Available online at www.sciencedirect.com

Available online at www.sciencedirect.com

Procedia Engineering

Procedia Engineering 00 (2011) 000–000 Procedia Engineering 15 (2011) 2767 – 2772 www.elsevier.com/locate/procedia

Advanced in Control Engineering and Information Science

A Novel Secure Communication Protocol Combining Steganography and Cryptography Shouchao Songa,b,*, Jie Zhangb, Xin Liaoa, Jiao Dua, Qiaoyan Wena, a State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China b School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China

Abstract In this paper, a new secure communication protocol that combines steganography and cryptography techniques organically is proposed. It is based on the LSB matching method and the well-developed Boolean functions in stream ciphers. The cover media employed focuses on grayscale images, and the Boolean function is used for encryption and controlling the pseudo-random increment or decrement of LSB. Unlike the existing methods of doing encrypting and hiding separately, this protocol is one-stop, accomplishing them all at once. Therefore, it needs less computation than the existing methods do while maintaining high secure quality. To our knowledge, this is the first secure protocol of this kind. And this method not only is easy to be implemented, but also has almost optimal embedding ratio, what’s more, it is highly robust to resist regular steganalysis, such as RS analysis, GPC analysis, χ2 –analysis.

© 2011 Published by Elsevier Ltd. Open access under CC BY-NC-ND license. Selection and/or peer-review under responsibility of [CEIS 2011] Keywords: Information security; Secure communication; LSB matching; Boolean functions

* Corresponding author. Tel.: +86-10-6228-6774; fax: +86-10-6228-3192. E-mail address: [email protected]

1877-7058 © 2011 Published by Elsevier Ltd. Open access under CC BY-NC-ND license. doi:10.1016/j.proeng.2011.08.521

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Shouchao Song et al. / Procedia Engineering (2011) 2767 – 2772 Shouchao Song et al. / Procedia Engineering 0015 (2011) 000–000

1. Introduction While people enjoy the convenient electronic information communication facilitated by the highly developed Internet and information technologies, they also run a risk that the sensitive information transmitted might be intercepted or distorted by unintended observers for the openness of the Internet. So it is of great significance to develop secure communication approaches. And so far, there have been two typical methods, cryptography and steganography, to protect sensitive information from being disclosed. As is well known, cryptography is a classical way that has a long history for secure communication. The main idea of cryptography can be illustrated as the following: The information-sender uses a key to translate the secret information (the plaintext) into a meaningless bit stream (the ciphertext) and transmits it to the intend recipient via an unsecure communication channel, and the intended recipient would decrypt the cipher into the plaintext with a secret key that has been negotiated in advance. The advantage of cryptography is that unintended recipients can’t interpret the ciphertext without the secret key even when they get the whole ciphertext. But on the other hand, because the ciphertext is an irregular bit stream, which flags the fact that some sensitive information is being transmitted, the communication would attract illegal parties’ attention and invite a danger of being decrypted or even being destroyed. Steganography, a branch of information hiding techniques, is another way for secure communication. The main idea of steganography is to embed the secret information into an unrelated plain digital media, such as an image, a piece of video or audio, and transmit this slightly altered digital media to the intended recipient without attracting illegal observers’ attention, so that the recipient can get the sensitive information secretly. Apparently, the advantage of steganography is that it successfully covers the fact that some sensitive information is being transmitted, so that this method can avoid attracting attackers’ attention. This method not only is simple but also maintains good visual or aural quality. But regular steganography also faces a risk that the secret information might be extract illegally by a third party when he knows the very steganography protocol. Considering the respective advantages and disadvantages of steganography and cryptography, we can naturally get an idea that combining them in practice, then the new method would simultaneously possess the advantages of steganography and cryptography while avoid the respective defects. And there have been a lot of works applying this idea and one may refer to [1-8], they encrypt the secret information firstly and then hide them in the digital media. But the common thing is that they all do the encryption and hiding separately. And to our knowledge, there has no study on doing them simultaneously up until now. In this paper, we proposed a novel method doing encryption and hiding at the same time, organically combining steganography and cryptography. This protocol is based on the LSB matching method which is very popular in steganography and Boolean functions which is widely used in cryptography. It not only is easy to be implemented, but also needs less computation than the previous works do while maintaining high secure quality. The rest of the paper is organized as follows. Section 2 recalls the basic concepts，denotation and properties. Section 3 proposes a new secure communication protocol combining the LSB matching method and the Boolean functions. In Section 4, we make brief comments on this protocol. Finally, Section 5concludes this paper.

