=Paper=
{{Paper
|id=Vol-2732/20200214
|storemode=property
|title=New Technique for Hiding Data Using Adaptively Generated
Pseudorandom Sequences
|pdfUrl=https://ceur-ws.org/Vol-2732/20200214.pdf
|volume=Vol-2732
|authors=Alexandr Kuznetsov,Alexey Smirnov,Diana Kovalchuk,Tetiana Kuznetsova
|dblpUrl=https://dblp.org/rec/conf/icteri/KuznetsovSKK20
}}
==New Technique for Hiding Data Using Adaptively Generated
Pseudorandom Sequences==
https://ceur-ws.org/Vol-2732/20200214.pdf
New Technique for Hiding Data Using Adaptively
Generated Pseudorandom Sequences
Alexandr Kuznetsov 1 [0000-0003-2331-6326], Oleksii Smirnov 2[0000-0001-9543-874X],
Diana Kovalchuk 1[0000-0002-4499-3732] and Tetiana Kuznetsova 1[0000-0002-5605-9293]
1
V. N. Karazin Kharkiv National University, Svobody sq., 4, Kharkiv, 61022, Ukraine
kuznetsov@karazin.ua, dianakovalhyk@ukr.net
2
Central Ukrainian National Technical University, avenue University, 8, Kropivnitskiy, 25006,
Ukraine, dr.smirnovoa@gmail.com
Abstract. This article explores the steganographic techniques of hiding in-
formation using direct spectrum expansion technology. Using noise-like pseu-
dorandom sequences (discrete signals), it is possible to reliably hide in-
formation messages in redundant digital data (cover files), for example, im-
ages, video and audio files, etc. However, the correlation of discrete signals and
cover files can be a problem; the extracted information messages can cover a lot
of the number of errors. Our experiments (on still images) show that the error
rate in the reconstructed information messages is very high. We offer a new
technique when the statistical properties of covers are taken into account when
generating discrete signals. In this case, it is possible to significantly reduce the
error rate without introducing additional distortion in-to the cover.
Keywords: pseudorandom sequence, hidden information, direct spectrum
spread technology, steganography
1 Introduction
Direct spread spectrum technology has traditionally been used in code division multi-
ple access radio communication systems (CDMA). These techniques are used for a
variety of reasons, including the establishment of secure communications, increasing
resistance to natural interference, noise, and jamming, to prevent detection, to limit
power flux density (e.g., in satellite down links), and to enable multiple-access com-
munications [1-3].
The technology of direct spectrum expansion uses discrete noise-like sequences
(discrete signals) to expand a usually narrowband information signal over a relatively
wideband (radio) frequency range. The receiver correlates received signals to extract
the original information signal.
Thus, the basic principle of direct spectrum spreading is the use of noise-like carri-
ers and the bandwidth is much wider than that required for simple point-to-point
communication with the same data rate. This allows you to get significant advantages
in the organization of communication, for example [1-3]:
Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
Resistance to jamming (interference). High resistance to narrowband interference
is provided;
Resistance to eavesdropping. The selection of a particular pseudo-random se-
quence can be saved as a secret key. In this case, it is very difficult to find the right
key and eavesdrop on the negotiations. In addition, when using very long pseu-
dorandom sequences, it is possible to arrange communication at very low signal to
noise ratios, which does not even allow the secret transmission of information to be
detected;
Resistance to fading. The expansion of the frequency band leads to an increase in
the quality of communication, even in conditions of fading (attenuation) of the sig-
nal;
Multiple access capability. A large number of sequences allows to increase the
subscriber capacity of the communication system, i.e. after all, makes communica-
tion much cheaper.
Direct spectrum spreading technology can also be used for steganographic purpos-
es, i.e. to hide information messages in redundant digital data (cover files), for exam-
ple, in images, video and audio files, etc. Moreover, cover files are interpreted as
noise in communication channels, and the number of different discrete signals deter-
mines the channel capacity of the steganosystem (similar to multiple access to
CDMA).
This article explores the steganographic techniques of hiding information using di-
rect spectrum expansion technology. We offer a new technique when the statistical
properties of cover files are taken into account when generating discrete signals. This
allows you to significantly improve individual performance indicators of the ste-
ganosystem. In particular, we manage to significantly reduce the bit error rate in the
extracted informational messages.
