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Advance Access publication on 28 October 2011 doi:10.1093/comjnl/bxr112

Weighted Stego-Image Steganalysis of

Messages Hidden into Each Bit Plane

Chunfang Yang

1,∗

, Fenlin Liu

, Shiguo Lian

, Xiangyang Luo

and Daoshun Wang

Zhengzhou Information Science and Technology Institute, Zhengzhou 450002, China

Corporate Research, Huawei Technologies, Beijing 100034, China

Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China

∗

Corresponding author: chunfangyang@126.com

For hiding messages into multiple least signiﬁcant bit (MLSB) planes, a new weighted stego-image

(WS) steganalysis method is proposed to estimate the ratio of messages hidden into each bit plane.

First, a new WS with multiple weights is constructed, and it is proved that when the squared Euclidean

distance between the WS and the cover image is minimal, the weight parameters are equal to the

embedding ratios in MLSB planes.Afterward, based on this result and an estimation of cover image, a

simple estimation equation is derived to estimate the embedding ratio in each bit plane. Experimental

results show that the new steganalysis method performs more stably with the change of embedding

ratios than typical structural steganalysis, and outperforms the typical structural steganalysis method

on the estimation accuracy when the embedding ratio in any bit plane is larger than 0.4.

Keywords: steganography; steganalysis; MLSB; weighted stego-image

Received 30 June 2011; revised 26 August 2011

Handling editor: Wojciech Mazurczyk

1. INTRODUCTION

Steganography is the art of hiding the very presence of

communication by embedding secret messages into innocuous

looking covers, such as digital images [1]. As an increasing

amount of data stored on computers and transmitted over

networks, steganography has been one of the key technologies

of multimedia information security [2, 3]. Simultaneously,

steganography also has a number of nefarious applications, such

as hiding records of illegal activity, ﬁnancial fraud, industrial

espionage and communication amongst members of criminal or

terrorist organizations [4]. These may cause tremendous socio-

economic impact on individuals, enterprises and even countries;

thus steganography has been a serious challenge to the

digital forensics. Therefore, steganalysis (which is the opposite

technology of steganography) has attracted great attentions and

been one of the key technologies of digital forensics.

Technically, steganography is considered broken when the

mere presence of secret message can be established [1].

However, the digital forensics investigators can use the

steganalysis technologies not only to detect the hidden records

of illegal activities and the secret communication amongst

members of criminal or terrorist organizations, but also to

estimate the length of secret message or the modiﬁcation

ratio of the cover signal [5]. The estimation of the secret

message’s length or the modiﬁcation ratio can not only be

used to distinguish the stego objects, but also help in the

estimation of stego positions and the search of stego key [6–8].

Steganalysis that can estimate the length of the secret message

or the modiﬁcation ratio of the signal samples is called as

quantitative steganalysis [5].

Nowadays, amongst numerous steganography methods,

replacement of bit planes is a category of important

steganography methods because of its simple implementation.

The widespread availability of steganography tools developed

based on these methods has led to an increased interest

in steganalysis techniques for them. For the replacement of

LSB (least signiﬁcant bit) plane, many relevant quantitative

steganalysis methods have been designed, such as RS (regular

and singular groups) method [9], DIH (difference image

histogram) method [10], SPA (sample pair analysis) method

[11], WS (weighted stego-image) method [12] and some

improved variant [13–15] of these steganalysis methods. But all

of above were just designed for LSB replacement speciﬁcally;

it cannot be expected that they can give correct answers for the

size of payload in LSB plane when embedding is also carried

The Computer Journal, Vol. 55 No. 6, 2012

at National University of Defense Technology on December 17, 2012http://comjnl.oxfordjournals.org/Downloaded from

718 C. Yang et al.

out in the other-LSB planes ([16] has given the reason for two

least signiﬁcant bits (2LSB) embedding). Some relevant works

have reported that secret message can not only be embedded into

LSB plane, but also be embedded into multiple least signiﬁcant

bit (MLSB) planes in [17, 18].

