Method and Apparatus for Secure Digital Communications Using Chaotic Signals

• US 20080107268A1
• Filed: 09/10/2007
• Published: 05/08/2008
• Est. Priority Date: 09/08/2006
• Status: Active Grant

• Current Assignee: United States Department Of Health And Human Services (Government of the United States of America)
• Original Assignee: Government of The United States In The Name Secretary of The Navy
• Inventors: Rohde, Gustavo, Bucholtz, Frank, Nichols, Jonathan
• Granted Patent: US 8,385,547 B2
• Time in Patent Office: Days
• US Class Current: 380/263
• CPC Class Codes: H04K 1/025 using an analogue chaotic signal
• CPC Class Codes: H04L 27/001 using chaotic signals for secret or secure communication H04L9/001
• CPC Class Codes: H04L 9/001 using chaotic signals

Abstract

A system and method for encoding zero and one bits for transmission, including generating a first signal from a non-linear chaotic system to represent the one bit, with the signal'"'"'s embedded vectors being within the non-linear system'"'"'s attractor set, and generating a second signal from the non-linear system to represent the zero bit, with the signal'"'"'s embedded vectors being outside the non-linear system'"'"'s attractor set. The second signal encoding the zero bit can be generated by adding together two chaotic signals arising from the non-linear system initialized with different initial conditions, and weighting the second signal to have approximately the same energy as the first signal. One suitable chaotic systems is a Lorenz system. Systems and methods for decoding a transmitted stream of signals compare a detection statistic of the received stream of signals to a threshold value that depends on the chaotic system.

Claims

1. A method for encoding zero and one bits for transmission, the method comprising:

generating a first signal from a non-linear chaotic system to represent the one bit, with the signal'"'"'s embedded vectors being within the non-linear system'"'"'s attractor set; and

generating a second signal from the non-linear system to represent the zero bit, with the signal'"'"'s embedded vectors being outside the non-linear system'"'"'s attractor set.

2. The method according to claim 1, further comprising:

weighting at least one of the first signal and the second signal so the first signal and the second signal have approximately equal energy.

3. The method according to claim 1, wherein said generating of the second signal comprises:

adding together two chaotic signals arising from the non-linear system initialized with different initial conditions.

4. The method according to claim 1, wherein the non-linear chaotic system is a Lorenz system.

5. The method according to claim 1, wherein the non-linear chaotic system is a Lorenz, Rossler, or Henon system.

6. The method according to claim 1, further comprising:

frequency translating the encoded bits.

7. The method according to claim 1, further comprising:

transmitting a plurality of encoded bits.

8. The method according to claim 7, further comprising:

receiving the transmitted plurality of encoded bits.

9. The method according to claim 8, further comprising:

determining whether each signal portion corresponds to a zero bit or a one bit based on a detection statistic to a threshold value, said threshold value incorporates parameters of the chaotic system equations.

10. The method according to claim 7, further comprising:

receiving the transmitted plurality of encoded bits,

digitally sampling a received signal at a time interval τ

;

splitting the signal of length N into windows of a predetermined width d;

calculating a detection statistic

$q^2=\underset{m=1}{\overset{N/d}{\sum <br><br>}}<br><br>{<br><br>{\hat{x}}_m<br><br>}^2;<br><br>$

wherein {circumflex over (x)}_m={r(mτ

), . . . , r(mτ

+(d−

1)τ

)},

comparing the detection statistic to a threshold value;

and assigning a bit zero or a bit one based on the comparison of the detection statistic to the threshold value.

11. A method of decoding a received transmission, said transmission being encoded with signals generated by a chaotic system, the method comprising:

digitally sampling a received signal at a time interval τ

; and

for each bit, splitting the signal of length N into windows of a predetermined width d,

calculating a detection statistic

$q^2=\underset{m=1}{\overset{N/d}{\sum <br><br>}}<br><br>{<br><br>{\hat{x}}_m<br><br>}^2,$

wherein {circumflex over (x)}_m={r(mτ

), . . . , r(mτ

+(d−

1)τ

)},

comparing the detection statistic to a threshold value, and

and assigning a bit zero or a bit one based on the comparison of the detection statistic to the threshold value.

12. A signal processor adapted to operationally decode a received transmission, said transmission being encoded with signals generated by a chaotic system, the processor operable to:

digitally sample a received signal at a time interval τ

; and

for each bit, splitting the signal of length N into windows of a predetermined width d,

calculate a detection statistic

$q^2=\underset{m=1}{\overset{N/d}{\sum <br><br>}}<br><br>{<br><br>{\hat{x}}_m<br><br>}^2,$

wherein {circumflex over (x)}_m={r(mτ

), . . . , r(mτ

+(d−

1)τ

},

compare the detection statistic to a threshold value, and

and assign a bit zero or a bit one based on the comparison of the detection statistic to the threshold value.