Identity-Based Steganography in Spatial Domain

This paper proposed an identity-based steganographic scheme, where a receiver with certain authority can recover the secret message ready for him, but cannot detect the existence of other secret messages. The proposed scheme created several separate covert communication channels tagged by the Fuzzy Identity-Based Encryption (FIBE) in one grayscale image. Then each channel is used to embed one secret message by using any content-aware steganographic scheme. Receivers with different attributes can extract different messages corresponded. The Experiments illustrated the feasibility of this identity-based secret message extraction. Further, the proposed scheme presents high undetectability against steganalytic attack launched by receivers without corresponded attributes.


Journal of Computer and Communications
image. For example, schemes in [6] [7] extract the directional residuals of a cover image through filtering to define the textural region that is hard to model. Scheme in [8] [9] uses the multivariate Gaussian cover model to minimize the embedding distortion on statistics. What's more, thanks to the research of Syndrome-Trellis Codes (STC) [10], researchers no longer need to pay attention on the site of embedding, but only consider how to choose more appropriate distortion function.
Existed steganographic schemes only consider honest receivers and improve the entire security of the hidden messages. Due to the speciality of STC, every receiver with the knowledge of the existence of the hidden messages can extract all the secrets from the cover. However, some receivers may be corrupted in practice. If there are betrayers in the receivers, the secret will be leaked. What's more, secret messages are usually at specified sensitive levels, one cannot access, or even detect the existence of all these messages. If there are several messages at different security levels that want to be sent, existed steganographic schemes can only embed them into several covers to avoid secret leakage, which increases the communication cost. Additional information will also be necessary to distinguish different owners of these stego images. This is unsafe and inconvenient for practical secure communication.
In this paper, we propose a multiple embedding scheme by combining the Fuzzy Identity-Based Encryption [11] with the typical steganographic techniques.
In our scheme, the sender can embed multiple messages associated with different attributes into one cover simultaneously, so that receivers extract the messages in accordance with their identity attributes. Each message needs a specific set of attributes to extract. For those attributes unmatched, receivers even won't know the existence of other embedded messages. In order to embed multiple messages, we generate masks for each message by using the FIBE based on their specific set of attributes. We embed messages according to their masks, and integrate them into one stego image. The receiver can locate the corresponding messages if and only if their identity attributes are matched, or they wouldn't know where or whether the messages are hidden.
There are various utilities for the proposed scheme. First, the embedded messages can be partially secure in the presence of corrupted receivers. As shown in the experiments, these receivers cannot detect the other embedded messages with their current knowledge. Second, a hierarchical extraction is available.
Consider such a scenario where an operator receives a piece of digital works and finds that there are secret messages with the aid of his identity. He then forwards it to the persons concerned. The ones with higher-level identities can extract more messages, whose existence would not be known to the operator or the others.
The rest of this paper is organized as follows. Section 2 is to introduce the related works of our scheme. In Section 3, we will introduce our propose methods in detail. The experimental result will be show in Section 4 to compare our me-

Fuzzy Identity-Based Encryption
Fuzzy Identity-Based Encryption (FIBE) is a kind of public key cryptography. Its algorithm model designed is based on the Shamir's Secret Sharing [12] and bilinear pairings in cyclical group. The sender has a set of attributes and some of them are employ to encrypt the plain text, and only receivers whose attributes conform to the decryption attribute set can decrypt the cipher text. The specific steps of FIBE are described as following:

Steganographic Algorithm with Minimum Embedded Distortion
, , ∑∑ n 1 and n 2 indicate how many pixels are in the horizontal and vertical columns of the cover image, and X i,j and Y i,j denote the values of the pixel corresponding to the i-th row and j-th column of the cover image respectively.
respectively the low-pass and high-pass filters of the Daubechies 8 wavelet decomposition filter. * represents the image filling convolution operation,  represents the matrix is rotated 90 degrees counterclockwise. After calculating the cost of each point, it is sent to the STC to get the embedded image.

