Abstract

We evaluate the security performance of the recently proposed “stealth” approach to covert communications over a public fiber-optical network. We present quantitative security analysis to assess the vulnerability of such systems against different attacks executed by an eavesdropper. We demonstrate the security advantage of the system by examining the BER/SNR performance as a function of the fidelity of the decoder used by an eavesdropper. Effective key length is constructed as a security metric to gauge the level of confidentiality implicit in the secure transmission.

© 2007 Optical Society of America

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References

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  1. T. Jamil, "Steganography: the art of hiding information in plain sight," IEEE Potentials 18, 10-12 (1999)
    [CrossRef]
  2. A.J. Viterbi, "Spread spectrum communications - myths and realities," IEEE Commun. Mag. 17, 11-18 (1979)
    [CrossRef]
  3. B. B. Wu and E. E. Narimanov, "A method for secure communications over a public fiber-optical network," Opt. Express 14, 3738-3751 (2006)
    [CrossRef] [PubMed]
  4. A.J. Viterbi, CDMA: Principles of Spread Spectrum Communications, Addison-Wesley, Reading, Massachusetts (1995)
  5. J. Shah, "Optical CDMA," Opt. Photon. News 14, 42-47 (2003)
    [CrossRef]
  6. Z. Jiang, D. S. Seo, S.-D. Yang, D. E. Leaird, A. M. Weiner, R. V. Roussev, C. Langrock and M. M. Fejer, "Four user, 2.5 Gb/s, spectrally coded O-CDMA system demonstration using low power nonlinear processing," J. Lightwave Technol. 23, 143-158 (2005)
    [CrossRef]
  7. Z. Jiang, D.E. Leaird and A.M. Weiner, " Experimental Investigation of Security Issues in OCDMA," OFC 2006 OThT2
  8. T. H. Shake, "Confidentiality Performance of Spectral-Phase-Encoded Optical CDMA," J. Lightwave Technol. 23, 1652-1663
  9. G. P. Agrawal, Fiber-Optical Communication Systems 3rd Edition (Wiley-Interscience, 2002)
    [PubMed]
  10. C. E. Shannon. A mathematical theory of communication. The Bell System Technical Journal27 379-423, 623-656 (1948).

2006

2005

2003

J. Shah, "Optical CDMA," Opt. Photon. News 14, 42-47 (2003)
[CrossRef]

1999

T. Jamil, "Steganography: the art of hiding information in plain sight," IEEE Potentials 18, 10-12 (1999)
[CrossRef]

1979

A.J. Viterbi, "Spread spectrum communications - myths and realities," IEEE Commun. Mag. 17, 11-18 (1979)
[CrossRef]

Fejer, M. M.

Jamil, T.

T. Jamil, "Steganography: the art of hiding information in plain sight," IEEE Potentials 18, 10-12 (1999)
[CrossRef]

Jiang, Z.

Langrock, C.

Leaird, D. E.

Narimanov, E. E.

Roussev, R. V.

Seo, D. S.

Shah, J.

J. Shah, "Optical CDMA," Opt. Photon. News 14, 42-47 (2003)
[CrossRef]

Shake, T. H.

Shannon, C. E.

C. E. Shannon. A mathematical theory of communication. The Bell System Technical Journal27 379-423, 623-656 (1948).

Viterbi, A.J.

A.J. Viterbi, "Spread spectrum communications - myths and realities," IEEE Commun. Mag. 17, 11-18 (1979)
[CrossRef]

Weiner, A. M.

Wu, B. B.

Yang, S.-D.

IEEE Commun. Mag.

