GEMD与RGEMD的渐进(k,n)有意义阴影图像的秘密共享方案
124 浏览量
更新于2024-08-26
收藏 2.05MB PDF 举报
本文主要探讨了一种结合渐进式(k,n)秘密图像共享（Progressive Secret Image Sharing, PSIS）与有意义阴影图像（Meaningful Shadow Images）的创新方法，即使用GEMD (Generalized Entropy Maximizing Diffusion) 和 RGEMD (Regularized Generalized Entropy Maximizing Diffusion) 技术。该研究由西安科技大学计算机科学与工程学院的Yan-Xiao Liua等人进行，并与台湾东华大学计算机科学与工程系的Ching-Nung Yang、Yung-Shun Chu以及Song-Yu Wu和Qin-Dong Sun合作。
在传统的(k,n) PSIS中，秘密图像被分解成多个阴影部分，其中少于k个阴影包含关于图像的任何信息，而k到n个阴影可以逐步恢复原图像。然而，大多数此类方案中的阴影通常呈现出噪声般的特性，这可能引起攻击者的怀疑。为了提高安全性并降低被察觉的可能性，研究者提出将秘密图像分享融入到有意义的阴影图像中，使得阴影部分看起来更自然，从而降低攻击者的警惕性。
GEMD和RGEMD算法在此场景下发挥了关键作用。GEMD是一种扩散技术，通过最大化信息熵来增强图像的局部特征分布，使得生成的阴影部分更加逼真。RGEMD是对GEMD的改进，它引入了正则化机制，进一步提升了阴影图像的质量和真实性。通过这种方法，秘密图像在被分解成阴影时，不仅满足了渐进恢复的要求，而且这些阴影在视觉上具有意义，不易引起攻击者的注意。
文章于2017年11月4日接收，经过修订后于2018年7月5日接受，最终于同年8月11日在线发布。关键词包括：渐进式秘密图像分享、有意义阴影图像、GEMD、RGEMD。本文的研究成果对于提升秘密图像传输的安全性和隐蔽性具有重要意义，为信息安全领域提供了新的理论支持和技术手段。
- Else if ðd ¼ 2
n
Þ; P
s
1
¼ P
1
þ 1; P
s
n
¼ P
n
þ 1; P
s
i
¼ P
i
; i ¼ 2; 3; ...;
n 1.
- Else if ð0 < d < 2
n
Þ, transform d to binary ðb
n
b
n1
...b
0
Þ
2
.
For ði ¼ n; i P 1; i Þ
{ifðb
i
¼¼ 0 and b
i1
¼¼ 1) P
s
i
¼ P
i
þ 1;
else if ðb
i
¼¼ 1 and b
i1
¼¼ 0Þ P
s
i
¼ P
i
1;
else P
s
i
¼ P
i
}
- Else d
0
¼ 2
nþ1
d, transform d
0
to binary ðb
n
b
n1
...b
0
Þ
2
Forði ¼ n; i P 1; i Þ
{if(b
i
¼¼ 0 and b
i1
¼¼ 1) P
s
i
¼ P
i
1;
else if ðb
i
¼¼ 1 and b
i1
¼¼ 0Þ P
s
i
¼ P
i
þ 1;
else P
s
i
¼ P
i
}
(4) Outputs n stego-pixels: P
s
1
; P
s
2
; ...; P
s
n
.
Extracting phase: Input n stego-pixels P
s
1
; P
s
2
; ...; P
s
n
; Output:
the n þ 1 bits secret s.
(1) The decimal secret s
ð10Þ
can be extracted by:
s
ð10Þ
¼ f
s
GEMD
¼½
P
n
i¼1
P
s
i
ð2
i
1Þðmod2
nþ1
Þ.
(2) Transform s
ð10Þ
into n þ 1 bits secret s.
Scheme 1 (GEMD) embeds a secret of n þ 1 bits into n stego-
pixels. It has higher embedding capacity than EMD. The following
Scheme 2 (RGEMD) is extended from GEMD that embed a 2n bits
secret into n stego-pixels.
Scheme 2: RGEMD
Embedding phase: Input: n cover-pixels P
1
; P
2
; ...; P
n
, a secret s
of 2n bits; Output: n stego-pixels P
s
1
; P
s
2
; ...; P
s
n
.
(1) Divide s into first n þ 1 bits secret s
ðnþ1Þ
and last n 1 bits
secret s
ðn1Þ
.
(2) Embedding s
ðnþ1Þ
into n cover-pixels using Scheme 1 , and
generates n stego-pixels P
s
1
; P
s
2
; ...; P
s
n
.
(3) s
ðn1Þ
¼ðb
n2
b
n3
...b
0
Þ
2
for(i ¼ n 2; i P 1; i )
{if(P
s
iþ2
P P
iþ2
and P
s
iþ1
6 P
iþ1
)
P
s
iþ2
¼ P
s
iþ2
1; P
s
iþ1
¼ P
s
iþ1
þ 2; P
s
1
¼ P
s
1
þ 1;
else
P
s
iþ2
¼ P
s
iþ2
þ 1; P
s
iþ1
¼ P
s
iþ1
2; P
s
1
¼ P
s
1
1;}
(4) Outputs n stego-pixels: P
s
1
; P
s
2
; ...; P
s
n
.
