Mem. Fac. Eng., Osaka City Univ., Vol. 49, pp. 13-17 (2008)

Security Evaluation of Optical CDMA Systern against Statistical Code Detection

Tomohiro YOKOHAMA* and Tetsuo TSUJIOKA**

(Received September 30, 2008)

SynopsisOptical orthogonal codes (OOC) have been investigated as an important technology to achieve

optical CDMA systems. Recently, some security analyses were published, where they have a problemof weakness against eavesdropping. In this paper, we propose a new security measure for an opticalCDl\1A system from the viewpoint of eavesdroppers. We derive distributions of code detection time byusing a technique based on statistical approach, and evaluate robustness of the optical CDMA systemusing for several well-known OOCs.

1 Introduction

Optical orthogonal codes (OOe) realize asynchronous optical CDMA systems via all optical circuitby intensity modulation and incoherent direct detection, and there are many studies for a long time[l].However, there is a security problem that eavesdropping is easy for the asynchronous optical CDMAsystems, so we have make to security enhancement on OOCs[2].

A security measure of optical CDMA systems is evaluated by Shake[3] [4] based on a probabilityof code detection. Even in condition that the probability of code detection is low, we might say thatsecurity measure is low if time until the codewords are detected entirely is short. In other words, toevaluate security strength, we must show difficulty of the code detection for eavesdroppers. Therefore,in this paper, we pay our attention to required time to detect codewords as a difficulty. \Ve can say thatsecurity strength is high, if ,ve observe that the eavesdroppers need long time for code detection. Weshow one of eavesdropping methods based on a statistical approach. The distribution of the codeworddetection time using this method, and a trade-off between the accuracy of detection and detectiontime.

2 Optical CDMA Systen1. and Weakness

Figure 1 shows a transmission part of an optical CDMA system in which users' signals are spreadingin time domain using an optical orthogonal code. There are k users with different codewords. Users'

To Receiver

User

Fig. 1 : The model of optical CDMA system andtapping position for eavesdropping.

Fig. 2 : An example of overlapped optical signaland easily detectable codeword.

* Student, l\'la.ster Course of Dept. of Information and Communication Engineering** Lecturer, Master Course of Dept. of Information and Communication Engineering

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signals are encoded by their codewords after on-off-keying(OOK) data modulation. In Fig. I, aneavesdropper taps a mixed signal from optical fiber. He detects a signal that overlapped all users'codewords and has to make codeword separation.

However, actually the codewords of all users may not always sent at the same time when OOK isused. Figure 2 shows an example that only one user sends a codeword and the other users do not. Inthis case, only one codeword appear in the fiber as non-mixed signal, the eavesdropper can detect thecodeword by just tapping the optical fiber. This is the weakness of the optical CDMA systems usingoptical orthogonal codes.

3 An Eavesdropping Method Based on Statistical Approach

As the eavesdropping method based on statistical approach, the eavesdropper acquires a series oflots of samples from optical fiber, and estimates codewords using its distribution. Code length, codeweight and the gap between pulses in codewords is required to estimate codewords. But it needs totake long time to estimate all parameters perfectly due to huge code search space. Therefore, in thispaper, we estimate code weight first, and then estimate codewords using estimated code weight.

3.1 Code Weight Estimation

As shown in Fig. 3 (a), it begins with estimation of the code weight that the eavesdropper samplesthe mixed optical signal that did in tapping in length L. In addition, we assume that the code weightof all users is the same, and the eavesdropper can sample in correct chip rate. The eavesdroppercounts optical pulses of each sample and makes a histogram of optical pulses as shows in Fig. 3 (b).The eavesdropper N times samples mixed signals.

Next, the eavesdropper estimates the code weight by refferring the histogram of optical pulses;"\iVhen L is larger than the code length and N is large enough, the histogram becomes non-uniform.It is seen peaks at measurement times of code weight w. Although high floors that is not the peak bymismatch of the sequence length and codeword, the eavesdropper can improve estimation accuracyof code weight by setting appropriate detection condition. The proposed detection methods and thedetection conditions are as follows. First, the eavesdropper demands frequency while adding to lengthL of the sample sequence till a peak is seen in distribution. If the first peak of pulse count, WI, is halfof the second peak, W2, assuming code weight is WI, and set w to be WI. Figure 4 shows a flowchartof code weight estimation process. If the code length is already turn out, the length L might be thecode length. Also in this case, the distribution of pulses shows some peaks, the first peak WI might acode weight.