2. Preliminaries In this paper, we partially borrow the idea of LSB Matching and the usage of Boolean functions in stream cipher. Before presenting our protocol, we recall the basic concepts, denotation and properties of LSB Matching method and Boolean functions in this section.

Shouchao Song et al. / Procedia Engineering 15 (2011) 2767 – 2772 Shouchao Song et al. / Procedia Engineering 00 (2011) 000–000

2.1. LSB Matching In this paper, we focus on grayscale images. The gray value, ranged from 0 to 255, of each pixel is represented in an 8-bit binary form in the computer. Apparently, these 8 bits weigh differently in significance in view of presenting the gray degree, and the higher the bit is, the more significant it is. We call the lowest bit Least Significant Bit (abbreviated as LSB). It is easy to see that the visual quality of the image is less sensitive to the change of the lower bits, as is the theory foundation of LSB Replacement and LSB Matching. LSB Matching [1] which is developed from LSB Replacement method is very a popular steganography method in image media. And it not only maintains the favorable characteristics of LSB Replacement method, but also has better performance on resisting attacks and detecting [1]. The main idea of LSB Matching is related as follows. In LSB Matching embedding algorithm, one compare the LSB of each pixel with the secret bit one by one, if they are equal, do nothing; else, pseudorandomly make a decrement or increment on the gray value. And in decoding algorithm, the recipient can get the hided secret bits directly from the LSB of the received image. Initial images for covering are called cover images, and the images embedded with secret information are called stego images. 2.2. Boolean functions Boolean functions are widely used in cryptography, especially in stream ciphers, and have received lots of attention [9-11] on them. Let Fn be the finite field of characteristic of 2 and F2n be the n -dimensional vector space over F2 . Then an n -variable Boolean functions is defined as a mapping from F2n to F2 . The set of all n -variable Boolean functions is denoted by Bn . We denote the addition modulo 2 by the symbol “ ⊕ ” and regular addition by “ + ”. And for convenience, we abbreviate f ( x1 , x2 ,L , xn ) as f n or f , if there is no confusion. As is well known, any function f n admits a unique multivariate polynomialn over F2 : 2 −1 f ( x1 , x2 ,L , xn ) = ∑ i = 0 ai ( x1 )i1 ( x2 )i2 L ( xn )in where ai ∈ F2 , and i1i2 L in is the binary representation of i . Any n -variable Boolean function can be represented as a 2n -length binary vector, which is called its truth table: → f = [ f (0, 0,L , 0), f (1, 0,L , 0),L , f (1,1,L ,1)] We say f is balanced, if its truth table has equal number of 1 and 0.

3. A novel secure communication protocol Assume Alice wants to send an N -length secret bit stream M to Bob secretly. According to Kerckhoffs’ principle [12] in using keys for secure communication, it is presumed that the sender and the intended recipient share an 8-variable balanced Boolean function as the secret key. 3.1. For the sender It is easy for Alice to get a matrix C p×q from the cover grayscale image which has p rows and q columns of pixels, ( p × q) > N . Elements of C p×q are the gray values of the corresponding pixels from the cover image. For the convenience of describing, we denote M = m0 m1 L mN −1 , mi ∈ F2 , and

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L c1 c2 cq ⎡ ⎤ ⎢ c ⎥ L c c (1× q ) +1 (1× q ) + 2 (1× q ) + q ⎥ C p×q = ⎢ ⎢ ⎥ M M O M ⎢ ⎥ ⎣⎢ c(( p −1)×q ) +1 c(( p −1)× q ) + 2 L c(( p −1)×q ) + q ⎦⎥ where the 8-bit binary representation of ci is ci =i8i7 Li1 . Then the process of manipulation by the sender can be stated as follows: Step 1: find the function value: f ci = f ( i1 , i2 ,L , i8 ) , i = 1, 2,L , N ; Step 2: generate a bit stream H =h0 , h1 , L , hN −1 : hi = mi ⊕ f ci+1 , i = 0,1,L , N − 1 ; Step 3: construct a new matrix C ' p× q : L c2 ' cq ' ⎤ ⎡ c1 ' ⎢ c c(1×q ) + 2 ' L c(1× q ) + q ' ⎥⎥ (1× q ) +1 ' C p× q ' = ⎢ ⎢ ⎥ M M O M ⎢ ⎥ ⎣⎢ c(( p −1)× q ) +1 ' c(( p −1)×q ) + 2 ' L c(( p −1)× q ) + q '⎦⎥

