Jurnal Fizik Malaysia Volume 39 Issue 2 (2018) pgs 30054-30058 M. Kalpana

Audio Encryption Based On Chaotic FCNNs

M. Kalpana and K. Ratnavelu

Institute of Mathematical Sciences, Faculty of Science, University ofMalaya, Malaysia.

(Received: 20.3.2018 ; Published: 5.10.2018)

Abstract. Extensive theoretical work and few application part in the area of imageprocessing have been done in fuzzy cellular neural networks (FCNNs). However, thereis lack of utilizing of FCNNs for audio encryption. The sound file is ciphered by ina state of complete confusion and disorder signal in which accomplished via FCNNssystem. While, the risky task is to evaluate the variables of the FCNNs as followsδ , ζ , η , α, β , γ.

Keywords: Chaos, Cipher, Fuzzy cellular neural networks.

I. INTRODUCTION

In this 21st century, the artificial neural network plays a immense role in the applica-tion part, specifically in the field of encryption. While, Chua and Yang initiated the locallyconnected Cellular neural networks (CNNs) in the year 1988 [1, 2]. The CNNs was furtherimproved by the technique of FCNNs [3, 4].

Nowadays, sending the voice message to the friends, relatives, colleagues, and so on,becomes more often, so that one can easily convey their message via the net. However, thehackers may hack peoples information via the internet, which causes vulnerable to people. So,the secure encryption becomes hot area of research, nowadays.

Here, we have performed a powerful audio cipher by FCNNs. Generally, for any n secondsaudio file, each second has 44100 values, totally n∗44100 values are there in each audio fileto receive the sound. The state trajectories r(t) of FCNNs system (1) has ∞ values, amongthem, we have chosen n∗44100 values to encrypt any given audio files.

FIGURE 1. Encryption/decryption flow chart.

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Jurnal Fizik Malaysia Volume 39 Issue 2 (2018) pgs 30054-30058 M. Kalpana

The risk task is to find the values of the parameters δ , ζ , η , α, β , γ, of FCNNs system(1), to obtain the chaotic trajectories, that is the state trajectories r(t) would be in a state ofchaos [5]-[8], which is adequate from hackers attack.

The theoretical work for the problem on stability [9], synchronization [10], and applicationwork for image encryption [11] have been done based on the FCNNs. However, its a neweffort by utilizing the FCNNs system to encrypt an audio file. Figure 1 illustrates the processof cipher WAV file by the symmetric key.

Inspired by the aforementioned discussions, the chaotic signals obtained via FCNNs sys-tem (1) has been utilized to encrypt an audio signals A. Also, the number of secret key is fortyeight and they are δ , ζ , η , α, β , with initial value vector γ . If the precision is 10−10, thenthe key space is (1010)48 = 10480 > 21440. Moreover, the brute-force attack is infeasible.

II. SYSTEM DESCRIPTION

The following delayed chaotic FCNNs is to be consideredr`(t) =−η`r`(t)+∑

n℘=1 δ`℘ϑ℘(r℘(t))+∑

n℘=1 ζ`℘ϑ℘(r℘(t−ρ(t)))+I`

+∧n

℘=1 α`℘∫ t−∞

ξ℘(t− s)ϑ℘(r℘(s))ds+∨n

℘=1 β`℘∫ t−∞

ξ℘(t− s)ϑ℘(r℘(s))ds,

r`(s) = γ`(s), s ∈ (−∞,0], ` ∈ {1,2, ...,n},

(1)

where γ`(·) ∈C((−∞,0],R); δ`℘, ζ`℘ are the elements of feedback template;∧,∨

denotethe fuzzy AND and OR operation, respectively; α`℘ and β`℘ are the elements of fuzzy feed-back MIN and MAX template, respectively; r` and I` denote the state and external input ofthe `th neuron, respectively; η is a diagonal matrix; ξ℘(·)≥ 0 is the delay kernel function andsatisfies

∫∞

0 ξ℘(s)ds = 1, ℘∈ {1,2, ...,n}.

The hypotheses are(H1) The neuron activation function ϑ℘(·) is ϑ℘(r℘)= 1

2(|r℘+1|−|r℘−1|),℘∈{1,2, ...,n}.(H2) The time varying transmission delay is ρ(t), which satisfies 0 ≤ ρ(t)≤ ρ, where ρ is apositive constant.