For the replacement of MLSB planes, there have been

some steganalysis methods proposed for two distinct MLSB

steganography paradigms—TMLSB steganography (‘T’means

this embedding paradigm is typical.) and IMLSB steganography

(‘I’ means the messages are embedded into each bit plane

independently.), which embed equal ratio of message bits into

MLSB planes. And these steganalysis methods for MLSB

steganography can mainly be classiﬁed as two categories:

structural steganalysis [16, 19–21] and WS steganalysis [22–

24]. However, the embedders likely embed message into

different bit planes with different ratios independently, and

this category of MLSB steganography is called as ID-MLSB

steganography (where ‘ID’ denotes that the message lengths

may be embedded into different bit planes independently

with different ratios). Furthermore, some other steganography

methods can be classiﬁed into the ID-MLSB steganography,

such as the adaptive steganography in [18]. Therefore, the

quantitative steganalysis of ID-MLSB steganography should be

very important to the forensics steganalysis. For this category

of MLSB steganography, the steganalysis methods above all

fail to estimate the embedding ratio in each bit plane. And so

far, only the literature [25] presented a method to estimate the

embedding ratio in each bit plane based on the SPA model

for MLSB replacement steganography (MSPA model) in [21].

The obtained method was called IDMSPA method, and would

be called ID3SPA method when being used to estimate the

embedding ratios in the three LSB planes. In [26], the IDMSPA

method also has been adapted for the quantitative steganalysis

of a category of adaptive steganography that embeds message

bits into different bit planes with different ratios based on the

block’s noise level of MLSB planes.

Although the methods in [25, 26] can estimate the embedding

ratio in each bit plane of MLSB planes, they all own the inherent

defect—their performances degrade rapidly with the increase of

embedding ratio in any bit plane, and when the embedding ratio

in any stego bit plane is middle or large, they will fail to estimate

the embedding ratios accurately. Contrarily, the WS steganalysis

usually performs more stably and owns good performance for

the case of a high embedding ratio [21]. Therefore, we try

to estimate the embedding ratios of ID-MLSB steganography

based on WS more stably and accurately than the existing

methods. The main results of this paper are as follows.

(i) A new WS with multiple weight parameters is deﬁned

for ID-MLSB steganography.

(ii) A theorem is proved that when the squared Euclidean

distance between the WS and the cover image is

minimal, the obtained weight parameters are equal to

the embedding ratios in the MLSB planes.

(iii) Based on this theorem and an estimated cover

image, a quantitative steganalysis method is proposed

for estimating the ratio of message hidden into

each bit plane. Experimental results show that

the new steganalysis method performs more stably

with the change of embedding ratio than typical

structural steganalysis, and outperforms the structural

steganalysis on estimation accuracy when the

embedding ratio in any bit plane is middling or large.

The remainder of this paper is organized as follows. Section 2

introduces the related works, including the WS steganalysis for

LSB steganography and the ID-MLSB steganography brieﬂy.

Section 3 describes the proposed weighted stego steganalysis

for ID-MLSB steganography. Finally, a series of experimental

results are given in Section 4. The paper closes in Section 5 with

the conclusions.

2. RELATED WORKS

2.1. WS steganalysis for LSB steganography

The WS steganalysis was proposed by Fridrich and Goljan

[12], and occupies an unusual position in the steganalysis of

LSB replacement. Unlike the structural detectors, this method

does not use the pixel group analysis on which almost every

other reasonably accurate detector relies, but has fairly good

accuracy; moreover, it retains its estimation accuracy when

embedding changes are not distributed evenly over the cover

[15]. In the following, the basic principle of WS steganalysis

for LSB replacement will be introduced brieﬂy.

