decrypted data.
Claim 29
Dependent Claim
53 words
summing the encrypted data with the periodic sequence of decrypting iterates in binary form to generate a second set of decrypting iterates; delaying the second set of decrypting iterates for a selected time period; and summing the delayed second set of decrypting iterates with encrypted data to be decrypted to generate decrypted data.
Claim 30
Dependent Claim
38 words
The method of Claim 22 further comprising the steps of: iterating the logistic difference equation and performing the domain transformation a selected number of times; and then summing the decrypted iterates with encrypted data to generate decrypted data.
Claim 31
Dependent Claim
122 words
A cryptographic system comprising: a random number generator; a memory for storing one or more cryptographic keys; an arithmetic logic unit and controller means coupled to the random number generator and memory for iterating a predetermined chaotic equation using random numbers generated by the random number generator and the cryptographic key, and for generating a periodic sequence of iterates, and for performing a domain transformation by converting the periodic sequence of iterates into binary form; adder means coupled to the arithmetic logic unit and controller means for summing the iterates with digital data: and controller means for controlling the operation of and transfer of data between the random number generator, the memory, the arithmetic logic unit and controller means, and the adder.
Claim 32
Dependent Claim
122 words
A cryptographic system comprising: a random number generator; a memory for storing one or more cryptographic keys; an arithmetic logic unit and controller means coupled to the random number generator and memory for iterating a predetermined chaotic equation using random numbers generated by the random number generator and the cryptographic key, and for generating a periodic sequence of iterates, and for performing a domain transformation by converting the periodic sequence of iterates into binary form; adder means coupled to the arithmetic logic unit and controller means for summing the iterates with digital data: and controller means for controlling the operation of and transfer of data between the random number generator, the memory, the arithmetic logic unit and controller means, and the adder.
Claim 33
Dependent Claim
41 words
The system of Claim 27 wherein the arithmetic logic unit and controller means iterates a chaotic equation comprising the logistic difference equation x n+1 = µx n (1-x n ), where µ is a constant and x is an iterated result.
Claim 34
Dependent Claim
33 words
The system of Claim 27 wherein the arithmetic logic unit and controller means comprises: means for adjusting the mathematical precision of the arithmetic logic unit to adjust the periodic sequence of encrypting iterates.
Claim 35
Dependent Claim
27 words
The system of Claim 27 wherein the arithmetic logic unit and controller means comprises: means for iterating the chaotic equation using a discontinuous set of encrypting iterates.
Claim 36
Dependent Claim
36 words
The system of Claim 27 wherein the arithmetic logic unit and controller means comprises: means for periodically perturbing the iterates to add a further discontinuity in the binary encrypting iterates generated by the domain transformation step.
Claim 37
Dependent Claim
78 words
The system of Claim 27 wherein the arithmetic logic unit and controller means comprises: means for feeding back the encrypted data; means for summing the encrypted data with the periodic sequence of encrypting iterates to generate a second set of encrypting iterates; means for delaying the summed second set of encrypting iterates for a selected time period; and means for summing the delayed second set of encrypting iterates with digital data to be encrypted to generate encrypted data.
Claim 38
Dependent Claim
47 words
The system of Claim 27 wherein the arithmetic logic unit and controller means comprises: means for iterating the chaotic equation and performing the domain transformation a selected number of times; and means for summing the encrypting iterates with digital data to be encrypted to generate encrypted data.
References Cited (Backward Citations)
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