where i =1 ⎧ci ⎪c 2 ≤ i ≤ N − 1, ci mod 2 = hi ⎪ i ⎪c − 1 2 ≤ i ≤ N − 1, ci = 255, hi = 0 ci ' = ⎨ i ⎪c + 1 2 ≤ i ≤ N − 1, ci = 0, hi = 1 ⎪ i f ci −1 ⎪⎩ci + (−1) else Step 4: replace the gray value of each pixel of the cover image by the corresponding value of the matrix C ' p× q . Then the image obtained, whose gray-value matrix is C ' p× q , is the stego image to transmit.

3.2. For the recipient Step 1: Attract the gray-value matrix R ' p× q from the received image; r1 ' r2 ' rq ' ⎤ L ⎡ ⎢ r r(1× q ) + 2 ' L r(1×q ) + q ' ⎥⎥ (1× q ) +1 ' R p× q ' = ⎢ ⎢ ⎥ M M O M ⎢ ⎥ ⎣⎢ r(( p −1)× q ) +1 ' r(( p −1)× q ) + 2 ' L r(( p −1)×q ) + q '⎦⎥ Step 2: get the hided bit stream T =t0 , t1 , L , t N −1 , where ti = ri + 2 mod 2 , i = 0,1,L , N − 1 ; Step 3: find the function value: f ri = f ( i1 , i2 ,L , i8 ) , i = 1, 2,L , N − 1 ; Step 4: generate the bits stream S =s0 , s1 ,L , sN −1 : si = ti ⊕ f ri+1 , i = 0,1,L , N − 1 . In fact, the bit stream S is the secret information communicated, as accomplishes the decoding.

4. Comments on this protocol In this section, we analysis the protocol proposed in Section 3, and our comments on it are made as follows: • This protocol is easy to be implemented, as can be seen from the process presented in Section 3; • This protocol has almost optimal embedding ratio. Every pixel can be used for hiding secret bit except the first one.

Shouchao Song et al. / Procedia Engineering 15 (2011) 2767 – 2772 Shouchao Song et al. / Procedia Engineering 00 (2011) 000–000

• It needs less computation than the existing methods do while maintaining high visual quality. Unlike the existing methods of doing the encrypting and hiding separately, this protocol accomplishes the encryption and hiding at the same time. • In this protocol, an 8-variable Boolean function is used as a key shared by the sender and the recipient securely prior to communicating. The requirement of an initial secure exchange may seem undesirable at first sight, but considering that the intended recipient would be no wiser than the illegal observer about which media the secret has been hided, so they need do the negotiation at first, then it is reasonable for them to share the Boolean function used secretly; • As can be seen, this protocol provides double protection for the secret information. It organically combines steganography and cryptography techniques, so it simultaneously possesses the advantages of steganography and cryptography. Encryption provides another level of security in case of a successful stego attack; • It is highly robust to resist regular steganalysis, such asχ2 –analysis [13,14,17] ,RS analysis[15], GPC analysis[16]. • The original cover image is not required for the recipient to restore the secret information.

5. Conclusion In this paper, we focused on grayscale images, and proposed a new secure communication protocol that organically combines steganography and cryptography techniques. This protocol, based on the LSB matching steganography method and the well developed Boolean functions in stream ciphers, simultaneously possesses the advantages of steganography and cryptography. And this protocol, unlike the traditional methods of doing the encrypting and hiding separately, accomplishes encryption and hiding at the same time, so it needs less computation than the existing methods do while maintaining high visual quality. This method not only is easy to be implemented, but also has almost optimal embedding ratio, what’s more, it is highly robust to resist regular steganalysis, such as RS analysis, GPC analysis, χ2 –analysis. Acknowledgements

