Robust hyper-chaotic encryption-decryption system and method for digital secure-communication

• US 20070050614A1
• Filed: 08/14/2006
• Published: 03/01/2007
• Est. Priority Date: 08/24/2005
• Status: Abandoned Application

• Current Assignee: Chung-Hsi Li, Wen-Wei Lin
• Original Assignee: Chung-Hsi Li, Wen-Wei Lin
• Inventors: Lin, Wen-Wei, Li, Chung-Hsi
• Application Number:
  US11/503,276
• Publication Number:
  US 20070050614A1
• Time in Patent Office: Days
• US Class Current: 713/150
• CPC Class Codes: H04L 2209/04 Masking or blinding
• CPC Class Codes: H04L 9/001 using chaotic signals
• CPC Class Codes: H04L 9/12 Transmitting and receiving encryption devices synchronised or initially set up in a particular manner

Abstract

A robust hyper-chaotic encryption-decryption system, for digital secure-communication from a transmitter to a receiver, utilizing two robust hyper-chaotic means in the transmitter and receiver respectively, wherein the transmitter includes a hyper-chaotic signal generator and a transmitter'"'"'s adjusting parameter device, and the receiver includes a hyper-chaotic synchronization receiver and a receiver'"'"'s adjusting parameter device. A method is also disclosed, comprising an encryption and a decryption process wherein the encryption process including steps of decomposing a plaintext message into a sequence and carrying the sequence into a masking sequence of a hyper-chaotic signal via an XOR operation for generating a hyper-chaotic ciphertext, and the decryption process including steps of generating unmasking sequence of a hyper-chaotic signal to realize synchronization with the masking sequence after receiving the ciphertext and transforming the ciphertext into a decrypted plaintext massage via an XOR operation.

Claims

1. A robust hyper-chaotic encryption-decryption system for digital secure-communication, used to convey data confidentially from a transmitter to a receiver, comprising:

a hyper-chaotic signal generator, located in the transmitter for carrying a plaintext message into a masking sequence of a hyper-chaotic signal;

a transmitter'"'"'s adjusting parameter device, located in the transmitter for adjusting parameters of the hyper-chaotic signal generator, causing the hyper-chaotic signal generator transforming the plaintext massage and the masking sequence into a hyper-chaotic ciphertext;

a hyper-chaotic synchronization receiver, located in the receiver for generating unmasking sequence of a hyper-chaotic signal and transforming the hyper-chaotic ciphertext with the unmasking sequence into a decrypted plaintext massage via an XOR operation; and

a receiver'"'"'s adjusting parameter device, located in the receiver for adjusting parameters of the hyper-chaotic synchronization receiver to cause the hyper-chaotic synchronization receiver generating the unmasking sequence to realize synchronization with the masking sequence after the receiver receiving the hyper-chaotic ciphertext.

2. The robust hyper-chaotic encryption-decryption system for digital secure-communication as claimed in claim 1, wherein the hyper-chaotic signal generator in the transmitter functions by utilizing a first robust hyper-chaotic means, which is constructed by a plurality of coupling robust logistic maps, one carrier map and several hidden maps.

3. The robust hyper-chaotic encryption-decryption system for digital secure-communication as claimed in claim 2, wherein the first robust hyper-chaotic means can be defined as

x⁽ⁱ⁾=F(r,x⁽ⁱ⁻

1));