In [12], let X ={x

}

i=1

be a set of integers in the range

[0, 255] representing a grayscale cover image whose size is

n = M × N. The value of x

after ﬂipping its LSB will be

denoted as ¯x

, viz. ¯x

= x

+ 1 − 2(x

mod 2). Let S ={s

}

i=1

denote the stego-image after embedding pn (0 ≤ p ≤ 1) bits

using LSB replacement in pn pixels randomly selected from

the cover image X. Fridrich and Goljan deﬁned the WS with

weight parameter q as follows:



(q)

={s

(q)

= s

(¯s

− s

(1)

where 0 ≤ q ≤ 1, i = 1, 2,...,n. Then, Fridrich and Goljan

proved that the weight parameter q and the embedding ratio p

satisfy the following relationship:

p = arg min



i=1

(q)

− x

)

, (2)

which shows that S

(p)

is the closest WS to the cover image in the

least square sense among all WSs S

(q)

for 0 ≤ q ≤ 1. Based on

this, Fridrich and Goljan formulated the procedure of estimating

the unknown embedding ratio p from the stego-image as a

The Computer Journal, Vol. 55 No. 6, 2012

at National University of Defense Technology on December 17, 2012http://comjnl.oxfordjournals.org/Downloaded from

Weighted Stego-Image Steganalysis 719

minimization problem as follows:

ˆp = arg min



i=1

(q)

−ˆx

)

=−



i=1

−ˆx

)(1 − 2(s

mod 2)), (3)

where ˆx

denotes the prediction of x

So far the WS steganalysis has been enhanced from

many aspects and applied to the steganalysis of some other

steganography, such as TMLSB and JSteg steganography.

2.2. ID-MLSB steganography

When one wants to replace the bits in the l (l denotes the number

of stego least-signiﬁcant bit planes) LSB planes with the mes-

sage bits, at least the following three methods can be adopted:

(i) TMLSB steganography, which randomly selects ﬁxed

number of pixels and replaces their l LSBs with the

message fragments with size of l (seeing Fig. 1a for

l = 3);

(ii) IMLSB steganography, which randomly selects ﬁxed

number of bits from the l LSB planes and replaces

them with the message bits (seeing Fig. 1b for l = 3);

(iii) ID-MLSB steganography, for each bit plane of the

MLSB planes, which randomly selects ﬁxed number

of bits from the bit plane, and replaces them with the

message bits (seeing Fig. 1c for l = 3).

From Fig. 1, it can be seen that being different from the

TMLSB and IMLSB steganography, the ID-MLSB steganog-

raphy possibly embeds message bits into different bit planes

with different ratios. Furthermore, some other steganography

methods can be classiﬁed into the ID-MLSB steganography,

such as the adaptive steganography in [18]. The main steps of

ID-MLSB steganography can be described as follows:

(i) Determine the number of LSB planes that will contain

the message bits, viz. l;

(ii) For each bit plane in the l LSB planes, randomly select

ﬁxed number of bit positions from the bit plane;

(iii) If the bit in the selected position is different from

the message bit, ﬂip the bit in the selected position;

otherwise, do not change the bit.

3. PROPOSED WS STEGANALYSIS FOR ID-MLSB

STEGANOGRAPHY

3.1. WS for ID-MLSB steganography

In ID-MLSB steganography, the messages hidden into l LSB

planes may own different lengths independently. Thus, let p =

,...,p

) denote the vector of embedding ratios where

FIGURE 1. Comparison among ID-MLSB steganography and other

two categories of MLSB steganography. (a) TMLSB steganography

for l = 3. (b) IMLSB steganography for l = 3. (c) ID-MLSB

steganography for l = 3.

(1 ≤ i ≤ l) is the embedding ratio in the ith LSB plane. Then

the WS for ID-MLSB steganography can be deﬁned as follows:

⎧

⎪

⎨

⎪

⎩

(q,l)

={s

(q,l)

= s



j=1

j−1

− 2(s

⊕ 2

j−1

)],

(4)

The Computer Journal, Vol. 55 No. 6, 2012

at National University of Defense Technology on December 17, 2012http://comjnl.oxfordjournals.org/Downloaded from

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