Reversible AMBTC-based secret sharing scheme with abilities of two decryptions

https://doi.org/10.1016/j.jvcir.2013.12.018Get rights and content

Highlights

  • We report a reversible secret sharing scheme from stego shadows to their original covers.

  • The generated AMBTC-compressed shadows are meaningful.

  • The meaningful shadows maintain the same image quality as their original covers.

  • There are two ways to recover the secret, stacking and complete decryptions.

  • The stego-compressed codes can be decoded by the normal decoding procedure.

Abstract

This paper presents a secret sharing scheme to encode a secret binary image in images which are compressed by absolute moment block truncation coding (AMBTC) method. The generated shadows by the proposed scheme are in AMBTC-compressed format and meaningful, the visual quality of which is the same as that of its original AMBTC version. In the proposed scheme, the secret image can be reconstructed in two situations: (1) if some light-weight computational devices are available, the secret image can be completely decrypted without any distortion, and (2) otherwise, the secret image can also be revealed by human visual system. Furthermore, the proposed scheme provides the reversibility for protecting the valuable cover images. In addition, underlying the proposed (2,2) scheme, this paper gives a construction for the (2,n) scheme where one participant may require more than one shadow. Theoretical analysis and simulation results demonstrate the superiority of the proposed scheme.

Introduction

With the development of network technologies, digital data are distributed via the internet more conveniently. However, distributing the sensitive or important data, such as those used by the military or by commercial businesses, over the public network makes them vulnerable to be attacked. Hence, protection of sensitive data becomes a critical issue in recent years. Some techniques have been developed to protect the transmitted data from being intercepted or tampered. Cryptography and steganography are the two traditional techniques used for protecting the sensitive data. However, both of these methods accommodate the sensitive information in one single information-carrier, so that the secret would be easily lost or destructed. Secret sharing mechanism is one alternative method which has been proposed for addressing the above problem. In 1979, a (k,n)-threshold secret sharing system was first introduced by Blakely [1] and Shamir [2]. It is different from the traditional encryption method which utilizes an encryption key or a particular cipher algorithm. In a (k,n)-threshold scheme, a dealer encodes and splits a secret message into n pieces (called shadows or shares) which are then distributed to the involved participants. With any k out of n shadows, the secret can be recovered accurately. However, the knowledge of any k-1 or fewer shadows gives no clue about the secret.

Using the (k,n)-threshold secret sharing concept, a secret image sharing technique known as visual secret image (VSS) was designed by Naor and Shamir in 1995 [3]. In a (k,n)-threshold VSS, the secret image is shared by constructing n noised-like images, called shadows or shares. The noised-like shadows are transmitted instead of the original secret image. Once k or more shadows are collected and stacked, the secret image can be revealed by visual perception without the aid of any computational device. However, the VSS scheme usually lead to the problems of pixel expansion, contrast lost and meaningless. The visual quality of the revealed secret image by the VSS scheme is low due to the stacking operation. What’s more, meaningless appearance of the shadows further increases the chance of suspicion on secret image communication and imposes difficulty for managing the shadows. To reduce the chance of suspicions and to manage the shadows friendly, extended VSS [4], [5] and halftone VSS [6], [7] were presented. The shadows constructed by these schemes include meaningful contents, but their format style is limited to a binary image. To extend the application, a secret image sharing scheme [8] was presented to share the secret into the original grey-scale images in 2002. It may attract the attackers’ attention to distribute the original grey-scale images as shadows, since most digital images transmitted over the Internet are usually in compressed format, such as JPEG [9], vector quantization (VQ) [10] and block truncation coding (BTC) [11].