=C L(r,x<sup>(i−

1)</sup>), where x⁽ⁱ⁾=[x₁⁽ⁱ⁾, . . . , x_n⁽ⁱ⁾]^T,

L(r, x<sup>(i−

1)</sup>)=[L(γ

1, x₁<sup>(i−

1)</sup>), . . . , L(γ

_n, x_n<sup>(i−

1)</sup>)]^T, in which L(r,x) is a robust logistic function defined as

$L<br><br>\left(\mathrm{\gamma <br><br>},x\right)=\{\begin{array}{cc}\mathrm{\gamma <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>x<br><br>\left(1-x\right)<br><br>\left(\mathrm{mod}<br><br>\text{\hspace{1em}<br><br>}<br><br>1\right),& x\in <br><br>I_{\mathrm{ext}}\\ x<br><br>\left(1-x\right)<br><br>\left(\mathrm{mod}<br><br>\text{\hspace{1em}<br><br>}<br><br>1\right)/\mathrm{\gamma <br><br>}/4<br><br>\left(\mathrm{mod}<br><br>\text{\hspace{1em}<br><br>}<br><br>1\right),& x\in <br><br>I_{\mathrm{int}}\end{array}<br><br><br><br>\mathrm{where}<br><br><br><br>I_{\mathrm{ext}}\in <br><br>\left(0,1\right)<br><br>\backslash <br><br>I_{\mathrm{int}},I_{\mathrm{int}}=\left[{\mathrm{\eta <br><br>}}_{1,}<br><br>{\mathrm{\eta <br><br>}}_2\right],<br><br>{\mathrm{\eta <br><br>}}_1=1/2-\sqrt{1/4-\left[\left(\mathrm{\gamma <br><br>}/4\right)\right]/\mathrm{\gamma <br><br>}},<br><br>{\mathrm{\eta <br><br>}}_2=1/2+\sqrt{1/4-\left[\left(\mathrm{\gamma <br><br>}/4\right)\right]/\mathrm{\gamma <br><br>}};<br><br><br><br>\mathrm{in}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{which}<br><br>\text{\hspace{1em}<br><br>}\left[\mathrm{\omega <br><br>}\right]<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{is}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{the}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{greatest}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{integer}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{less}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{than}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{or}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{equal}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{to}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\omega <br><br>}$

η

₂=1/2+√

{square root over (1/4−

[(γ

/4) ]/γ

)} in which [ω

] is the greatest integer less than or equal to ω

,

and C is a positive stochastic coupling matrix with all elements 0<

c_ij<

1 and

$\underset{j}{\sum <br><br>}<br><br>c_{\mathrm{ij}}=1$$\mathrm{for}$$i,j=1,\mathrm{\cdots <br><br>}<br><br>\text{\hspace{1em}<br><br>},n.<br><br>\left(\begin{array}{cccc}{c}_{11}& c_{12}& \mathrm{\dots <br><br>}& c_{1<br><br>n}\\ c_{21}& c_{22}& \mathrm{\dots <br><br>}& c_{2<br><br>n}\\ \mathrm{\dots <br><br>}& \mathrm{\dots <br><br>}& \text{\hspace{1em}<br><br>}& \mathrm{\dots <br><br>}\\ c_{\mathrm{n1}}& c_{\mathrm{n2}}& \mathrm{\dots <br><br>}& c_{\mathrm{nn}}\end{array}\right)$

the robust logistic map is defined as x(i+1)=L(γ

, x(i)); and

the masking sequence generated by the hyper-chaotic signal generator is used to encrypt the plaintext massage and can be defined as z⁽ⁱ⁾=x₁⁽ⁱ⁾.

4. The robust hyper-chaotic encryption-decryption system for digital secure-communication as claimed in claim 1, wherein the hyper-chaotic synchronization receiver in the receiver functions by utilizing a second robust hyper-chaotic means, which is constructed by a plurality of coupling robust logistic maps, one carrier map and several hidden maps.

5. The robust hyper-chaotic encryption-decryption system for digital secure-communication as claimed in claim 4, wherein the second robust hyper-chaotic means can be defined as

y⁽ⁱ⁾=G(r,y⁽ⁱ⁻

1));

=C L(r,x<sup>(i−

1)</sup>), where y⁽ⁱ⁾=[y₁⁽ⁱ⁾, . . . , y_n⁽ⁱ⁾]^T for i>

0; and

the unmasking sequence generated by the hyper-chaotic synchronization receiver in the receiver is used to decrypt the ciphertext into decrypted plaintext massage and can be defined as {tilde over (z)}⁽ⁱ⁾=y₁⁽ⁱ⁾.

6. The robust hyper-chaotic encryption-decryption system for digital secure-communication as claimed in claim 1, wherein the parameters including an n-by-n stochastic matrix C=[c_ij] and a chaotic parameter vector r=[γ

₁, . . . , γ

_n]^T, where 0<

c_ij<

1 for i ,j=1, . . . ,n and γ

_i≧

4 for i=1, . . . ,n.

