Journal of Robotics, Networking and Artificial Life, Vol. 3, No. 3 (December 2016), 193-196

A Method for Secure Communication Using a Discrete Wavelet Transform for Audio DataYuji Tsuda1, Kouhei Nishimura2, Haruka Oyaizu3, Yasunari Yoshitomi2, Taro Asada2, and Masayoshi Tabuse2

1: Software Service, Inc.
Nishi-Miyahara, Yodogawa-Ku, Osaka 532-0004, Japan
2: Graduate School of Life and Environmental Sciences, Kyoto Prefectural University,
1-5 Nakaragi-cho, Shimogamo, Sakyo-ku, Kyoto 606-8522, Japan
E-mail: {yoshitomi, tabuse}@kpu.ac.jp, t_asada@mei.kpu.ac.jp}
http://www2.kpu.ac.jp/ningen/infsys/English_index.html
3: NHK Media Technology, Inc.
Kamiyama-cho, Shibuya-ku, Tokyo 150-0047, JapanAbstract
We developed a secure communication method using a discrete wavelet transform. Two users must both have a
copy of the same piece of music to be able to communicate with each other. The music and the sender's message
are encoded using the scaling coefficients obtained from a discrete wavelet transformation. The message receivercan produce the audio data similar to the sending user's speech using an inverse discrete wavelet transform, togetherwith information on the difference between these two codes.
Keywords: Secure communication, Audio data processing, Wavelet transform, Encoding.

1. Introduction
Recently, there has been an increase in certain kinds offraud. Specifically, the elderly are often the targets oftelephone fraud. The fraudster pretends to be agrandchild of the elderly person while talking on thephone, and appeals to the elderly person to send money,for example, through a bank transfer. When the elderly
person mistakes the fraudster for a grandchild, thefraudster can obtain money. Even if the voice of thefraudster is not similar to that of the grandchild, theelderly victim might send money to the fraudster. Thisis because the fraudster skillfully convinces the elderly
person, who cherishes their real grandchild, of a serious
monetary problem, such as might exist following a
traffic accident.
In the present study, we propose a method for
secure communication using a discrete wavelet
transform (DWT). The method can be used with
Internet protocol (IP) telephones, and has the potential
to help prevent telephone fraud.

2. Wavelet TransformIn this section, we provide a brief introduction to theDWT.1
Original audio data s k(0) ,which are used as the level0 wavelet decomposition coefficient sequence, where kdenotes the element number, are decomposed into theelements of a multi-resolution representation (MRR)
and the elements of a multi-resolution analysis (MRA)by repeatedly applying the DWT. The wavelet
decomposition coefficient sequence s k( j ) at level j isdecomposed into two wavelet decomposition coefficientsequences at level j + 1 using the following equations:∑p= ∑qsk( j +1) =wk( j +1)( j)n − 2 k sn

(1)

( j)
n − 2 k sn ,

(2)

nn

where p k and q k denote the scaling and wavelet
sequences, respectively, and wk( j +1) denotes thePublished by Atlantis Press
Copyright: the authors
193

Yuji Tsuda, Kouhei Nishimura, Haruka Oyaizu, Yasunari Yoshitomi, Taro Asada, Masayoshi Tabusedevelopment coefficient at level j + 1 . The development
coefficients at level J are obtained using (1) and (2)iteratively from j = 0,…,J-1. Figure 1 shows the process
for the multi-resolution analysis by DWT.
In the present study, we use the Daubechies
wavelet for the DWT.2 As a result, we obtain thefollowing relation between p k and q k :qk = (－1) k p1− k(3)

Fig. 2. Schematic diagram of the histogram of the MRA
scaling coefficients.

1) T 1 < Th(minus) < T 2 < 0 < T 3 < Th(plus) < T 4 .
Fig. 1. Multi-resolution analysis by DWT.

2) The value of ST 1 , which is the number of scaling1

coefficients in (T 1, Th(minus)) , is equal to ST 2 ,which is the number of scaling coefficients in[Th(minus), T 2) , i.e., ST 1 = ST 2 .