3.2 Codeword Estimation

Since the code length and the code weight are already detected by the previous process, theeavesdropper sets code length L and he repeats to sample of optical sequence. The number of pulsesin each sample sequence is checked one by one whether it is equal to w. If the condition doesn'tsatisfied, the sequence is discarded. Otherwise, the sequence is shifted so that the shortest gap maybecon'les the first in order to be easy to compare with others. The distribution shown in Fig. 5 isprovided if sequences is sorted by the number of detections. In this paper, we pay attention to themajor detected sequences as estimated codewords of the code. A threshold is introduced for decision ofmajor sequences. After arranging the frequencies of the sequences in descending order, Each frequencyis checked whether it is less than ~ times the previous frequency. If so, we assume the sequences afterthat is not major. In this manner, we find out major sequences that the frequencies are relatively highcompared to others. Here r is defined as the code detection threshold.

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(a) Sampling

User

I - I . . I 3 I - I C3 . I C3 I . I C I . III . I C2 I C2 II C2 I C2 I . I . I C2 I C2 . I 2 I - I

I . I C1 I 1 I . I C1 . I . I C1 I - I C1 . I1+-----+ ~ +----+

EYes

No

Find 151 peak & 2nd peakon the histogram of

number of pulses

Fig. 4 : Flowchart of estimation process of codeweight.

LengthL

Count pulses

and build histogram.

number ofpulses

Length

J L

2nd

peak If w2~2wl' we assumeWI is code weight.

LengthL

weight

151 peak

frequency

(e) Analyzing

(b) Gathering

-jeT!nl."•...,I.....eTlTTlI TTII"I."'II__• Tnllf-L

Fig. 3 : Code weight estimation method based onstatistical approach.

r is called a code detection threshold. Figure 6 shows a flowchart of the process of estimatingcodeword.

4 Simulation Results and Discussions

In this paper, we simulated by the same constitution as Fig. 1. Each user uses the same bit rate,the same code length, the same code weight and difl'erent codeword. We have made some additionalassumptions that each user also has specific delay less than code length, synchronization in termof chip time, and non-synchronization in term of codeword. The eavesdropper uses receiver that issynchronized in term of chip time, can completely distinguish chips of codewords, and already detectedcode length.

4.1 Estimation Result of Code Weight

Figure 7 shows estimation results of code 'weight in the case of OOC(31,3,l,1) with code length of31, code weight of 3, and optimal correction design. The presumption accuracy improves when thenumber of samples, N, increases, and also the sequence length which is necessary for the code weightestimation increases too.

Figure 8 shows estimation results of code weight in the case of various codes. L becomes largeby the short code length or less active users. Because there are few optical pulses in each samplesequence, it takes long time to make the histogram.

4.2 Estimation Result of Codeword

Figures 9 and 10 show distributions that the number of samples until codeword estimation com­pletely ends under code length and code weight are already detected. OOC(31,3,1,1) is used in Fig. 9and OOC(61,4,1,l) is used in Fig. 10.

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User

I - I - - I 3 I - I C3 - I C3 I - I C I - III - I C2 I C2 ,I C2 I C2 I I - II C2 I C2 - I 2 I - I

I - I C1 I 1 I - II Cl - I - I c, I - I Cl - I~ ~ +-------->

Shift left so that the shortest gap maybecome the first. ~

,IJIUlllllllllllllll1

L L

(a) Sampling

(b) Gathering

LengthL

LengthL

LengthL

Yes

No

Sort sequence stockby a number of same sequence

in ascending order

Fig. 5: Estimation process of finding major se­quences as codewords detection. (based on sta­tistical approach,)

(c) Analyzing

No

E

For all sequence:Search a sequence ,a number of which

is "r" times higher thanthat of adjoined sequence

Codeword is a sequence thata number of which is greater

than that found sequence.

