## A method for secure communications over a public fiber-optical network

Optics Express, Vol. 14, Issue 9, pp. 3738-3751 (2006)

http://dx.doi.org/10.1364/OE.14.003738

Acrobat PDF (459 KB)

### Abstract

We develop a spread-spectrum based approach to secure communications over existing fiber-optical networks. Secure transmission for a dedicated user is achieved by overlaying a covert channel onto a host channel in the existing active fiber link. The covert channel is optically encoded and temporally spread, and has average power below the noise floor in the fiber, making it hidden for a direct detection thus allowing for cryptographic and steganographic security capabilities. The presence for the host channel in the network provides an ad hoc security expansion and increases the difficulty for an eavesdropper to intercept and decode the secure signal.

© 2006 Optical Society of America

## 1. Introduction

2. P. R. Prucnal, M. A. Santoro, and T. R. Fan, “Spread spectrum fiber-optic local area network using optical processing,” J. Lightwave Technol. **4**, 547 (1986). [CrossRef]

6. S. Shen and A.M. Weiner “Suppression of WDM interference for error-free detection of ultrashort-pulse CDMA signals in spectrally overlaid hybrid WDM-CDMA operation,” IEEE Photonics Technol Lett. **13**, 82–84 (2001) [CrossRef]

6. S. Shen and A.M. Weiner “Suppression of WDM interference for error-free detection of ultrashort-pulse CDMA signals in spectrally overlaid hybrid WDM-CDMA operation,” IEEE Photonics Technol Lett. **13**, 82–84 (2001) [CrossRef]

## 2. The system

9. A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of a 128-element liquid crystal phase modulator,” IEEE J. Quantum Electron. **28**, 908–920 (1992) [CrossRef]

4. J. A. Salehi, A. M. Weiner, and J. P. Heritage, “Coherent ultrashort light pulse code-division multiple access communication systems,” J. Lightwave Technol. **8**, 478–491 (1990) [CrossRef]

## 3. Theoretical description

4. J. A. Salehi, A. M. Weiner, and J. P. Heritage, “Coherent ultrashort light pulse code-division multiple access communication systems,” J. Lightwave Technol. **8**, 478–491 (1990) [CrossRef]

### 3.1. Probability density function

*C*is the number of chips in the phase mask of the SS encoder, in the limit when

*C*>> 1, by virtue of the central limit theorem, the multi-access interference noise distribution (in both host and secure channels) approaches zero mean Gaussian with the spectrum defined by the original pulse [11, 12]. Figure 4 demonstrates the Gaussian distribution behavior of the real part of the encoded waveform.

*A*at location

*R*and

*S*for the host and secure channel shown in Fig. 3 is given by Eq. (1) where √P denotes the signal amplitude,

*θ*∈ |-

*π,π*| is the random phase and

*n*is the complex noise amplitude characterized by zero mean Gaussian distribution.

*A*=

*n*. The corresponding intensity probability density function (PDF) has a negative exponential distribution [13

13. S. M. Ross, *Introduction To Probability Models 6 ^{th} Edition* (Academic Press, 1997) [PubMed]

*N*̄

_{0}=〈|

*n*|

^{2}〉 and

*n*∈ {

*n*,

^{host}*n*} for the host and secure channel respectively. In order to compute the intensity PDF of a bit one in the host channel or a correctly decoded bit in the secure channel, we first rewrite and decompose the components of Eq. (1) into its real and imaginary parts with:

^{eav}*n*and

_{Re}*n*are independent and identically Gaussian distributed with zero mean and standard deviation

_{Im}*n*∈{

*n*,

^{host}*n*} for the host and secure channel respectively. Note that in this case the secure user noise component is no longer

^{secure}*n*due to correct decoding. The distribution functions of

^{eav}*U*and

*V*are identical and can be calculated using the Gaussian distribution of the noise and uniform distribution of

*θ*. E.g. the cumulative distribution function of

*U*is given by:

*u*in Eq. (4), the PDF

*f*is given in Eq. (5a) and similarly the PDF

_{U}(u)*f*(

_{V}*v*) is given in Eq. (5b).

*P*becomes large. The expressions for

*N*̄

_{0}and

*N*̄

_{1}for both secure and host users are obtained in the next subsection.

### 3.2. Statistical description of the signal

*f(t)*which has a bandwidth

*W*and arbitrary spectrum

*F(ω)*(Fig. 5 with a phase mask of

*C*chips, the spectrum of the pulse is divided into

*C*equally spaced sections, each having a bandwidth of

*Ω*=

*W/C*. Each chip acquires an independent random phase

*ϕ*. The general expression for the encoded signal is given by:

_{ne}[-π, π]*rect*(

*x*) = 1 for |

*x*| ≤ 0.5 and equal to zero otherwise.