The authors would like to thank all the anonymous reviewers for their valuable comments and advice on this manuscript. And this work is supported by National Natural Science Foundation of China (Grant Nos. 60873191，60903152, 61003286, 60821001) and the Fundamental Research Funds for the Central Universities (Grant Nos. BUPT2011YB01, BUPT2011RC0505). References [1] T. Sharp. An implementation of key-based digital signal steganography. Proc. 4th. Information Hiding Workshop, LNCS, vol. 2137, Berlin: Springer-Verlag, 2001, pp. 13–26. [2] R.Z. Wang, C.F. Lin, J.C. Lin. Image hiding by optimal LSB substitution and genetic algorithm. Pattern Recognition. Vol.34 (3), 2001, pp. 671–683. [3] X.L. Li, B. Yang, D.F. Cheng, T.Y. Zeng. A Generalization of LSB Matching. Signal Processing Letters, IEEE, Vol. 16(2), 2009, pp. 69-72. [4] C.K. Chan, L.M. Chen. Hiding data in images by simple LSB substitution. Pattern Recognition. Vol.37 (3), 2004, pp. 469– 474.

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[5] K. Bhowal, A.J. Pal, G.S. Tomar, P.P.Sarkar. Audio Steganography Using GA. Computational Intelligence and Communication Networks (CICN), 2010 International Conference on. 2010, pp.449-453. [6] J.K.Mandal, M.Sengupta. Steganographic Technique Based on Minimum Deviation of Fidelity (STMDF). Emerging Applications of Information Technology (EAIT), 2011 Second International Conference on. 2011, pp. 298-301. [7] I.C. Lin, Y.B. Lin, C.M. Wang. Hiding data in spatial domain images with distortion tolerance, Comput. Stand. Inter. Vol.31 (2), 2009, pp.458–464. [8] ZHANG Xin-peng; WANG Shuo-zhong. Steganography using multiple-base notational system and human vision sensitivity, Signal Processing Letters, IEEE, 2005 . Vol. 12(1), pp.67 - 70. [9]W.C. Thomas, S. Pantelimon. Cryptographic Boolean functions and applications. Elsevier: Academic Press, first edition 2009, pp.119-156. [10] S.S. Song, J. Zhang, J. Du, Q.Y. Wen. On the construction of Boolean functions with optimal algebraic immunity and good other properties by concatenation, Progress in Informatics and Computing (PIC), 2010 IEEE International Conference on, Volume 1, pp: 417 – 422. [11] C. Carlet, K. Q. Feng. New balanced Boolean functions satisfying all the main cryptographic criteria [EB/OL]. http://eprint.iacr.org/2008/244.pdf. [12] A. Kerckhoffs. La cryptographie militaire. Journal des Sciences Militaries, Vol.4(1), 1883, pp.5-38. [13] Westfeld A. Detecting Low Embedding Rates. Proc. 5th. Information Hiding Workshop, LNCS，Vol.2578， Berlin: Springer-Verlag, 2003, pp.324-339. [14] Westfeld A, Pfitzmann A. Attacks on Steganographic Systems, Proc. 3rd. Information Hiding Workshop, LNCS,Vol.1768, Berlin: Springer-Verlag, 2000, pp.61-76. [15] Fridrich J, Goljan M, Du R. Detecting LSB steganography in color and gray-scale images. IEEE Multimedia, 2001, Vol.8(4), pp.22-28. [16] ZHANG Xin-peng; WANG Shuo-zhong, ZHANG Kai-wen . Steganalysis Based on the Statistics Method for LSB Insertion . Journal of Applied Sciences, 2004. Vol.22(1), pp.16-19. In Chinese. [17] Ker, Andrew D. Resampling and the detection of LSB matching in color bitmaps. Security, Steganography, and Watermarking of Multimedia Contents VII. Edited by Delp, Edward J., III; Wong, Ping W. Proceedings of the SPIE, 2005, Vol.5681, pp. 1-15.

Available online at www.sciencedirect.com

Procedia Engineering

Procedia Engineering 00 (2011) 000–000 Procedia Engineering 15 (2011) 2767 – 2772 www.elsevier.com/locate/procedia

Advanced in Control Engineering and Information Science

A Novel Secure Communication Protocol Combining Steganography and Cryptography Shouchao Songa,b,*, Jie Zhangb, Xin Liaoa, Jiao Dua, Qiaoyan Wena, a State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China b School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China

Abstract In this paper, a new secure communication protocol that combines steganography and cryptography techniques organically is proposed. It is based on the LSB matching method and the well-developed Boolean functions in stream ciphers. The cover media employed focuses on grayscale images, and the Boolean function is used for encryption and controlling the pseudo-random increment or decrement of LSB. Unlike the existing methods of doing encrypting and hiding separately, this protocol is one-stop, accomplishing them all at once. Therefore, it needs less computation than the existing methods do while maintaining high secure quality. To our knowledge, this is the first secure protocol of this kind. And this method not only is easy to be implemented, but also has almost optimal embedding ratio, what’s more, it is highly robust to resist regular steganalysis, such as RS analysis, GPC analysis, χ2 –analysis.