Fig. 6 Flowchart of codeword estimation.

number ofsequences

After sorting sequence by the detection number,the sequence in which detection numberis "r" limes higher than the neighbor

threshold is estimated as one of codewords.

I Mr~ times hIgher•

+------+eStlmated ascodewords

frequency

70 70N=100(PEE=049) ----+--- OOC (31,3,1,1), 2-User ----+---

60 N=1000(P <10-2) ---x--- 60 OOC (31,3,1,1), 3-User ---x---N=10000 (P~~<10-2) - - --ll(- OOC (61,4,1,1), 2-User - -ll(--

50~

50 OOC (61,4,1,1) , 3-User H>- >-

~u uc 40 c 40(1) (1)::J ::J0- 30 lI! 0- 30(1) (1) ,0--- x,u:: ,~ u:: ~ , ,

20 ' .' 20 .", ,

, " if. "0 x

'x,' 'x. 0 x10 10 , ,

,X' x--'K it c___/ * <~~-.->.(-- ' :>( -0 0

10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90

Required Sequence Length L Required Sequence Length L

Fig, 7: Histogram of length of sample se­quence necessary for estimating code weight(OOC(3l,3,l,l), N = 100,1000, and 1000).

Fig. 8 : Histogram of length of sample sequencenecessary for estimating code weight (variouscodeword, N = 1000).

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90000 12000Average,2-User ,, Average,2-User --+--

80000~ , 11000Average,3-User ---x--- , Average,3-

"0.8 0.870000 PEundeteet,2-User .•. ?I( ... , 10000 PE un e eet' -User .•. ?I(.

QJ PE:undeteet, 3-User ······0 .. , QJ P :undeteet,3-User ··0E 60000

, E 9000 uuf=,

0.6 "' f= 0.6 "',c 50000 , a; c 8000 a;, u u

.Q

"c .2 c

t5 40000 , ". t5 7000 "QJ ,, 0.4 w ill 0.4 w·ill 30000 "

, CL ill 6000 CL0 ,

0 , 0";1(."~

,20000 ,

0.2 5000 0.210000 -

_~';ilc~::,:-::-,:~' .4000 _~~~~'~~,.-:.:::~;_---x-- -- _-x-- ----

--,,/0 0 3000 0

5 6 7 8 9 10 5 6 7 8 9 10

Fig. 9: The trade-off between the accuracy ofdetection and detection time (OOC(31,3,1,l)).

Fig. 10: The trade-off between the accuracy ofdetection and detection time (OOC(61,4,1,1)).

If the probability of undetected codeword, PE,undetect> is compared with code detection thresholdr, as much as r increases, PE,undetect decreases, and the required time until codeword detection, codedetection time increases. Because the number of optical pulses in sample sequence is insufficient tobuild the histogram, PE,undetect decreases and the code detection time increases when the long codelength is used. If the active users are increased, then code detection time increases. However, as shownin Fig. 10, when the number of active users is few and the number of optical pulses in the samplesequences is very few, most sample sequences are discarded and code detection time increases, and atime of codeword detection increases as well as increasing the code length.

5 CancIusian

In this paper, we consider the code detection time as the security measure of optical CDMAsystems, and we proposed the eavesdropping method based on statistical approach. The simulationresults of eavesdropping showed, we found that the code detection time increases if the code lengthor the number of active users increase. As the result of discussion in this paper, we conclude that wecan use the code detection time for the security measure.

References

[1] J. Salehi, B. Res, and N. Morristown, "Code division multiple-access techniques in optical fibernetworks-Part:I Fundamental principles," IEEE Trans. Commun., vol. 37, no. 8, pp. 824-833,Aug. 1989.

[2] T. Tsujioka, "A study on secure optical orthogonal codes," IEICE Technical Report, vol. 107,no.18, CS2007-10, pp. 55-59, Apr. 2007.

[3] T. Shake, "Security performance of optical CDIVIA against eavesdropping," J. Lightwave Technol.,vol. 23, no. 2, pp. 655-670, Feb. 2005.

[4] T. Shake, "Confidentiality performance of spectral-phase-encoded optical CDMA," 1. LightwaveTechnol., vol. 23, no. 4, pp. 1652-1663, Apr. 2005.

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