III. NUMERICAL EXAMPLE

The parameters of (1) is chosen by trial and error method

γ = [1,0.7,1.7]T , I= [0.1,0.1,0.1]T ρ(t) = 0.5 |sin(t)|,

δ =

3 4 32.9 1.1 01 4.4 0.9

, ζ =

4.3 1 0−2.5 1.2 −4.9−2.7 4.5 2.2

, η =

4 0 00 2 00 0 2

,α = β =

1/10 1/10 1/101/10 1/10 1/101/10 1/10 1/10

.Figure 2 illustrates the dynamical signals r(t) of the chaotic FCNNs system (1).

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Jurnal Fizik Malaysia Volume 39 Issue 2 (2018) pgs 30054-30058 M. Kalpana

0 50 100 150 200 250 300−5

0

5

time t

r 1(t)0 50 100 150 200 250 300

−5

0

5

time tr 2(t)

0 50 100 150 200 250 300−10

0

10

time t

r 3(t)

FIGURE 2. Chaotic signals via (1).

Steps for audio encryption/decryption

1. Read the audio file music.wav

2. Further, some portion of the above-mentioned audio file has been segmented from tenthto fourteenth seconds as follows

A← music(44100∗10 : 44100∗17)

3. Based on the processed chaotic signals through FCNNs system (1) and audio signal A,the ciphered audio signal is

E(`) ← A(`)+[(1011)∗

( 3

∑℘=1

r℘(`)+ sum(γ))]

4. Finally, the deciphered audio signal D, will be achieved by the proceeded chaotic signalsthrough system (1) and ciphered signal E.

D(`) ← E(`)−[(1011)∗

( 3

∑℘=1

r℘(`)+ sum(γ))]

Obviously, view the Figure 3.

IV. EXPERIMENTAL RESULTS

Based on the proposed method the secret keys are case sensitive, that is if an element of theparameters mismatched even to the decimal place of 0.0000000001 (Table 1), we will obtainfalse output. This shows that the audio files would be secured adequate from hackers attack.

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Jurnal Fizik Malaysia Volume 39 Issue 2 (2018) pgs 30054-30058 M. Kalpana

TABLE 1. Correlation analysis

Case Parameters Original Mismatched Correlation betweenoriginal & original &

encrypted signal decrypted signal1 δ ,ζ ,η ,α,β ,γ - - -0.007043 0.999999

are as in Example 12 δ23 0 -0.0000000001 -0.007043 -0.0002373 ζ33 2.2 2.1999999999 -0.007043 -0.0002524 η11 4 4.0000000001 -0.007043 0.0004535 α22 0.1 0.0999999999 -0.007043 -0.0001196 β13 0.1 0.1000000001 -0.007043 -0.0005347 γ11 1 1.0000000001 -0.007043 0.058591

0 1 2 3 4 5 6 7 8−1

−0.5

0

0.5

1Music

Time (s)

Am

plitu

de

Time (s)

Frequency (

Hz)

Spectrogram − Music

0 1 2 3 4 5 60

0.5

1

1.5

2

x 104

−100

−50

0

0 1 2 3 4 5 6 7 8−1

−0.5

0

0.5

1Music

Time (s)

Am

plitu

de

Time (s)

Frequency (

Hz)

Spectrogram − Music

0 1 2 3 4 5 60

0.5

1

1.5

2

x 104

−50

0

50

0 1 2 3 4 5 6 7 8−1

−0.5

0

0.5

1Music

Time (s)

Am

plitu

de

Time (s)

Frequency (

Hz)

Spectrogram − Music

0 1 2 3 4 5 60

0.5

1

1.5

2

x 104

−100

−50

0

(b)(a)

(c)

FIGURE 3. (a) Original audio signal A and its spectrogram, (b) Ciphered audio signal E and its spectrogram, and (c)Successful deciphered audio signal D and its spectrogram with correct keys in Case 1 of Table 1

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Jurnal Fizik Malaysia Volume 39 Issue 2 (2018) pgs 30054-30058 M. Kalpana

V. CONCLUSION

In this work, the chaotic FCNNs with time delay is proposed to cipher an audio signal A.However, the key sensitivity was checked to be in the order of 10−10. Moreover, the exper-imental results demonstrate the effectiveness of our proposed method along with numericalexample and its simulations. In the future, we will do the work on encryption/decryption forthe noise audio files based on the FCNNs.

ACKNOWLEDGMENTS

This effort was assisted by the Fundamental Research Grant Scheme (FRGS) MoHE GrantNo. FP051-2016. Dr. M. Kalpana is working as a Post-Doctoral Research Fellow at theUniversity of Malaya.

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