Cryptography Reference
In-Depth Information
with BPCS steganography (see the top box of the right part in Fig. 8.12). The
quantized wavelet coe
cients modified by embedding are then subjected to
JPEG2000 encoding again, which produces secret-data-embedded JPEG2000
bit-stream. Data embedding into an already compressed JPEG2000 file is also
possible. In this case, the process starts with a JPEG2000 compressed image,
i.e., a bit-stream from the bottom of the middle part in Fig. 8.12 and follows
the same process as the aforementioned one.
The data extraction procedure follows the dashed arrows in the middle
part of Fig. 8.12. JPEG2000 decoding of the secret-data-embedded bit-stream
starts from bit-stream unorganization and is halted right after ROI descaling.
At this point, extraction of secret data is carried out by the BPCS method
using the bit-planes of quantized wavelet coe
cients. We assume that the data
extraction starts after the entire file of the bit-stream has been received.
8.5.3 Experimental Results
The JPEG2000-BPCS steganography was implemented using JJ2000 Java
software of JPEG2000 compression [17], with which the program module for
BPCS steganography was integrated. It was tested on several standard images
including Lena, Barbara and Mandrill, Lena and Barbara are 8bpp
gray images and Mandrill 24bpp true color image, all of which were 512512
pixels in size. Here 44 patch size was used as an embedding unit and random
binary data was used as secret data.
In the implementation of JPEG2000-BPCS steganography, an error correc-
tion scheme was devised to decrease the distortion of a data-embedded image.
As data is being embedded into the wavelet coe
cients, each bit that is used
for embedding is recorded. After all the data has been embedded, the bits of
each coe
cient that have not been used are changed to bring the new value
of the coe
cient as close to the original value as possible. The change of bits
is only allowed unless the change makes the complexity value for the relevant
patch larger than the complexity threshold for embedding. The PSNR with
the error correction increased by about 1.7 dB. In the following experiments,
the error correction was always applied.
Results of embedding experiments are shown in Fig. 8.13. The least signifi-
cant bit-plane and the two least significant bit-planes were used to embed data
for 0.5bpp and 1.0bpp compressed image, respectively. 9 data points within
each line in Fig. 8.13 were obtained by changing the complexity threshold
α
0
3
from 2 to 10. In Fig. 8.13 data points for no data embedding are also
included. Note that the compression rate for color Mandrill image is in fact
three times less than those for the other gray images.
Generally, the JPEG2000-BPCS steganography was able to achieve embed-
ding rates of around 9% of the final compressed image size for pre-embedding
3
The complexity is hereinafter measured by k in Eq. (8.1), i.e., the total length
of the black-and-white border without normalization by the maximum possible
border length.