2 Literature review
In the first works [4-7] on steganographic systems based on direct spectrum expan-
sion, the fundamental possibility of hiding data in various cover files was shown, the
main advantages of using pseudorandom sequences, as well as some dependences of
the error rate in the restored messages and cover file distortions are shown. Subse-
quently, many techniques were finalized and improved. In particular, in [8], combined
methods combining error correction, random positioning in pixels of a cover image,
and direct-sequence spread spectrum (DSSS) spectrum expansion were investigated.
In [9], concealment is implemented in the frequency domain, i.e. spreading modula-
tion was applied to discrete cosine transform (DCT) coefficients. In [10], the imple-
mentation of the steganosystem was supplemented by several levels of security, in-
cluding cryptographic transformations. In [11], aspects of the practical implementa-
tion of steganosystems when hiding information in audio files by the method of direct
spectrum expansion are considered. In [12], steganoanalysis methods using video files
and direct spectral expansion methods were studied. The work [13] is devoted to the
use of steganographic security techniques for transmitting medical images and elec-
tronic medical records in teleradiology. Article [14] is devoted to a theoretical panaly-
sis of the safety of steganosystems based on direct sequence spreading of the spec-
trum.
Thus, methods of direct expansion of the spectrum are used to conceal data in vari-
ous multimedia files (images, video, audio, etc.). Moreover, transformations can be
used both in the spatial domain [4-7] and in the field of orthogonal transformations,
for example, in DCT [9]. At the same time, the main problem of using DSSS in ste-
ganography is the high level of errors in the restored messages.
3 Purpose and objectives of the article
The main goal of this work is to introduce a new technique for hiding informational
messages in cover files using direct spectrum expansion and adaptively generated
pseudorandom sequences. We propose a new approach consisting in the formation of
noise-like sequences taking into account the statistical properties of cover files. The
task is to ensure that each sequence does not correlate with the cover file used. This
can significantly reduce the bit error rate in the extracted informational messages. Our
experiments clearly confirm this.
The article is organized as follows. First, we briefly present the known information
on the use of direct spectrum spreading technology in steganography (we use basic
information from several articles and US patents), and also show that the practical
failure to fulfill certain theoretical assumptions will lead to the guaranteed occurrence
of errors in the restored information data. Our experiments on still images clearly
demonstrate this, and the error rate remains very high even with amplification of the
spreading signal and with a small number of hidden data. We also show examples of
specific images of covers, as well as an assessment of their distortions at various pa-
rameters of the steganosystem. Finally, we propose a new technique for hiding infor-
mation, which is based on the obligatory fulfillment of the theoretical assumption
about the uncorrelatedness of extension sequences and cover files. The experiments
presented in the article show that in practical implementation it is really possible to
significantly reduce the bit error rate. Preliminary results were abridged at the confer-
ence [15].
4 Hiding data in images using direct spread spectrum
technology
As a prototype of an improved method of hiding data in cover images, the technique
proposed in the dissertation by L. Marvel was selected, described in detail and studied
in [6, 7, 16, 17]. Let's consider it in more detail.
The method of concealing data using the direct spread spectrum, proposed in US
patent [17], based on the fact that (on the transmission side after encryption and noise
immunity coding) separate blocks mi mi0 , mi1 ,..., mik 1 , i 0,..., N 1 of data of
information message m m0 , m1 ,..., mN 1 the blocks are modulated by noise-like
discrete signals with the help of appropriate devices
i i0 ,i1 ,..., in1 ,
i 0 , 1 ,..., M 1 , k M , with a base B TF , where T is the duration
of the signal element i j , F is the frequency band of the signal i . Since
1
F n we have B n 1 and the signal base sets the frequency spread of the
T
frequency band of signal i with respect to elementary signals i j and / or mi j . As a
result, a modulated information signal block is generated for each mi information
block
k 1
Ei m* ,
j 0
ij j (1)
where
1, mi j 1;
m *i j
1, mi j 0;
which, according to statistical properties, takes the form of a random (noise-like)
sequence
k 1 k 1 k 1
Ei
j 0
m *i j j0 , m *i j j1 ,..., m *i j jn1 ,
j 0 j 0
and due to the large base of discrete signals, the frequency spectrum is spreaded by
B n times.
The resulting modulated message Ei is supplied to an alternationing device on
which the elements of Ei are mixed with the corresponding rule f by means of a
secret key K1 . The obtained data Ei f ( Ei , K1 ) з using the appropriate device is
added to the data of the image Ci (digital image data in the spatial domain)
according to the rule: Si Ci Ei G , where G 0 is the gain of the expansion
signal, which sets the "power" of the hidden blocks of information messages.
