-The steganography point is in that, the fact of confidential data existence in some container was a secret for the third parties. Methods of the digital steganography allow to hide an information in different digital objects: images, audio-and video files. In particular, information hiding in digital images can be used successfully for its subsequent imperceptible storage and transmission, for example, exchange of images in the Internet is a commonplace and will not draw attention. However changes made to data items of digital images in case of steganographic embedding can cause essential distortions of the received stegoimage, and attachments can be found. Therefore the approach allowing to reduce quantity of the changes made to data items of digital images when embedding is offered. This approach is directed on increase in efficiency of steganographic embedding of information into a phase spectrum of the discrete Fourier transformation (DFT) of digital images. Feature of the offered approach is minimization of quantity of changes made to frequency coefficients. The approach is applied for improvement of earlier developed (by authors of this paper) algorithm of faultless information embedding into a phase spectrum of the DFT of digital images. Computing experiments' results confirm that the offered approach allows to increase embedding quality and capacity of the image container at the same time.
The problem of information security in the century of the active information technology development is relevant and requires special attention. The most widespread decision of the task of data confidentiality support is application of cryptographyc conversion when information becomes unreadable for a person who has no secret key. However
INFORMATION EMBEDDING INTO THE PHASE SPECTRUM
OF THE DFT
There are many steganographic algorithms based on the DFT. The majority of such algorithms is intended for embedding of digital watermarks (DW). As a rule, amplitude values of the frequency coefficients are changed during embedding. For example, in [9] authors use the pseudorandomly generated key on the basis of which DW is created. During embedding process those elements of amplitude Fourier spectrum of the digital image to which correspond the DW elements with values 1, are recalculated by an averaging path on the vicinity 3×3 with multiplying by intensification coefficient.
In [
There are also algorithms directed to concealment of large
capacity of the arbitrariest information in the DFT coefficients.
For example, the method described in [
However authors of similar works avoid a problem of
mistakes appearance when extraction of the embedded
message. Reason of this problem appearance is transition from
imaginaries to integer values for receiving a pixels matrix. The
solution of the described problem is provided by authors of this
paper in [
The offered approach to minimization of changes quantity
was developed for improvement of the algorithm [
0 , if 0 , 0 1 ,1 and bi 0, ' 1, if 0 , 0 1 ,1 and bi 1, (1) , otherwise, where – original phase value from embedding area; ' – changed phase value; 0 , 1 , – algorithm parameters; bi – secret message’s bit.
The feature of this algorithm is faultless extraction of information through an iterated procedure of embedding. After embedding of a message part into the image block, a check whether it is possible to extract all embedded bits without mistakes is made. If there are mistakes, they are corrected by path of repeated embedding of a message fragment into the changed block of coefficients. If faultless extraction does not manage to be reached for the given iterations number, then the block is processed so that any of its elements could not be interpreted as the containing embedded bit. This algorithm allows to avoid distortion of the embedded message and to extract it in an initial view.
III.
THE PROPOSED METHOD
Among variety of the works devoted to steganographic
embedding of information into frequency coefficients there are
many articles devoted to increase in embedding efficiency by
means of choice of such coefficients, change of which will lead
to smaller distortions on a stego-image. But in the majority of
such works, for example, in [
Any block of frequency coefficients can be interpreted as
containing some bit sequence. When embedding into the DFT
coefficients by means of the algorithm [
Let there is some block of phase values of the DFT coefficients and a confidential message’s fragment representing a line of bits M m1, m2 , , mk . We will extract the sequence which is initially contained in the block of phase values. If the phase value gets to an interval 0 ;0 , is extracted 0, if the phase value gets to an interval 1 ;1 , 1 is extracted. The phase values which haven't got in one of embedding intervals, are coded by value –1. The received sequence is F . Standing in a row i values, equal –1, where i 1, k , will be called "an empty interval".
We will compare the sequences M and F . The quantity of comparison options of these sequences is expressed by the formula v1 h1 1 h2 1 hn 1 , where hi – elements quantity in i -th empty interval; n – quantity of empty intervals.
Among all possible options of comparison are chosen such which allow to embed the greatest quantity of bits with the smallest number of changes.