The AMBTC method which is a variant of BTC, was presented by Lema and Mitchell [12] to further improve the performance of the traditional BTC technique. The AMBTC method is computationally simpler than the BTC method while preserving the first absolute moment along with the mean. In the AMBTC method, each image block is encoded by using one bit plane and two quantization levels. Due to its low computational cost, low complexity and ease to implement, it is suitable for less powerful processing kernel, such as the Arm-based application. Recently, most studies or applications on information security based on the BTC or BTC-like method have been proposed [13], [14], [15], [16]. In this paper, we study a novel secret sharing scheme that encodes a secret image into the AMBTC-compressed shadows. The reversibility that means restoring the original cover image without distortion, is especially important for military, artistic or medical images. Recently, most image-processing techniques focus on achieving reversibility, such as digital watermarking, image hiding and image authentication [17], [18], [19]. Unfortunately, most sharing schemes [20], [21], [22], [23] are incapable of restoring the stego image to the original cover image. Inspired by potential practicability, this paper provides a reversibility for preserving the fidelity of valuable cover images. Different with other reversible schemes [24], [25], any extra information such as the location map does not need in our scheme. In the proposed scheme, the dealer receives a secret binary image and the two same AMBTC-compressed codes. Then, the secret binary image is shared into the two bitmaps with the aid of the toggle operation on the bitmaps. Anyone can decode the AMBTC-compressed image from stego compression codes by using the original decoding procedure of the AMBTC method. This criterion is very important, because if the illegal receivers cannot decode the compressed image by using the original decoding procedure of the AMBTC method, they may develop a suspicion and start detecting the secret data. In the reconstruction phase, there are two decryption ways to reconstruct the secret image. If light-weight computational devices based XOR operation are available, the secret image can be completely decrypted without any distortion; otherwise, qualified participants can use their eyes to reveal the secret image by directly stacking the two corresponding bitmaps, each of which gives no clue about the secret image. In the stacking decryption, the reconstruction of black pixels is perfect, that is, all the sub pixels associated to the secret black pixel are black [26]. Hence, the secret information in the stacked result can be well identified. Furthermore, the meaningless problem is solved as well by our scheme, where the meaningful shadows maintain the same image quality as their original cover images.

The rest of this paper is organized as follows. In Section 2, related works including the AMBTC compression technique and visual cryptography are briefly described. The reversible (2,2) secret sharing scheme based on the AMBTC method is introduced in Section 3, as well as the (2,n) scheme. The experimental results and analysis are given in Section 4, and finally some conclusions are stated in Section 5.

Section snippets

Related works

In this paper, a reversible secret sharing scheme based on the AMBTC method is proposed. The algorithm of the AMBTC method is briefly introduced in this section for offering a better comprehension of the proposed scheme. The AMBTC method is introduced in Section 2.1. Then the visual concept is briefly reviewed in Section 2.2.

The proposed reversible VSS scheme based on AMBTC

In some reported VSS schemes, the secret image can be revealed by human visual system, but the revealed image often suffers from contrast lost due to the stacking operation. In addition, the shadows are generally noised-like and limited to binary images, which may be attracted by malicious intruders. For addressing the above problems, we propose a reversible AMBTC-based secret sharing scheme, where a secret image is encoded into two bitmaps of AMBTC-compressed codes. The proposed scheme

Experimental results and analysis

In the experiments, the visual qualities of the AMBTC-compressed images or shadows are evaluated determined by the Peak to Signal Noise Ratio (PSNR). Higher PSNR indicates better quality or more natural looking image. The computation of PSNR is defined as given:PSNR=10log102552MSE,where MSE is the mean square error between the original grey-scale image and AMBTC-compressed image. MSE for a M×M grey-scale image isMSE=1M×Mi=1Mj=1M(Xi,j-Xi,j)2,where Xi,j and Xi,j indicate the pixel values of

Conclusion

In this paper, a novel AMBTC-based VSS scheme with reversibility has been presented. In the proposed scheme, a secret image is shared into meaningful AMBTC-compressed shadows, which satisfy the camouflage purpose and reduce the risk of attracting intruders. Sharing the secret image into the AMBTC-compressed images instead of the original images with 8 bits per pixel can improve the efficiency for data transmission and storing. Different from some reported steganography image sharing schemes

Acknowledgments

This work was in part supported by 973 Program (Grant No. 2011CB302400) and Natural Science Foundation of Guangdong Province, China (Grant No. S2013010013728).

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