The obtained data Si is supplied to the quantization device, which performs a
certain transformation to store the primary dynamic range of the cover image,
resulting in the formation of separate blocks of the steganogram S i and the cover
S S0 S1 ... S N 1 , which is transmitted to the receiving side.
On the receiving side, the resulting steganogram blocks S i after filtration, are,
supplied to a reverse interleaving device, on which the elements of the filtered blocks
of the stegogram Si are mixed by rule f 1 , which is an inverse rule of alternation f
on the transmitting side. The extraction of blocks of information data is carried out
using a correlation receiver, which calculates the value of the correlation coefficient
obtained after the reverse alternation of data S *i f 1 (Si , K1 ) and corresponding
discrete j , signals identical to those used on the transmitting side:
n 1
S *i , j
1
S *iz jz . (2)
n z 0
Since Si Ci Ei G we have:
n 1 n 1 n 1
1 1 1
S *iz jz G Eiz jz Ci j
n z 0 n z 0 n z 0 z z
Suppose that the data block of the image block Ci has a random statistical
structure, that is, suppose that the second term on the right side of expression (2) is
close to zero and can be ignored. Then we have:
k 1
S *i , j G m * , .iu u j (3)
u 0
Since all sequences of the set are formed by a pseudorandom sequence
generator initiated by a secret key K 2 , the corresponding discrete signals are weakly
correlated, that is, at u j we have u , j 0 .
According to this, all terms, except case u j , in the right-hand side of equation
(3) can be ignored. Where do we have:
n 1
G;
S *i , j G m *i j
1 2
j G m *i j (4)
n z 0 z G.
The corresponding value of the seized data is taken with a threshold device
according to the calculated correlation coefficient.
Since G 0 and n 0 of S *i , j character in (4) depends only on m *i ,
j
from where we have:
1, Si , j 0;
m *i j sign S *i , j
(5)
1, Si , j 0.
If S *i , j 0 in (5) we will assume that the hidden information has been lost
(erased). Separate blocks of data are formed from the extracted data on the receiving
side
mi mi0 , mi1 ,..., mik 1 , i 0,..., N 1 of information messages
1, m *i j 1;
m m0 , m1 ,..., mN 1 , where mi j of which information messages
0, m *i j 1;
are generated after noise immunity decoding and decryption of the extracted data.
The secret key K 2 sets the rule for the formation of pseudorandom sequences
i i0 ,i1 ,..., in1 , which are formed by the corresponding generator and are used
as noise-like discrete signals i 0 , 1 ,..., M 1 from the ensemble (set)
of power M .
The encryption and decryption rule on the transmitting and receiving side is
initiated by the secret key K 3 .
The use of encryption and alternation devices in the process of hiding and
retrieving data can improve the statistical properties of the modulated message Ei , ie
to bring it closer to a random sequence. The use of noise immunity coding devices
can improve the reliability of the transmission of information messages
m m0 , m1 ,..., mN 1 during steganographic conversions.
5 Experimental researches
The disadvantage of the prototype under consideration is that in the process of ste-
ganographic hiding, the statistical properties of the blocks of the image Ci , are not
taken into account, that is, the digital image data can be correlated with the applied
discrete signals, which will lead to an error when extracting information data on the
receiving side.
So, for example, if the correlation coefficient of the i -th block Ci of the image
will be higher behind the module and opposite in value of sign G m *i j , that is, when
the second summand in the right part of expression (2) will be higher in module and
opposite in value of sign of the first summand (and the condition of mutual
orthogonality of applied discrete signals will be fulfilled), it is guaranteed that an
error will the result at data extract according to rule (5). In practice, as our researches
have shown, such cases occur very often. This is due to the fact that the digital data of
real images used to hide information messages do not have a random statistical
structure, that is, the applied assumption in the transition from formula (2) to formula
(3) is not fulfilled in practice and is false. Typically, steganographic hiding uses
realistic images and the corresponding digital data is not a random process, and even
in its statistical properties are not similar to pseudorandom sequences. The
n 1
corresponding values of the correlation coefficient Сi , j 1
Ci j 0 , and
n z 0 z z
can take large amplitude ( Сi , j 1 ) and random values. In this case, it is
possible to increase the reliability of the extracted data only by applying low-speed
noise immunity codes (as in the prototype discussed above [6, 7, 16, 17]), which
leads to a decrease in the relative transmission rate of information, or an increase in
the gain G , which leads to an increase in the introduced errors.