© 2011 Published by Elsevier Ltd. Open access under CC BY-NC-ND license. Selection and/or peer-review under responsibility of [CEIS 2011] Keywords: Information security; Secure communication; LSB matching; Boolean functions

* Corresponding author. Tel.: +86-10-6228-6774; fax: +86-10-6228-3192. E-mail address: [email protected]

1877-7058 © 2011 Published by Elsevier Ltd. Open access under CC BY-NC-ND license. doi:10.1016/j.proeng.2011.08.521

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Shouchao Song et al. / Procedia Engineering (2011) 2767 – 2772 Shouchao Song et al. / Procedia Engineering 0015 (2011) 000–000

1. Introduction While people enjoy the convenient electronic information communication facilitated by the highly developed Internet and information technologies, they also run a risk that the sensitive information transmitted might be intercepted or distorted by unintended observers for the openness of the Internet. So it is of great significance to develop secure communication approaches. And so far, there have been two typical methods, cryptography and steganography, to protect sensitive information from being disclosed. As is well known, cryptography is a classical way that has a long history for secure communication. The main idea of cryptography can be illustrated as the following: The information-sender uses a key to translate the secret information (the plaintext) into a meaningless bit stream (the ciphertext) and transmits it to the intend recipient via an unsecure communication channel, and the intended recipient would decrypt the cipher into the plaintext with a secret key that has been negotiated in advance. The advantage of cryptography is that unintended recipients can’t interpret the ciphertext without the secret key even when they get the whole ciphertext. But on the other hand, because the ciphertext is an irregular bit stream, which flags the fact that some sensitive information is being transmitted, the communication would attract illegal parties’ attention and invite a danger of being decrypted or even being destroyed. Steganography, a branch of information hiding techniques, is another way for secure communication. The main idea of steganography is to embed the secret information into an unrelated plain digital media, such as an image, a piece of video or audio, and transmit this slightly altered digital media to the intended recipient without attracting illegal observers’ attention, so that the recipient can get the sensitive information secretly. Apparently, the advantage of steganography is that it successfully covers the fact that some sensitive information is being transmitted, so that this method can avoid attracting attackers’ attention. This method not only is simple but also maintains good visual or aural quality. But regular steganography also faces a risk that the secret information might be extract illegally by a third party when he knows the very steganography protocol. Considering the respective advantages and disadvantages of steganography and cryptography, we can naturally get an idea that combining them in practice, then the new method would simultaneously possess the advantages of steganography and cryptography while avoid the respective defects. And there have been a lot of works applying this idea and one may refer to [1-8], they encrypt the secret information firstly and then hide them in the digital media. But the common thing is that they all do the encryption and hiding separately. And to our knowledge, there has no study on doing them simultaneously up until now. In this paper, we proposed a novel method doing encryption and hiding at the same time, organically combining steganography and cryptography. This protocol is based on the LSB matching method which is very popular in steganography and Boolean functions which is widely used in cryptography. It not only is easy to be implemented, but also needs less computation than the previous works do while maintaining high secure quality. The rest of the paper is organized as follows. Section 2 recalls the basic concepts，denotation and properties. Section 3 proposes a new secure communication protocol combining the LSB matching method and the Boolean functions. In Section 4, we make brief comments on this protocol. Finally, Section 5concludes this paper.

2. Preliminaries In this paper, we partially borrow the idea of LSB Matching and the usage of Boolean functions in stream cipher. Before presenting our protocol, we recall the basic concepts, denotation and properties of LSB Matching method and Boolean functions in this section.

