32N +D bit key encryption-decryption system using chaos
First Claim
1. A method of encryption comprising the steps of;
- a) selecting four initializer values which are used to generate n chaotic iterates from a chaotic equation, where n is the lifetime of the chaotic equation, and wherein said chaotic equation is zt+1 =zt2 +c, where z and c are complex numbers;
b) generating two chaotic iterates from said chaotic equation;
c) converting the two chaotic iterates into a predetermined number of chaotic keys;
d) encrypting a block of plaintext message as a block of ciphertext based on one of said chaotic keys;
e) repeating step d) until a predetermined number of blocks of plaintext message have been encrypted with one each of said chaotic keys;
f) repeating steps b) through e) until the entire plaintext message is encrypted as ciphertext.
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Abstract
A cryptographic method and system based on chaos theory is provided. Unique random 64-bit binary strings generated from an iterative chaotic equation are used as logic and arithmetic operands during encryption/decryption. The random 64-bit binary strings are generated based on 4 initializer values that produce thousands of iterated values from the chaotic equation zt+1 =Zt2 +c, where z and c are complex numbers. The 64-bit random numbers are translated into two 32-bit keys so that each 32 bits of message are encrypted/decrypted, using a bitwise logic operator such as an exclusive-or, with a unique 32-bit key for the length of the message file. For additional security, a combination of logic and arithmetic operators are used on the 32-bit keys and the 32-bit blocks of message text to produce 32N-bit blocks of ciphertext, where N=2r and r≦2. For any set of 4 initializer values, the lifetime, n, is the number of iterations of the equation Zt+1 =zt2 +c before divergence of the output to infinity, and the number of unique 32-bit keys is 4n, where n can be over 300,000 for a multitude of initializer values.
155 Citations
37 Claims
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1. A method of encryption comprising the steps of;
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a) selecting four initializer values which are used to generate n chaotic iterates from a chaotic equation, where n is the lifetime of the chaotic equation, and wherein said chaotic equation is zt+1 =zt2 +c, where z and c are complex numbers; b) generating two chaotic iterates from said chaotic equation; c) converting the two chaotic iterates into a predetermined number of chaotic keys; d) encrypting a block of plaintext message as a block of ciphertext based on one of said chaotic keys; e) repeating step d) until a predetermined number of blocks of plaintext message have been encrypted with one each of said chaotic keys; f) repeating steps b) through e) until the entire plaintext message is encrypted as ciphertext. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8)
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9. A method of encryption comprising the steps of;
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a) selecting four initializer values which are used to generate n chaotic iterates from a chaotic equation, where n is the lifetime of the chaotic equation, and wherein said chaotic equation is zt+1 =zt2 +c, where z and c are complex numbers; b) generating two chaotic iterates, each of length L, from said chaotic equation; c) converting the two chaotic iterates into four chaotic keys of length L; d) separating each of said four chaotic keys into a first portion and a second portion; e) converting four blocks of plaintext message to four blocks of length 2L by multiplying each said block of length L of plaintext message by one of said first portions of each of said four chaotic keys; f) separating each block of said multiplied plaintext message of length 2L into two blocks of length L; g) encrypting four blocks of said multiplied plaintext message of length L as ciphertext based on said second portion of each of said four chaotic keys; h) combining the ciphertext into blocks of length 2L; i) repeating steps b) through h) until the entire plaintext message is encrypted as ciphertext. - View Dependent Claims (10)
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11. A method of encryption comprising the steps of;
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a) selecting four initializer values which are used to generate n chaotic iterates from a chaotic equation, where n is the lifetime of the chaotic equation, and wherein said chaotic equation is Zt+1 zt2 +c, where z and c are complex numbers; b) generating two chaotic iterates from said chaotic equation; c) converting the two chaotic iterates into four chaotic keys; d) separating each of said chaotic keys into a first portion and a second portion; e) converting four blocks of plaintext message into four blocks of multiplied plaintext message by multiplying each said block of plaintext message by said first portion of a specific chaotic key; f) repeat steps b) through e) which generate four new chaotic keys which are different than all previously generated chaotic keys, each said new chaotic key first portion is multiplied with one of said four blocks of plaintext message, said plaintext message being separate from all plaintext messages previously converted, and continue step f) until all of said plaintext message is converted to multiplied plaintext; g) separating each block of said multiplied plaintext message into two blocks; h) encrypting each separated block of said multiplied plaintext message with said second portion of a predetermined chaotic key to produce a block of ciphertext; i) combining consecutive blocks of ciphertext to produce an encrypted message; j) repeating steps h) and i) until all blocks of ciphertext have been converted into encrypted messages. - View Dependent Claims (12, 13, 14, 15, 16, 17, 18)
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19. A method of encryption comprising the steps of;
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a) selecting four initializer values which are used to generate n chaotic iterates from a chaotic equation, where n is the lifetime of the chaotic equation, and wherein said chaotic equation is zt+1 =zt2 +c, where z and c are complex numbers; b) generating chaotic iterates, each of length 2L, from said chaotic equation; c) converting each chaotic iterate of length 2L into two chaotic keys of length L; d) encrypting blocks of length L of plaintext message as ciphertext based on said chaotic keys; and e) repeating steps b) through d) until the entire plaintext message is encrypted as ciphertext. - View Dependent Claims (20, 21, 22, 23, 24, 25, 26, 27)
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28. A system for encryption comprising;
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means for selecting four initializer values which are used to generate n chaotic iterates from a chaotic equation, where n is the lifetime of the chaotic equation, and wherein said chaotic equation is zt+1 =zt2 +c, where z and c are complex numbers; means for generating at least one chaotic iterate from said chaotic equation; means for converting each of said at least one chaotic iterates into two chaotic keys; means for encrypting at least one block of plaintext message as at least one block of ciphertext based on said chaotic keys. - View Dependent Claims (29, 30, 31, 32, 33, 34, 35, 36, 37)
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Specification