*C*defines the code length.

*n*for the host channel as:

^{host}(t)*q*(the noise contributed by the secure user’s spread signal) and

^{secure}(t)*q*the additive Gaussian noise present in the fiber. The average noise intensity <

^{add}(t)*N*> in Eq. (9) is given by:

^{host}(t)*Q*= |

^{secure}(t)*q*|

^{secure}(t)^{2}and

*Q*is the average additive Gaussian noise power coming from the optical amplifier.

^{add}*Q*>, we need to take into account of the contributions from adjacent bits. In the general case, sufficient number of neighboring slots should be included in

^{secure}(t)*q*which depends on the amount of spreading and the bit period of secure user. In the case if spreading is limited to the nearest neighboring slots. The signal sent by secure user is given by:

^{secure}(t)*T*is the bit period of secure user,

_{S}*θ’s*are the random phases between different time frames,

*ψ’s*are random Bernoulli variable with mean 0.5 for the different code keying and the functional form

*h( )*and

*k( )*represent the amplitude function for the encoded bit 1 and bit 0 and are defined by Eq. (7–8).

*T*is approximately on the order of the time spreading of the pulse ~

_{S}*2π/Ω. Ω*is defined by

*W/C*, where

*W*is the pulse bandwidth and

*C*is the number chips in the phase mask. The random phases

*θ’s*between different time frames are based on the assumption that the bit intervals are much longer than the coherence time of the laser. The functional form of

*h( )*and

*k( )*generally depends on the pulse spectrum used. The ensemble average of the intensity of Eq. (11) is given as:

*Q*> with respect to

^{secure}(t)*T*to account for the different positions of host signal under the secure time spread signal, hence Eq. (12b) becomes:

_{s}*n*and

^{eav}(t)*n*are the noise amplitudes when incorrect and correct decoding takes place respectively.

^{secure}(t)*q*is the effective noise from the spreading of the host signal during the decoding stage,

^{host}(t)*q*is the effective noise originating from the secure user due to incorrect decoding and

^{incorrect}(t)*q*is the same as before. We take the average of the noise intensities in Eqs. (15) and (16) and obtain:

^{add}(t)*Q*, the time spread signal amplitude

^{host}(t)*q*of the host user after decoding is given by:

^{host}(t)*k*spans over adjacent slots to take into account of neighboring contributions,

*ψ’s*and

*θ’s*have identical definitions as before,

*T*is the bit period of the host user and the function

_{H}*h*again represents the functional form of the spread signal amplitude of host user. As a result the ensemble average of the intensity is given as:

_{()}*Q*> is given by the first component of Eq. (12b) i.e., the ensemble average of the intensity of encoded waveform:

^{incorrect}(t)*Sinc(t)*=

*Sin(t)/t)*

*P*is the initial peak power of secure signal.

_{S}*P*is the initial peak power of host signal.

_{H}### 3.3 Bit-error rate

_{th}is the optimal threshold power defined by:

*P*=

*P*or

_{S}*P*. Eq. (27) can be used to compute the bit-error-rate of the system subject to different code lengths, amounts of additive noise in the fiber, and operating signal powers and bit rates between secure and host users.

_{H}## 4. Simulation results

## 5. System performance

## 6. Communication security

### 6.1 Analysis of spectrum

6. S. Shen and A.M. Weiner “Suppression of WDM interference for error-free detection of ultrashort-pulse CDMA signals in spectrally overlaid hybrid WDM-CDMA operation,” IEEE Photonics Technol Lett. **13**, 82–84 (2001) [CrossRef]

### 6.2. Monitoring of signal power

### 6.3. Statistical analysis of power fluctuations

### 6.4. Quantitative description

14. G. P. Agrawal, *Fiber-Optical Communication Systems 3 ^{rd} Edition* (Wiley-Interscience, 2002) [PubMed]

*I*,

^{secure}*σ*) and (

^{secure}*I*,

^{eav}*σ*) represent the mean and the standard deviation of the intensity from decoding using a pseudo correct phase mask (superscripted by

^{eav}*secure*) and a totally incorrect phase mask (superscripted by

*eav*).