Shouchao Song et al. / Procedia Engineering 15 (2011) 2767 – 2772 Shouchao Song et al. / Procedia Engineering 00 (2011) 000–000

2.1. LSB Matching In this paper, we focus on grayscale images. The gray value, ranged from 0 to 255, of each pixel is represented in an 8-bit binary form in the computer. Apparently, these 8 bits weigh differently in significance in view of presenting the gray degree, and the higher the bit is, the more significant it is. We call the lowest bit Least Significant Bit (abbreviated as LSB). It is easy to see that the visual quality of the image is less sensitive to the change of the lower bits, as is the theory foundation of LSB Replacement and LSB Matching. LSB Matching [1] which is developed from LSB Replacement method is very a popular steganography method in image media. And it not only maintains the favorable characteristics of LSB Replacement method, but also has better performance on resisting attacks and detecting [1]. The main idea of LSB Matching is related as follows. In LSB Matching embedding algorithm, one compare the LSB of each pixel with the secret bit one by one, if they are equal, do nothing; else, pseudorandomly make a decrement or increment on the gray value. And in decoding algorithm, the recipient can get the hided secret bits directly from the LSB of the received image. Initial images for covering are called cover images, and the images embedded with secret information are called stego images. 2.2. Boolean functions Boolean functions are widely used in cryptography, especially in stream ciphers, and have received lots of attention [9-11] on them. Let Fn be the finite field of characteristic of 2 and F2n be the n -dimensional vector space over F2 . Then an n -variable Boolean functions is defined as a mapping from F2n to F2 . The set of all n -variable Boolean functions is denoted by Bn . We denote the addition modulo 2 by the symbol “ ⊕ ” and regular addition by “ + ”. And for convenience, we abbreviate f ( x1 , x2 ,L , xn ) as f n or f , if there is no confusion. As is well known, any function f n admits a unique multivariate polynomialn over F2 : 2 −1 f ( x1 , x2 ,L , xn ) = ∑ i = 0 ai ( x1 )i1 ( x2 )i2 L ( xn )in where ai ∈ F2 , and i1i2 L in is the binary representation of i . Any n -variable Boolean function can be represented as a 2n -length binary vector, which is called its truth table: → f = [ f (0, 0,L , 0), f (1, 0,L , 0),L , f (1,1,L ,1)] We say f is balanced, if its truth table has equal number of 1 and 0.

3. A novel secure communication protocol Assume Alice wants to send an N -length secret bit stream M to Bob secretly. According to Kerckhoffs’ principle [12] in using keys for secure communication, it is presumed that the sender and the intended recipient share an 8-variable balanced Boolean function as the secret key. 3.1. For the sender It is easy for Alice to get a matrix C p×q from the cover grayscale image which has p rows and q columns of pixels, ( p × q) > N . Elements of C p×q are the gray values of the corresponding pixels from the cover image. For the convenience of describing, we denote M = m0 m1 L mN −1 , mi ∈ F2 , and

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L c1 c2 cq ⎡ ⎤ ⎢ c ⎥ L c c (1× q ) +1 (1× q ) + 2 (1× q ) + q ⎥ C p×q = ⎢ ⎢ ⎥ M M O M ⎢ ⎥ ⎣⎢ c(( p −1)×q ) +1 c(( p −1)× q ) + 2 L c(( p −1)×q ) + q ⎦⎥ where the 8-bit binary representation of ci is ci =i8i7 Li1 . Then the process of manipulation by the sender can be stated as follows: Step 1: find the function value: f ci = f ( i1 , i2 ,L , i8 ) , i = 1, 2,L , N ; Step 2: generate a bit stream H =h0 , h1 , L , hN −1 : hi = mi ⊕ f ci+1 , i = 0,1,L , N − 1 ; Step 3: construct a new matrix C ' p× q : L c2 ' cq ' ⎤ ⎡ c1 ' ⎢ c c(1×q ) + 2 ' L c(1× q ) + q ' ⎥⎥ (1× q ) +1 ' C p× q ' = ⎢ ⎢ ⎥ M M O M ⎢ ⎥ ⎣⎢ c(( p −1)× q ) +1 ' c(( p −1)×q ) + 2 ' L c(( p −1)× q ) + q '⎦⎥

where i =1 ⎧ci ⎪c 2 ≤ i ≤ N − 1, ci mod 2 = hi ⎪ i ⎪c − 1 2 ≤ i ≤ N − 1, ci = 255, hi = 0 ci ' = ⎨ i ⎪c + 1 2 ≤ i ≤ N − 1, ci = 0, hi = 1 ⎪ i f ci −1 ⎪⎩ci + (−1) else Step 4: replace the gray value of each pixel of the cover image by the corresponding value of the matrix C ' p× q . Then the image obtained, whose gray-value matrix is C ' p× q , is the stego image to transmit.