Further it is necessary to define how those confidential bits, which haven't coincided during comparison of the sequences M and F have to be placed. Quantity of various options of remained bits' placement, further - embedding variants, is calculated by the formula v2
h1! h2! b1!h1 b1 ! b2!h2 b2 !
hn! bn!hn bn ! where bi – the quantity of bits which have to be placed in i -th empty interval, bi hi
The formed sequence X by means of an arrangement of missing values 0 and 1 in empty intervals is an embedding variant. The formula of embedding becomes , ' 0 , 1, r, if fi xi , if fi xi and xi 0, if fi xi and xi 1, if fi xi and xi 1, where r – random phase value which isn't getting to embedding intervals.
Examples of the embedding variants X , possessing various characteristics, are shown in the fig. 1. In this case it is required to embed the bit sequence 0111011110001011000100 into the block of phase values. The sequence which is initially contained in the block is marked as F . Phase values which need to be changed when embedding are marked by gray color.
F -1 -1 1 0 0 -1 -1 1 -1 1 -1 0 -1 0 -1 1 -1 1 1 0 -1 0 X -1 -1 0 1 1 -1 -1 1 -1 0 -1 1 -1 1 -1 1 -1 1 0 0 -1 0
F -1 -1 1 0 0 -1 -1 1 -1 1 -1 0 -1 0 -1 1 -1 1 1 0 -1 0
The first variant shows how embedding without application of the offered approach would be made. In this case in the block it is possible to hide 12 bits, having changed 7 phase values. The second variant allows to increase significantly capacity by use of the phase values of the block, which aren't getting to embedding intervals, for embedding. Now it is possible to embed 19 bits, having changed 9 phase values. The third variant shows an opportunity to reduce quantity of the made changes, differently comparing two sequences. At the remained capacity in 19 bits it is required to make only 8 changes during embedding of the confidential message's fragment.
Thus, such greatest number of bits can be embed into each block which will allow to make the minimum quantity of changes of phase values and to avoid essential distortions of a stego-image’s block. (4)
To be convinced in efficiency of the offered approach, there was conducted a number of experiments. 20 standard test grayscale images (Lena, Baboon, Peppers, etc.), which size is 512×512 pixels, from the image base1 were used for embedding.
For visual assessment of embedding quality in the fig. 2 the image Lena and the corresponding stego-image are submitted. The incresed fragments of the image are presented in the fig. 3. It is obvious that distortion of the stego-container as a result of embedding are noticeable by eye only at repeated increase in the image.
The experimental results allowing to estimate influence of the offered approach on embedding quality are presented further.
Embedding was carried out by means of the algorithm [
The first experiment consisted in a comparison of the PSNR value received after application of both algorithms for concealment of identical amount of information.
Average schedules of PSNR's dependence on capacity are shown in the fig. 3. It is possible to see an improvement of the PSNR on 1–2 dB in all cases. 1 SIPI Image Database. http://sipi.usc.edu/database 42 B ,d40 R SN38 P 36 34 32 30 55000 50000 45000 40000 s35000 t i b ,y30000 t i s a25000 p a C20000 15000 10000 5000 4096 8192 12288 16384 20480 24576 28672 32768 36864 40960
Capasity, bits
Further the comparison of the greatest possible capacities of image-containers and PSNR values corresponding to them was made. In the fig. 4 the histogram reflecting the maximum capacity which was received for each of test images is shown.
The corresponding PSNR values are shown in the fig. 5. Original algorithm
Improved algorithm 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Image number 38 37 B36 d ,R35 N PS 34 33
The given experimental results show that the new algorithm, in which the offered approach to minimization of quantity of changes of frequency coefficients when information embedding was realized, differs in bigger efficiency in comparison with earlier developed algorithm. Both algorithms provide faultlessness extraction of embedded information. However application of the approach offered here allows to increase the PSNR value and the capacity at the same time.
The approach to minimization of quantity of the changes made to frequency coefficients when message embedding into the DFT phase spectrum was offered. This approach allowed to improve the embedding quality and to increase the capacity at the same time. The reliability of the received conclusions is confirmed by experimental results. The offered approach can be applied in developing of new algorithms of information concealment in a frequency domain of digital images, and not only in the DFT, but also in other frequency transformations.