3. Proposed Method

3) The value of ST 3 , the number of scaling coefficients3.1. Encodingin (T 3, Th(plus)] , is equal to ST 4 , the number of

3.1.1. Phenomenon exploited for the coding
algorithm for audio datascaling

It is known that the histogram of the wavelet
coefficients for each domain of the MRR sequences iscentered at approximately zero when the DWT is
performed on audio data.1 In the present study, wefound that the histogram of the scaling coefficients foreach domain of the MRA sequences is also centered at
approximately zero when the DWT is performed on
audio data. Exploiting this phenomenon, we havedeveloped a secure communication method using audio
data.
3.1.2. Parameter settings
As with digital watermark (DW) techniques forimages2,3 and digital sounds,4 we set the following
coding parameters.
The values of Th(minus) and Th(plus) in Fig. 2
are chosen such that the non-positive scalingcoefficients ( S m in total frequency) are equally divided
into two groups by Th(minus) , and the positive scalingcoefficients ( S p in total frequency) are equally divided
into two groups by Th(plus) . Next, the values of T1,T2, T3 and T4, which are the parameters for controllingthe authentication precision, are chosen to satisfy thefollowing conditions:coefficients
ST 3 = ST 4 .

in(Th(plus), T 4) , i.e.,4) ST 1 / S m = ST 3 / S p .

In the present study, the values of both ST 1 / S m andST 3 / S p

are set to 0.3, which was determined

experimentally.
3.1.3. Encoding
In the preprocessing of the audio data before encoding,the scaling coefficients V of an MRA sequence are
separated into five sets (hereinafter referred to as G0, G1,G2, G3, and G4), as shown in Fig. 3, under the following
criteria:• G0 = {V | V ∈ V SC , V ≤ T 1} ,• G1 = {V | V ∈ V SC , T 1 < V < T 2} ,• G2 = {V | V ∈ V SC , T 2 ≤ V ≤ T 3} ,• G3 = {V | V ∈ V SC , T 3 < V < T 4} ,• G4 = {V | V ∈ V SC , T 4 ≤ V } ,where V SC is the set of scaling coefficients in the audio
data file.

Published by Atlantis Press
Copyright: the authors
194

A Method for Secure

whereai ∈{m0A , m1A , m2A , m3A , m4A}

is the average of thescaling coefficients of A at the range denoted by
X i ∈{0,1,2,3,4} obtained from A .
Then, the audio data B′A is defined as having thescaling coefficient sequence S ( B ′A ) k and a value of zerofor all wavelet coefficient values at every level. S ( B′A ) k
is defined as:
S ( B′A ) k = {bA,1 , bA, 2 , bA,3 , …, bA, k } ,where b A,i ∈ m0B , m1B , m2B , m3B , m4B  is the average of scalingof B at the range denoted by
X i ∈{0,1,2,3,4} obtained from A .
S ( B′A ) k is obtained by replacing Yi with X i when

coefficients

Fig. 3. Schematic diagram for demonstrating the selection ofthe scaling coefficients for encoding the audio data.

The scaling coefficients for an MRA sequence areencoded according to the following rules, in which Vi
denotes one scaling coefficient:Yi ≠ X i , and then replacing bi with bA, i , where bi isthe average of the scaling coefficients of B at the range
denoted by Yi . Therefore, C ( B′A ) k = C ( A)k . As a result,B′A is expected to be similar to A .
3.3. Data for communication

When Vi ∈ G0 , ci = 0.
When Vi ∈ G1 , ci = 1.
When Vi ∈ G2 , ci = 2.

A sequence D1( B′A ) n is defined as:

When Vi ∈ G3 , ci = 3.
When Vi ∈ G4 , ci = 4.

and z p = [ yi ]mod 256 , and the integer p is increased

D1( B′A ) n = {z1 , z 2 , 2 , z n } ,where n is the total number of cases where Yi ≠ X i ,Then, the representative value for each set, G0, G1, G2,G3, and G4, is its average, m0, m1, m2, m3 and m4,respectively. For audio data formation, we use a code
C (hereinafter referred to as an original code), which isthe sequence of ci , and m j defined above.
3.2. Sound data formation using code replacement
The scaling coefficient sequence for audio data, A , isexpressed by
S ( A) k = {x1 , x2 , x3 ,…, xk } ,where k is the total number of scaling coefficient of A
at a level. Then, a sequence
C ( A) k = { X 1 , X 2 , X 3 , … , X k }is determined, where X i ∈{0,1,2,3,4} is the element index
denoting which of the five sets of scaling coefficientsxi of A belongs to.
Next, the audio data A′ is defined as having thescaling coefficient sequence S ( A′) k and a value of zerofor all wavelet coefficient values at every level. S ( A′) kis defined as:
S ( A′) k = {a1 , a2 , a3 ,…, ak } ,from 1 to n , in steps of size 1, when Yi ≠ X i . Here,[x] is the maximum integer that is not greater than x .
Then, a sequence D 2( B′A ) n is defined as:

D 2( B′A ) n = {Z1 , Z 2 , 2 , Z n } ,where n is the total number of cases where Yi ≠ X i ,and Z p = X i , in which the integer p is increased from 1to n , in steps of size 1, when Yi ≠ X i .
In communications between two users, both themessage sender and the receiver have the secret key B,
and the sender sends D1( B′A ) n and D 2( B′A ) n to thereceiver. Then, the receiver composes B′A′ , which isdefined in Section 3.4 and expected to be similar to A .
3.4. Audio data composition
The scaling coefficient sequence for audio data B isexpressed by
S ( B ) k = { y1 , y 2 , y3 ,…, y k } ,where k is the total number of scaling coefficient of B
at the level . Then, a sequence
C ( B) k = {Y1 , Y2 , Y3 ,…, Yk }Published by Atlantis Press
Copyright: the authors
195

Yuji Tsuda, Kouhei Nishimura, Haruka Oyaizu, Yasunari Yoshitomi, Taro Asada, Masayoshi Tabuse

is determined, where Yi ∈{0,1,2,3,4} is the element index
denoting which of the five sets of scaling coefficientsyi of B belongs to. S ( B′) k is defined as:
S ( B′) k = {b1 , b2 , b3 , …, bk } ,wherebi ∈ m0B , m1B , m2B , m3B , m4B is the average of thescaling coefficients of B at the range denoted byYi ∈{0,1,2,3,4} obtained from B .
A sequence D3( B) k is defined as:D3( B) k = z B ,1 , z B , 2 ,2 , z B , k ,{}where k is the total number of scaling coefficient of B
at the level, and z B , q = yq mod 256 . B′A′ is determined[ ]as follows; S ( B′A′ ) k is calculated from S ( B′) k byreplacing bq with mZ p when z B , q = z p , for p = 1 ,…,Bn , then the audio data B′A′ is composed by IDWT using
the scaling coefficient sequence S ( B′A′ ) k and a value ofzero for all wavelet coefficients at every level. The
receiver composes B′A′ using D1( B′A ) n and D 2( B′A ) n ,which are determined by both A and B , and are sentby the sender, in addition to B which the receiver hasprior to the conversation. B′A′ is expected to be similar
to A .

3.5. Communication of audio data with arbitrary
lengthIn general, the recording time for A is not the same asthat for B . For B we use a unit recording time such as
one second. Then, we apply the proposed method
described in the above sections to A every unit
recording time. When the recording time of A isindivisible by the unit recording time, the additional
scaling coefficients that are needed for application of
the proposed method are set to zero.
4. Numerical Experiment
We applied the proposed method using several voicerecordings for A and for B we used (1) ‘Classical’, (2)‘Hiphop’ music, with one second of recording time each.
The music was taken from a copyright free database5.
In all cases of the experiment, B′A′ was audible andsimilar to A . However, B′A′ contained low-frequency
background noise. After erasing this noise, the audio
recording became more audible and the tone of thesender’s voice changed as if the speaker was a different
person. Our next objective is to develop a method for
decreasing the background noise while preserving thetone of the speaker.

5. Conclusion
We developed a secure communication method using a
discrete wavelet transform for audio data. In thismethod, two users must each have a copy of the same
piece of music, which has a length of one second andfunctions as a secret key, before communicating witheach other. The music is transformed into a code before
the conversation using the scaling coefficients obtained
from a discrete wavelet transform. The audio data aretransformed into another code using the same method asthat for the music. Information on the difference
between these two codes is sent from one user to theother. The user who receives the information can largely
reconstruct the original recording using an inverse
discrete wavelet transform with the code obtained fromthe music, the information on the difference between
these two codes, and values of zero for all wavelet
coefficients. The voice produced by the proposed
method was audible.
References
1. Y. Yoshitomi, T. Asada, Y. Kinugawa, and M. Tabuse,
An authentication method for digital audio using a
discrete wavelet transform, J. Inf. Sec. 2(2) (2011) 59-68.
2. D. Inoue and Y. Yoshitomi, Watermarking using wavelet
transform and genetic algorithm for realizing hightolerance to image compression, J. IIEEJ, 38(2) (2009)
136-144.
3. M. Shino, Y. Choi, and K. Aizawa, Wavelet domain
digital watermarking based on threshold-variable
decision, Technical Report of IEICE, DSP2000-86,100(325) (2000) 29-34. (in Japanese)
4. S. Murata, Y. Yoshitomi, and H. Ishii, Audio
watermarking using wavelet transform and genetic
algorithm for realizing high tolerance to MP3compression, J. Inf. Sec. 2(3) (2011) 99-112.
5. M. Goto, H. Hashiguchi, T. Nishimura and R. Oka, RWC
music database: database of copyright-cleared musicalpieces and instrument sounds for research purposes,Trans. IPSJ, 45(3) (2004) 728-738.

Published by Atlantis PressCopyright: the authors
196