Proposed Embedding Method
Our method is demonstrated in Figure 1. We choose one gray level image to embed multiple messages. Assume we have m messages to embed. To embed the i-th message, we use the i-th key to generate a mask using FIBE. Then the cover is divided into several regions according to the mask. The i-th message will be embedded into one region selected. After m rounds' embedding, all the m messages are embedded in the corresponded regions. By combining all the selected regions and the rest region of the image, we can reconstruct the stego image. The details are introduced in the following subsection.
For the receiver, we suppose he has a set of j attributes. We choose a random j-1 order function ( ) p x satisfying ( ) Then the secret key of the receiver is

Embedding
Suppose there are m messages to be embedded. We will introduce the procedure of embedding one message, saying, the i-th message. Label each pixel of the image with a unique integer x (Note that the receiver and sender have negotiated the label method). At first, we choose 2 1 g ∈  , and calculate ( ) At last, we send the stego image I along with the decryption attribute sets ( )

Extraction
The extraction procedure is demonstrated in Figure 2. Unlike the decryption of FIBE, our scheme intends to locate the secret base on the plain text, but not to decrypt the secret.
After receiving the stego image, the receiver calculates ( )

Experiment Setup
To evaluate the performance of the proposed scheme, we employ 10,000 images of size 512 × 512 from the Boss Base 2 [13] as the test images. Pseudorandom binary sequences are employed as secret messages, which will be embedded in

Effectiveness Assessment
We suppose the region number is r, the message number is m. In each round, every region can employ 1/r of pixels to carry one message. Note that it is possible that averagely 1/r of the selected region's pixels appear at the regions selected in other m-1 rounds. To deal with this, we define the function of average maximal total payload (AMTP) as: ATMP represents the maximum total embedding payload that an image can embed in multiple messages in normal situation. According to Equation (1), we calculate the relationship of some situations as in Table 1. By choosing a suitable region number according to the message number, we can get a safe vocation for embedding. As a result, the message number is set as same as the region number in the propose method except noted. In Figure 3, we can observe that the two messages embedded in one cover at  Figure 4. Comparing security of identity-based embedding and other two general embedding method using the SRMQ (left) and Comparing security of different region number using the SRMQ (right). more difficult to analyze the statistical features. So our scheme has a higher undetectability. Secondly, we compared the influence of different region numbers in the same payload in Figure 4(b). When payload = 0.2, we can observe that the more regions, the higher E OOB . When payload = 0.4, the E OOB will reduce instead if the region number is relative high. It is because increasing the regions would reduce the AMTP value.
In Figure 5(a), we observe that when one message has been extracted, the E OOB of other messages stay in a high level. It means that if someone extracted one of the messages, he can hardly ensure whether there are other messages embedded or not. In Figure 5(b), we can observe that the more messages to extract, the higher E OOB of the remained messages to get. It means that the security of the remaining messages will not reduce with more messages have been extracted.  Instead, a higher undetectability is achieved.

Conclusions
In this paper, we introduce the risk of the receiver's unreliability, and present the idea of identity-based embedding. Based on the Fuzzy Identity-Based Encryption and WOW, we embed several messages simultaneously into one cover image.
The receivers can only extract the message if his attributes is consistent. We first use the attributes set of i-th message to encrypt all the pixels of the cover image, and get the i-th mask to divide several regions. Then we employed one region to embed the i-th message after dealing with the cost of embedding.
By comparing with traditional methods, it can be observed that our proposed scheme is not inferior to them when embedding multiple messages in a low payload. When the payload is higher, our proposed scheme has more excellent experimental result. It is because that the unpredictability of regions copes with the steganalysis well. We also make a discussion between region number and message number, and analyze their average maximal total payload against security. Experiments support that the security of the remained messages will not be affected by knowing that some messages have been extracted.
Regarding the future work, we will try to improve the AMTP of our scheme by using other cryptography methods. Another potential improvement is expanding our scheme from spatial domain to other domains.