7. The robust hyper-chaotic encryption-decryption system for digital secure-communication as claimed in claim 3, wherein when the parameter γ

≧

4, the number of positive Lyapunov exponents of the first robust hyper-chaotic means increases along with the number of robust hyper-chaotic maps utilized by the first robust hyper-chaotic means.

8. The robust hyper-chaotic encryption-decryption system for digital secure-communication as claimed in claim 5, wherein when the parameter γ

≧

4, the number of positive Lyapunov exponents of the second robust hyper-chaotic means increases along with the number of robust hyper-chaotic maps utilized by the second robust hyper-chaotic means.

9. The robust hyper-chaotic encryption-decryption system for digital secure-communication as claimed in claim 1, wherein the transmitter sending the hyper-chaotic ciphertext to the receiver is via the hyper-chaotic signal generator.

10. A robust hyper-chaotic encryption-decryption method for digital secure-communication, for conveying data confidentially from a transmitter to a receiver, comprising:

an encryption process, proceeding in the transmitter including the following steps in sequence;

decomposing a plaintext message into a sequence of {p⁽ⁱ⁾}, generating a masking sequence of a hyper-chaotic signal according to the input of an initial vector x⁽⁰⁾ and parameters, and carrying the sequence of {p⁽ⁱ⁾} into the masking sequence via an XOR operation for generating a hyper-chaotic ciphertext; and

a decryption process, proceeding in the receiver including the following steps in sequence;

generating a unmasking sequence of a hyper-chaotic signal according to the input of an initial vector y⁽⁰⁾ and parameters to realize synchronization with the masking sequence after receiving the hyper-chaotic ciphertext, and transforming the hyper-chaotic ciphertext into a decrypted plaintext massage via an XOR operation of the ciphertext and the unmasking sequence.

11. The robust hyper-chaotic encryption-decryption method for digital secure-communication as claimed in claim 10, wherein the initial vector x⁽⁰⁾ is created randomly first in the transmitter and is replaced by y⁽⁰⁾, and then it is sent to the receiver and is replaced again by x⁽⁰⁾.

12. The robust hyper-chaotic encryption-decryption method for digital secure-communication as claimed in claim 10, wherein the parameters including an n-by-n stochastic matrix C=[c_ij] and a chaotic parameter vector r=[γ

₁, . . . ,γ

_n]^T, where x_i⁽⁰⁾ ∈

{(0,1)\{1/2}, γ

₁≧

4for i=1, . . . ,n and 0<

c_ij<

1 for i, j=1, . . . ,n.

13. The robust hyper-chaotic encryption-decryption method for digital secure-communication as claimed in claim 10, wherein when the real numbers of a first robust hyper-chaotic means are represented as m digits, the length of each p⁽ⁱ⁾ is equal to d digits and d=m−

ι

∈

N, for i≧

1; and

under the condition mentioned above, the encryption process proceeding in the transmitter can be defined as

z⁽ⁱ⁾=└

x₁⁽ⁱ⁾┘

_ι

,

c⁽ⁱ⁾=z⁽ⁱ⁾{circle around (=)}p⁽ⁱ⁾, where {circle around (=)} is an XOR operation, and └

x₁┘

_ι

means dropping the first ι

digits from x.

14. The robust hyper-chaotic encryption-decryption method for digital secure-communication as claimed in claim 13, wherein based on the condition mentioned in claim 13, the decryption process proceeding in the receiver can be defined as

{tilde over (z)}⁽ⁱ⁾=└

y₁⁽ⁱ⁾┘

_ι

,

{tilde over (p)}⁽ⁱ⁾={tilde over (z)}⁽ⁱ⁾{circle around (+)}c⁽ⁱ⁾, where {tilde over (p)}⁽ⁱ⁾ is the decrypted plaintext massage;

15. The robust hyper-chaotic encryption-decryption method for digital secure-communication as claimed in claim 10, wherein the transmitter sending the hyper-chaotic ciphertext to the receiver is via the hyper-chaotic signal generator.