A.J. Viterbi, "Spread spectrum communications - myths and realities," IEEE Commun. Mag. 17, 11-18 (1979)
[CrossRef]

IEEE Potentials

T. Jamil, "Steganography: the art of hiding information in plain sight," IEEE Potentials 18, 10-12 (1999)
[CrossRef]

J. Lightwave Technol.

Opt. Express

Opt. Photon. News

J. Shah, "Optical CDMA," Opt. Photon. News 14, 42-47 (2003)
[CrossRef]

Other

Z. Jiang, D.E. Leaird and A.M. Weiner, " Experimental Investigation of Security Issues in OCDMA," OFC 2006 OThT2

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

C. E. Shannon. A mathematical theory of communication. The Bell System Technical Journal27 379-423, 623-656 (1948).

A.J. Viterbi, CDMA: Principles of Spread Spectrum Communications, Addison-Wesley, Reading, Massachusetts (1995)

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Figures (5)

Fig. 1
Fig. 1

Secure transmission over public fiber-optical communication network (Broadcast Star topology) Encryption of secure signal is performed at the physical layer by OCDMA encoder [3].

Fig. 2
Fig. 2

Intensity autocorrelation for a) secure signal and noise only, b) public signal and noise only, c) public signal, secure signal and noise. Simulations are performed where flat top band-limited pulses of bandwidth W (Sinc pulse profile in time domain) are used in both the public network and secure channel. The simulation parameters (see Appendix) are given by: Ps / Pp = 3, W = 0.6 rad /ps, C = 128 chips, Ts = 1320 ps, Tp = 60 ps and Nadd / Pp = 0.01.

Fig. 3
Fig. 3

a) Autocorrelation for composite signal obtain in simulations (red) and using analytical theory (blue) where Ps / Pp = 15, C=128 chips, Ts = 1320 ps and Nadd / Pp = 0.01. b) Autocorrelation comparison before (blue) and after (green) secure signal is applied to the public network (with the public signal and noise). Secure signal uses a spreading factor C=2048 chips, Ts = 21420 ps, Ps / Pp = 15 and Nadd / Pp = 0.01. (See Appendix)

Fig. 4
Fig. 4

The comparison of Q-factor for the secure channel vs. the fraction of correct chips (∏) present in an eavesdropper phase mask with public network (red, lower curve) and without public network (blue, upper curve). Symbols represent the simulation values and curves represent analytical values. The parameters are C=128 chips, Ts = 1320 ps and Ps : Pp = 3, Nadd : Pp = 0.01.

Fig. 5
Fig. 5

Effective key length vs. C (number of chips in a phase mask) for various values of SNR signal-to-noise ratio.

Equations (43)

