Improved Extended Polynomial-based Secret Image Sharing Scheme using QR
Code
Zhengxin Fu, Sijia Liu*, Kun Xia, Bin Yu
Zhengzhou Information Science and Technology Institute
Zhengzhou, China
1559776364@qq.com
Abstract—Secret image sharing technology is an effective ap-
proach to encode the secret image into several shares, and the
original image can be recovered by the remaining shares even
some shares are lost. As a typical two-dimensional machine
readable code, QR code is widely used in human life due to its
fast reading speed, high data density and strong error correc-
tion capability. Combined with the characteristics of QR code
secret image sharing, an extended secret image sharing
scheme was proposed based on QR code, where “extended”
means that the generated shares were visually similar to the
QR code. The main idea is to control the parameters’ selection
of polynomial using the binary QR codes. Meanwhile, the av-
erage gray difference of the shares was defined as α to measure
the similarity between QR-like shares and the original carrier
QR codes. Based on α, a secret sharing algorithm was designed
to generate QR
like shares. At last, upper and lower limits of α
are introduced through experimental analysis, and the rela-
tionship between the error correction level of carrier QR code
and the lower limit of α.
Keywords- secret image sharing; QR code; average gray differ-
ence;
I. INTRODUCTION
With the rapid development of the Internet and multimedia
technologies, the value on digital image security processing
technology are not only theoretical in research, but also prac-
tical in application. As a typical digital image that can be
read by a two-dimensional machine, the QR code is widely
used in all aspects
of life because of its fast reading speed,
high data density and strong error correction capability. In
addition, QR code is used as a connection medium for online
and offline information transmission, which provides a non-
contact information transmission channel, covering almost
all aspects of augmented reality from the huge O2O market
in China to the frontier. Therefore, the QR code can be used
as an effective carrier for transmitting secret information via
the public channel.
In some cases, it is necessary for a group of participants to
share a certain set of secret data. Shamir
[1]
proposed the con-
cept of (k, n)-threshold secret sharing to solve this problem
firstly. It studied how to decompose a secret into n shares,
where any k or more of the shares could be collected to re-
cover the secret, but any k-1 or fewer of them would gain no
information about the secret. If the secret is an image, there
will be many methods to realize the secret image sharing
scheme (SISS) such as polynomial-based SISS
[2]
and visual
cryptography
[3-7]
. However, the generated shares of above
schemes are all noise-like, which may be suspicious to in-
vaders. Since the QR code has a similar appearance as a
black and white dot matrix, some scholars have tried to com-
bine the QR code with SISS.
In particular, visual cryptography scheme (VCS) is used to
combine with a QR code to
produce a readable two-level QR
code where the public information can be gained by decod-
ing the QR code and the secret information can be obtained
by the corresponding decryption algorithm. The design of the
two-level QR code greatly reduced the probability of being
suspected by the potential attacker during the transmission of
secret information. Weir and Yan
[8]
achieved authentica
by embedding QR codes in shares. In order to reduce the risk
of secret information disclosure, Wang et.al
[9]
proposed a
security scheme aiming at finding the ideal embedded region
for QR code embedding. In addition, Wan
[10]
combined with
QR code technology to design a (k, n)-VCS scheme where
the secret image was
a general natural image that can be re-
covered by a certain number of shares and can be directly
recognized by the human visual system. However, due to the
limitation of the QR code error correction capability, the
readability of the QR code and the amount of embedded se-
cret information were mutually restricted. In addition, the
recovered secret information was distorted.
Compared with VCS, the polynomial-
sharing scheme (PSISS) can achieve accurate recovery of
digital image sharing
[11]
. If the QR code is processed as a
grayscale digital image, a larger capacity of secret infor-
mation embedding and lossless recovery can be realized by
PSISS. In order to ensure the readability of the QR code, the
QR code must be changed at the pixel level with an appro-
priate range to ensure that each pixel is regarded as a gray
scale consistent with the original pixel.
Two-in-one SISS (TiOSISS)
[12
13]
is a method where the
secret images can be directly obtained through human vision
and accurately recovered by complex calculation. It implicit-
ly embeds the shadow image generated by the PSISS into the
shares generated by the VCS to realize the decoding of two
different options. Most of the current researches improved
the visual quality of the extended shares based on steganog-
raphy
’s natural drawbacks were obvious such as
small-capacity for secret embedding and complex extraction
operations. Therefore, Liu et.al
[14]
proposed a new extend
polynomial-based SISS (EPSISS) to solve the problem. In
Ref[14], the QR code was used as the carrier image, and only
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2018 14th International Conference on Computational Intelligence and Security (CIS)
978-1-7281-0169-9/18/$31.00 ©2018 IEEE
DOI 10.1109/CIS2018.2018.00058