Extracting phase: Input n stego-pixels P
s
1
; P
s
2
; ...; P
s
n
; Output:
the 2n bits secret s.
(1) The decimal secret s
ðnþ1Þ
ð10Þ
of the first n þ 1 bits of s can be
extracted by s
ðnþ1Þ
ð10Þ
¼ f
s
GEMD
¼½
P
n
i¼1
P
s
i
ð2
i
1Þmod2
nþ1
.
Transform s
ðnþ1Þ
ð10Þ
into n þ 1 bits binary secret s
ðnþ1Þ
.
(2) The last n 1 bits secret s
ðn1Þ
¼ðb
n2
b
n3
...b
0
Þ of s can be
extracted from the LSBs of P
s
i
; i ¼ n; n 1; ...; 2.
For (i ¼ n; i P 2; i )
b
i2
¼ LSBðP
s
i
Þ
(3) The 2n bits secret s ¼ s
ðnþ1Þ
ks
ðn1Þ
.
Notice that Scheme 1 (GEMD) can embed n þ 1 bits secret into
n stego-pixels, Scheme 2 (RGEMD) can embed 2n bits secret into n
stego-pixels. Here we extend Scheme 2 to a Partial RGEMD
Scheme (Scheme 3) which embeds any tðn þ 1 < t < 2nÞ bits
secret into n stego-pixels. The Partial RGEMD can make a trade
of the number of embedded secret bits for the visual quality of
stego-image.
Scheme 3: Partial RGEMD
Embedding phase: Input: n cover-pixels P
1
; P
2
; ...; P
n
, a secret s
of t; ðn þ 1 < t < 2nÞ bits; Output: n stego-pixels P
s
1
; P
s
2
; ...; P
s
n
.
(1) Divide s into first n þ 1 bits secret s
ðnþ1Þ
and last t n 1
bits secret s
ðtn1Þ
.
(2) Embedding s
ðnþ1Þ
into n cover-pixels using Scheme 1, and
outputs n stego-pixels P
s
1
; P
s
2
; ...; P
s
n
.
(3) s
ðtn1Þ
¼ðb
tn2
b
tn3
...b
0
Þ
2
for(i ¼ t n 2; i P 1; i )
{if (P
s
iþ2
P P
iþ2
and P
s
iþ1
6 P
iþ1
)
P
s
iþ2
¼ P
s
iþ2
1; P
s
iþ1
¼ P
s
iþ1
þ 2; P
s
1
¼ P
s
1
þ 1;
else
P
s
iþ2
¼ P
s
iþ2
þ 1; P
s
iþ1
¼ P
s
iþ1
2; P
s
1
¼ P
s
1
1;}
(4) Outputs n stego-pixels: P
s
1
; P
s
2
; ...; P
s
n
.
Extracting phase: Input n stego-pixels P
s
1
; P
s
2
; ...; P
s
n
; Output:
the t bits secret s .
(1) The decimal secret s
ðnþ1Þ
ð10Þ
of the first n þ 1 bits in s can be
extracted by s
ðnþ1Þ
ð10Þ
¼ f
s
GEMD
¼½
P
n
i¼1
P
s
i
ð2
i
1Þmod2
nþ1
.
Transform s
ðnþ1Þ
ð10Þ
into n þ 1 bits binary secret s
ðnþ1Þ
.
(2) The last t n 1 bits secret s
ðtn1Þ
¼ðb
tn2
b
tn3
...b
0
Þ
2
can be extracted from the LSBs of
P
s
i
; i ¼ t n; t n 1; ...; 2.
For (i ¼ t n; i P 2; i )
b
i2
¼ LSBðP
s
i
Þ
(3) The t bits secret s ¼ s
ðnþ1Þ
ks
ðtn1Þ
.
3. Proposed scheme
In most PSIS schemes, the shadows are noise-like images
which would cause suspicious of attackers during transmission.
This problem can be solved by combining PSIS and steganography
together which embed a secret image into meaningful image
shadows. In this part, we adopt the approaches of GEMD and
RGEMD to embed secret image in PSIS scheme, and propose a
new ðk; nÞ PSIS Scheme with meaningful shadow images. The
approaches of GEMD and RGEMD can resist RS detection and
have higher embedding capacity than EMD. This part is divided
into two subsections. In first subsection we construct the scheme;
the properties of proposed Scheme is analyzed in second
subsection.
3.1. ðk; nÞ PSIS with meaningful shadows
In order to describe our Scheme clearly, we first introduce two
auxiliary algorithms. Let s be a secret and
Q
i
¼ðP
i
; P
i
Þ; i ¼ 1; 2; ...; n be n cover-shadows where each cover-
shadow Q
i
consists of two pixels P
i
and P
i
. We propose Algorithm
1 to embed the secret s into this n cover-shadows. The following
Algorithm 1 takes s and Q
i
; i ¼ 1; 2; ...; n as input, and outputs n
stego-shadows Q
s
i
; i ¼ 1; 2; ...; n, each stego-shadow also consists
of two pixels.
768 Y.-X. Liu et al. / J. Vis. Commun. Image R. 55 (2018) 766–777
剩余11页未读，继续阅读
2022-02-08 上传
2022-04-09 上传
2021-02-17 上传
点击了解资源详情
点击了解资源详情
2024-12-25 上传
weixin_38661852
- 粉丝: 5
- 资源: 978
我的内容管理
展开