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R ff ( τ ) = 1 Γ τ Γ 2 + τ Γ 2 f ( t ) f ( t τ ) dt
f ( t ) = s ( t ) + p ( t ) + n ( t ) 2
R ff ( τ ) = 1 Γ τ Γ 2 + τ Γ 2 dt · s ( t ) 2 s ( t τ ) 2 + p ( t ) 2 p ( t τ ) 2 + n ( t ) 2 n ( t τ ) 2 + s ( t ) 2 ( p ( t τ ) 2 + n ( t τ ) 2 ) + p ( t ) 2 ( s ( t τ ) 2 + n ( t τ ) 2 ) + n ( t ) 2 ( s ( t τ ) 2 + p ( t τ ) 2 ) + ( s ( t ) s ( t τ ) * p ( t ) * p ( t τ ) + c . c ) + [ n ( t ) n ( t τ ) * ( s ( t ) * s ( t τ ) + p ( t ) * p ( t τ ) ) + c . c ]
Q = I I 0 σ + σ 0
a ( t ) = s ˜ ( t ) + p ˜ ( t ) + n ( t )
I ( t ) = s ˜ ( t ) 2 + p ˜ ( t ) 2 + n ( t ) 2
I ( t ) 2 = s ˜ ( t ) 4 + p ˜ ( t ) 4 + n ( t ) 4 + 4 ( s ˜ ( t ) 2 n ( t ) 2 + p ˜ ( t ) 2 n ( t ) 2 + s ˜ ( t ) 2 p ˜ ( t ) 2 )
σ ( t ) = s ˜ ( t ) 4 + p ˜ ( t ) 4 + n ( t ) 4 ( s ˜ ( t ) 2 2 + p ˜ ( t ) 2 2 + n ( t ) 2 2 ) + 2 ( s ˜ ( t ) 2 n ( t ) 2 + p ˜ ( t ) 2 n ( t ) 2 + s ˜ ( t ) 2 p ˜ ( t ) 2 )
s ˜ ( t ) = ( ψ 1 h ˜ ( t + T s ) + ( 1 ψ 1 ) k ˜ ( t + T s ) ) e 1 + h ˜ ( t ) e 3 + ( ψ 2 h ˜ ( t T s ) + ( 1 ψ 2 ) k ˜ ( t T s ) ) e 2
s ˜ ( t ) 2 = h ˜ ( t ) 2 + 1 2 ( h ˜ ( t + T s ) 2 + h ˜ ( t T s ) 2 + k ˜ ( t + T s ) 2 + k ˜ ( t T s ) 2 )
s ˜ ( t ) 4 = h ˜ ( t ) 4 + 1 2 ( h ˜ ( t + T s ) 4 + h ˜ ( t T s ) 4 + k ˜ ( t + T s ) 4 + k ˜ ( t T s ) 4 )
+ 2 h ˜ ( t ) 2 ( k ˜ ( t + T s ) 2 + k ˜ ( t T s ) 2 ) + h ˜ ( t + T s ) 2 k ˜ ( t T s ) 2 + h ˜ ( t T s ) 2 k ˜ ( t + T s ) 2
+ 2 h ˜ ( t ) 2 h ˜ ( t T s ) 2 + 2 h ˜ ( t ) 2 h ˜ ( t + T s ) 2 + h ˜ ( t T s ) 2 h ˜ ( t + T s ) 2 + k ˜ ( t T s ) 2 k ˜ ( t + T s ) 2
h ˜ ( t ) = P s C Sinc ( Ω 2 t ) n = 1 C e i ( Ω t [ n C + 1 2 ] + θ n φ n )
h ˜ ( t ) 2 = P s C 2 Sinc 2 ( Ω 2 t ) ( C + n m = 1 C 2 e i Ω t ( n m ) )
k ˜ ( t ) 2 = P s C Sinc 2 ( Ω 2 t )
h ˜ ( t 1 ) 2 h ˜ ( t 2 ) 2 = P s 2 C 4 Sin c 2 ( Ω 2 t 1 ) Sin c 2 ( Ω 2 t 2 ) .
( 4 n m r s = 1 C e i Ω ( t 1 ( n r ) + t 2 ( m s ) ) ) + ( 2 3 ( n = m ) r s = 1 C e i Ω ( t 1 ( n r ) + t 2 ( m s ) ) ) + ( 2 ( n = r ) m s = 1 ( n = s ) m r = 1 ( m = r ) n s = 1 ( m = s ) n r = 1 C e i Ω ( t 1 ( n r ) + t 2 ( m s ) ) ) + ( 2 2 ( n = m = r ) s = 1 ( n = m = s ) r = 1 C e i Ω ( t 1 ( n r ) + t 2 ( m s ) ) ) + ( 2 ( n = m ) ( r = s ) = 1 C e i Ω ( t 1 ( n r ) + t 2 ( m s ) ) ) + ( ( n = s ) ( m = r ) = 1 C e i Ω ( t 1 ( n r ) + t 2 ( m s ) ) ) + C 2