To confirm this fact, Fig. 1 shows the empirical estimates of BER dependence in
message recovery using the considered prototype method (interrupted line). The
G 4 gain was applied, and the number of bits k , hidden in one block Ci of the
cover image varied from 1 to 255. Fig. 2. shows empirical estimations of dependence
of the average proportion of introduced errors (in relation to the dynamic range of 256
levels) in the cover image with respect to the number of bits embedded in one element
of the cover. From the given dependencies (Fig. 1, 2, interrupted line) it is visible, that
at entering errors in the cover image below a visual threshold of human sensitivity (2-
3%) it is possible to hide no more than 10 bits of data in one block of the image Ci .
But even with such an insignificant amount of hidden data, BER takes the value
0.05..0.25, which requires the use of low-speed noise immunity codes with the
permission to correct multiple errors.
Fig. 1. Bit error rate in recovered messages depending on message size
Fig. 2. The proportion of distortion introduced into the cover image depending on the size of
the message
In Fig. 3, 4 show, accordingly, the obtained empirical estimates of the BER
dependence when restoring the messages and the dependence of the average fraction
of the input errors on the G gain values using the considered prototype method
(intermittent lines). At the same time, k 4 bits of information data were embedded
in one block Ci of the cover, and the gain G changed from 1 to 8. From the given
dependencies (Fig. 3, 4, interrupted line) it is visible, that at value of gain G 6
hiding of the information data leads to entering of errors, part of which ( relative to a
dynamic range ) is above a visual threshold of human sensitivity (2-3 %). That is, the
fact of hiding data in the image turns out to be a visual observation and
steganographic hiding with these parameters is not reasonable But at G 6 gain
value, there is a large number of errors when extracting individual data bits from the
spatial area of the image corresponding to BER 0,2 .
Fig. 3. Rate of bit errors in recovered messages depending on the gain factor
Fig. 4. The proportion of introduced distortion in the cover image depending on the gain factor
In Fig. 5-7 shows examples of images used in research:
Fig. 5 – original image;
Fig. 6 – image with hidden messages using prototype method;
Fig. 7 – image with hidden messages using the proposed method.
Data hiding is done with the following parameters: G 4 , k 4 .
Fig. 5. Original image
Fig. 6. Example of cover image (using prototype method)
Fig. 7. Example of cover image (using the proposed method)
6 Proposed data hiding technique
Our task is based on the following: by taking into account the statistical properties of
cover Ci , significantly reduce the BER of hidden data. Indeed, the introduction of
additional constraints on the correlation coefficient of the discrete signals used and
individual fragments of the image can significantly reduce the number of errors when
recovering the message on the receiving side.
This problem is solved due to the special (we call adaptive) formation of
pseudorandom sequences j j0 , j1 ,..., jn1 , taking into account the statistical
properties of these blocks of cover Сi . That is, the value of the correlation coefficient
Сi , j for all i 0,.., N 1 and for all j 0,.., M 1 by the module should not
exceed some predetermined value max (value of the set threshold):
n 1
Сi , j
1
Ci j max . (6)
n z 0 z z
Thus, the formation of j 0 , 1 ,..., M 1 sequences is performed by a
pseudo-random rule, which is initiated by the secret key K 2 , and taking into account
conditions (6) for all i 0,.., N 1 and all j 0,.., M 1 .
In this formation of discrete signals, each sequence of the set of
0 , 1 ,..., M 1 will not be correlated (up to the set limit) with any block of
the cover image, and, accordingly, the correlation coefficient of the i -th block Ci of
the cover on the module will never be higher than the module and the opposite in sign
max . In accordance with this (and when the conditions of mutual orthogonality of
the applied discrete signals) the second term in the right part of expression (2) may
exceed in module and be opposite in sign to the first term only when
G m *i j max . It is in this case that an error of data extraction will happen, but the
probability of such an event will be much less than in case of an error of data
extraction in the prototype method. If the value of the max threshold is lower than
the G gain value, i.e. when the unequal is performed G m *i j max the error will
not occur at all, i.e. an unmistakable transfer of secret information will be achieved.