## 6. Conclusions

## Acknowledgments

## References and links

1. | A. J. Viterbi, “Spread spectrum communications - myths and realities,” IEEE Commun. Mag. |

2. | P. R. Prucnal, M. A. Santoro, and T. R. Fan, “Spread spectrum fiber-optic local area network using optical processing,” J. Lightwave Technol. |

3. | J. Shah, “Optical CDMA,” Opt. Photon. Newslett. |

4. | J. A. Salehi, A. M. Weiner, and J. P. Heritage, “Coherent ultrashort light pulse code-division multiple access communication systems,” J. Lightwave Technol. |

5. | S. Galli, R. Menendez, P. Toliver, T. Banwell, J. Jackel, J. Young, and S. Etermad “Experimental results on the simultaneous transmission of two 2.5 Gbps optical-CDMA channels and a 10 Gbps OOK channel within the same WDM window,” Proc. OFC 2005 OWB3 |

6. | S. Shen and A.M. Weiner “Suppression of WDM interference for error-free detection of ultrashort-pulse CDMA signals in spectrally overlaid hybrid WDM-CDMA operation,” IEEE Photonics Technol Lett. |

7. | Steganography defines the science of hiding information by embedding messages within other in such a way that no one apart from the intended recipient knows of the existence of the message. |

8. | E. E. Narimanov and B. B. Wu, “Advanced coding techniques for asynchronous fiber-optical CDMA,” Proc. CLEO 2005 JThE70 |

9. | A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of a 128-element liquid crystal phase modulator,” IEEE J. Quantum Electron. |

10. | E. Desurvire, |

11. | J. A. Salehi, A. M. Weiner, and J.P. Heritage, “Temporal and statistical analysis of ultrashort light pulse code-division multiple access communications network,” in Proceedings of IEEE Int. Conf. on Communications |

12. | E. E. Narimanov, “Information capacity of nonlinear fiber-optical systems: fundamental limits and OCDMA performance,” in |

13. | S. M. Ross, |

14. | G. P. Agrawal, |

**OCIS Codes**

(060.2330) Fiber optics and optical communications : Fiber optics communications

(060.2360) Fiber optics and optical communications : Fiber optics links and subsystems

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: February 27, 2006

Revised Manuscript: April 18, 2006

Manuscript Accepted: April 18, 2006

Published: May 1, 2006

**Citation**

Bernard B. Wu and Evgenii E. Narimanov, "A method for secure communications over a public fiber-optical network," Opt. Express **14**, 3738-3751 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-9-3738

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### References

- A. J. Viterbi, "Spread spectrum communications - myths and realities," IEEE Commun. Mag. 17, 11-18 (1979) [CrossRef]
- P. R. Prucnal, M. A. Santoro, and T. R. Fan, "Spread spectrum fiber-optic local area network using optical processing," J. Lightwave Technol. 4, 547 (1986). [CrossRef]
- J. Shah, "Optical CDMA," Opt. Photon. Newslett. 14, 42-47 (2003) [CrossRef]
- J. A. Salehi, A. M. Weiner, and J. P. Heritage, "Coherent ultrashort light pulse code-division multiple access communication systems," J. Lightwave Technol. 8, 478-491 (1990) [CrossRef]
- S. Galli, R. Menendez, P. Toliver, T. Banwell, J. Jackel, J. Young and S. Etermad "Experimental results on the simultaneous transmission of two 2.5 Gbps optical-CDMA channels and a 10 Gbps OOK channel within the same WDM window," Proc. OFC 2005 OWB3
- S. Shen and A.M. Weiner "Suppression of WDM interference for error-free detection of ultrashort-pulse CDMA signals in spectrally overlaid hybrid WDM-CDMA operation," IEEE Photonics Technol Lett. 13, 82-84 (2001) [CrossRef]
- Steganography defines the science of hiding information by embedding messages within other in such a way that no one apart from the intended recipient knows of the existence of the message.
- E. E. Narimanov and B. B. Wu, "Advanced coding techniques for asynchronous fiber-optical CDMA," Proc. CLEO 2005 JThE70
- A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert, "Programmable shaping of femtosecond optical pulses by use of a 128-element liquid crystal phase modulator," IEEE J. Quantum Electron. 28, 908-920 (1992) [CrossRef]
- E. Desurvire, Erbium-Doped Fiber Amplifiers, Principles and Applications (John Wiley & Sons, Inc., New York, 1994)
- J. A. Salehi, A. M. Weiner, and J.P. Heritage, "Temporal and statistical analysis of ultrashort light pulse code-division multiple access communications network," in Proceedings of IEEE Int. Conf. on Communications 2, 728-733 (1989)
- E. E. Narimanov, "Information capacity of nonlinear fiber-optical systems: fundamental limits and OCDMA performance," in Optical Code Division Multiple Access: Fundamentals and Applications, P. R. Prucnal, ed. (CRC, 2005)
- S. M. Ross, Introduction To Probability Models 6th Edition (Academic Press, 1997) [PubMed]
- G. P. Agrawal, Fiber-Optical Communication Systems 3rd Edition (Wiley-Interscience, 2002) [PubMed]

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