k ˜ ( t 1 ) 2 k ˜ ( t 2 ) 2 = P s 2 C 4 Sinc 2 ( Ω 2 t 1 ) Sinc 2 ( Ω 2 t 2 ) . ( C 2 + ( n = s ) ( m = r ) = 1 C e i Ω ( t 1 ( n r ) + t 2 ( m s ) ) )
p ˜ ( t ) 2 = P p 2 C k Sin c 2 ( Ω 2 ( t kT p ) )
p ˜ ( t ) 4 = u v P p 2 2 C 4 Sin c 2 ( Ω 2 ( t uT p ) ) Sin c 2 ( Ω 2 ( t vT p ) ) . ( C 2 + ( n = s ) ( m = r ) = 1 C e i Ω ( ( t uT p ) ( n r ) + ( t vT p ) ( m s ) ) ) + u P p 2 2 C 4 Sin c 2 ( Ω 2 ( t uT p ) ) ( 2 C 2 C )
y ω = x ω + n ω = y ω e i ( ϕ x + δϕ )
N ω = 2 π δ ϕ 2 ~ 2 π P ω P n
N eff = C Log 2 ( N ω ) = C Log 2 ( 2 πSNR )
s ( t ) = u ( ψ u h ( t uT s ) + ( 1 ψ u ) k ( t uT s ) ) e u
p ( t ) = r ψ r ( P p Sin c ( W 2 ( t rT p ε ) ) ) e r
h ( t ) = P s C Sin c ( Ω 2 t ) n = 1 C e i ( Ω t [ n C + 1 2 ] + φ n )
s ( t ) 2 = u P s C Sin c 2 ( Ω 2 ( t uT s ) )
p ( t ) 2 = r T p 2 T p 2 P p 2 T p Sin c 2 ( W 2 ( t rT p ε ) )
n ( t ) 2 = N add
s ( t ) 2 s ( t τ ) 2 = 1 2 u , v ( 1 + δ uv ) h ( t uT s ) 2 h ( t τ vT s ) 2
+ ( 1 δ uv ) [ h ( t uT s ) 2 h ( t τ vT s ) 2 + h ( t uT s ) h ( t τ uT s ) * h ( t vT s ) * h ( t τ vT s ) + h ( t uT s ) h ( t τ u T s ) * h ( t vT s ) * h ( t τ ν T s ) ]
A ( t 1 ) = P s C Sin c 2 ( Ω 2 t 1 )
B ( t 1 , t 2 ) = P s C 2 Sin c ( Ω 2 t 1 ) Sin c ( Ω 2 t 2 ) n = 1 C Cos [ Ω ( n C + 1 2 ) ( t 1 t 2 ) ]
X ( t 1 , t 2 , t 3 , t 4 ) = P s 2 C 4 Sin c ( Ω 2 t 1 ) Sin c ( Ω 2 t 2 ) Sin c ( Ω 2 t 3 ) Sin c ( Ω 2 t 4 ) .
[ ( n , m = 1 C Cos [ Ω ( n ( t 2 t 1 ) + m ( t 4 t 3 ) + ( t 1 t 2 + t 3 t 4 ) ( C + 1 ) 2 ) ] ) + ( n , m = 1 n m C Cos [ Ω ( n ( t 2 t 3 ) + m ( t 4 t 1 ) + ( t 1 t 2 + t 3 t 4 ) ( C + 1 ) 2 ) ] ) ]
s ( t ) 2 s ( t τ ) 2 = 1 2 u , v ( 1 + δ uv ) X ( t uT s , t uT s , t vT s , t vT s ) + ( 1 δ uv ) ( A ( t uT s ) A ( t τ vT s ) + B ( t uT s , t τ uT s ) B ( t τ vT s , t vT s ) + X ( t uT s , t τ uT s , t τ vT s , t vT s )
p ( t ) 2 p ( t τ ) 2
= 1 4 r , v ( 1 + δ rv ) P p 2 Sin c 2 ( W 2 ( t rT p ) ) Sin c 2 ( W 2 ( t τ vT p ) )
+ ( 1 δ rv ) [ P p 2 Sin c ( W 2 ( t rT p ) ) Sin c ( W 2 ( t vT p ) ) . Sin c ( W 2 ( t τ rT p ) ) Sin c ( W 2 ( t τ vT p ) ) ]
n ( t ) 2 n ( t τ ) 2 = { 2 N add 2 τ = 0 N add 2 otherwise }
s ( t ) s ( t τ ) * = u B ( t uT s , t τ uT s )
p ( t ) p ( t τ ) * = r T p 2 T p 2 P p 2 T p Sin c ( W 2 ( t rT p ε ) ) Sin c ( W 2 ( t rT p ε τ ) )

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