In Figs. 1-6, solid lines show empirical estimates of the probability properties of
steganographic concealment using the proposed method, which confirms our
conclusion:
in Fig. 1 shows the bit error rate in the recovered messages depending on the size
of the message;
in Fig. 2 shows the proportion of distortion introduced into the cover image
depending on the size of the message;
in Fig. 3 shows bit error rate in the recovered messages depending on the gain fac-
tor;
in Fig. 4 shows the proportion of distortion introduced into the cover image
depending on the gain factor.
7 Discussion of the results
From the above dependencies in Fig. 1, 2 (solid line) shows that when making errors
in the cover image lower than the visual threshold of human sensitivity (2-3%)
manages to embed no more than 10 bits of data in one block of the C coniner (as in
the prototype method). But with so a number of hidden data, the BER value is much
less than 0.1 and several dozen times less than in the prototype method.
From the given dependencies in the fig. 3, 4 (solid line) can be seen that at the
value of gain hiding information data in the cover image leads to the introduction of
errors whose fate (in relation to the dynamic range) is higher than the visual threshold
of human sensitivity (2-3%) as well as in the method prototype. At G 6 values, the
errors introduced into the cover image are lower than the human visual sensitivity
threshold, i.e. they are invisible. In compared with the method-prototype, there is a
significant reduction in the number of errors when extracting individual data bits from
the spatial area of the image. In addition, at the H gain value, there is a total non
occurrence of errors in remote data, which confirms the above conclusion about the
error-free transmission of hidden information. Indeed, if G 4 then the inequality is
being realized G m *i j max , that is, assuming the validity of the mutual
orthogonality of the applied discrete error signals, no errors occur at all and an error-
free transmission of hidden information is achieved.
From the given dependencies in the fig. 5, 6 (solid line) shows that in almost all
cases, when hiding data the proposed method is a gain in relation to the method-
prototype (interrupted line). Thus, when the number of k bits hidden in one element
of the cover image increases, as well as in the prototype method, there is an increase
in the probability of false data extracted on the receiving side. However, this increase
is much slower than in the prototype method. As the G gain increases, the probability
of false data extraction decreases, but the proposed method (solid line) has
significantly improved probabilistic properties than the prototype method (interrupted
line).
8 Conclusions
Spread spectrum technologies are traditionally used in multiple access radio commu-
nication systems. Direct-sequence modulation makes the transmitted signal wider in
bandwidth than the information signal. The resulting transmitted signal resembles
white noise limited in bandwidth. This noiselike signal is used to accurately restore
the source data on the host side by multiplying it by the same expansion sequence.
This process is mathematically a correlation, i.e. on the receiving side the recovery of
information data is performed by calculating the correlation coefficient of the accept-
ed sequence and the spreading sequence.
Application of the technology of direct spread-spectrum in radio communication
systems allows obtaining specific advantages: resistance to jamming (interference);
resistance to eavesdropping; resistance to fading; multiple access capabilities. Some
radiocommunication industry standards take advantage of these advantages. However,
this technology can also be successfully applied in steganography. Excess data (imag-
es, audio and video files, text documents, etc.) are interpreted as noise in a communi-
cation channel. The task is to hide information data in such a way that redundant data
(cover files) are not distorted, i.e., photo or video images are visually indistinguisha-
ble from the original data. The technology of direct spread-spectrum is suitable for
this very well.
The main theoretical assumption that explains the operation of this technology is
the uncorrelation of the spreading sequence and noise in the communication channel.
In radio communications systems with white noise, this assumption is fulfilled and
there are few errors on the receiving side. In steganographic systems, however, this
assumption may not work. Noise is understood here to be excess digital data, for ex-
ample, it can be realistic images. And such cover files can strongly correlate with the
spreading sequence. As a result of the correlation reception, a large number of errors
occur when restoring information messages. We offer an effective way to reduce such
errors. In fact, we offer a new way to form spreading sequences that takes into ac-
count the statistical properties of cover files. We call this method adaptive. As a re-
sult, we have a set of spreading sequences that do not correlate with cover files and
almost no errors occur when restoring information messages. Experiments show that
this is indeed the case. Our approach is much more efficient. Thus, a specific tech-
nical result is achieved, namely: by taking into account the statistical properties of the
digital data of the cover images (in the adaptive formation of pseudorandom sequenc-
es) it is possible to significantly reduce the number of errors in the recovery of infor-
mation data on the receiving side.
A promising trend is to study the properties of steganosystems using complex dis-
crete signals with special correlation properties. For example, we want to use se-
quences from our previous work [18-19] to hide information in cover images.
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