3.2. For the recipient Step 1: Attract the gray-value matrix R ' p× q from the received image; r1 ' r2 ' rq ' ⎤ L ⎡ ⎢ r r(1× q ) + 2 ' L r(1×q ) + q ' ⎥⎥ (1× q ) +1 ' R p× q ' = ⎢ ⎢ ⎥ M M O M ⎢ ⎥ ⎣⎢ r(( p −1)× q ) +1 ' r(( p −1)× q ) + 2 ' L r(( p −1)×q ) + q '⎦⎥ Step 2: get the hided bit stream T =t0 , t1 , L , t N −1 , where ti = ri + 2 mod 2 , i = 0,1,L , N − 1 ; Step 3: find the function value: f ri = f ( i1 , i2 ,L , i8 ) , i = 1, 2,L , N − 1 ; Step 4: generate the bits stream S =s0 , s1 ,L , sN −1 : si = ti ⊕ f ri+1 , i = 0,1,L , N − 1 . In fact, the bit stream S is the secret information communicated, as accomplishes the decoding.

4. Comments on this protocol In this section, we analysis the protocol proposed in Section 3, and our comments on it are made as follows: • This protocol is easy to be implemented, as can be seen from the process presented in Section 3; • This protocol has almost optimal embedding ratio. Every pixel can be used for hiding secret bit except the first one.

Shouchao Song et al. / Procedia Engineering 15 (2011) 2767 – 2772 Shouchao Song et al. / Procedia Engineering 00 (2011) 000–000

• It needs less computation than the existing methods do while maintaining high visual quality. Unlike the existing methods of doing the encrypting and hiding separately, this protocol accomplishes the encryption and hiding at the same time. • In this protocol, an 8-variable Boolean function is used as a key shared by the sender and the recipient securely prior to communicating. The requirement of an initial secure exchange may seem undesirable at first sight, but considering that the intended recipient would be no wiser than the illegal observer about which media the secret has been hided, so they need do the negotiation at first, then it is reasonable for them to share the Boolean function used secretly; • As can be seen, this protocol provides double protection for the secret information. It organically combines steganography and cryptography techniques, so it simultaneously possesses the advantages of steganography and cryptography. Encryption provides another level of security in case of a successful stego attack; • It is highly robust to resist regular steganalysis, such asχ2 –analysis [13,14,17] ,RS analysis[15], GPC analysis[16]. • The original cover image is not required for the recipient to restore the secret information.

5. Conclusion In this paper, we focused on grayscale images, and proposed a new secure communication protocol that organically combines steganography and cryptography techniques. This protocol, based on the LSB matching steganography method and the well developed Boolean functions in stream ciphers, simultaneously possesses the advantages of steganography and cryptography. And this protocol, unlike the traditional methods of doing the encrypting and hiding separately, accomplishes encryption and hiding at the same time, so it needs less computation than the existing methods do while maintaining high visual quality. This method not only is easy to be implemented, but also has almost optimal embedding ratio, what’s more, it is highly robust to resist regular steganalysis, such as RS analysis, GPC analysis, χ2 –analysis. Acknowledgements

The authors would like to thank all the anonymous reviewers for their valuable comments and advice on this manuscript. And this work is supported by National Natural Science Foundation of China (Grant Nos. 60873191，60903152, 61003286, 60821001) and the Fundamental Research Funds for the Central Universities (Grant Nos. BUPT2011YB01, BUPT2011RC0505). References [1] T. Sharp. An implementation of key-based digital signal steganography. Proc. 4th. Information Hiding Workshop, LNCS, vol. 2137, Berlin: Springer-Verlag, 2001, pp. 13–26. [2] R.Z. Wang, C.F. Lin, J.C. Lin. Image hiding by optimal LSB substitution and genetic algorithm. Pattern Recognition. Vol.34 (3), 2001, pp. 671–683. [3] X.L. Li, B. Yang, D.F. Cheng, T.Y. Zeng. A Generalization of LSB Matching. Signal Processing Letters, IEEE, Vol. 16(2), 2009, pp. 69-72. [4] C.K. Chan, L.M. Chen. Hiding data in images by simple LSB substitution. Pattern Recognition. Vol.37 (3), 2004, pp. 469– 474.

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[5] K. Bhowal, A.J. Pal, G.S. Tomar, P.P.Sarkar. Audio Steganography Using GA. Computational Intelligence and Communication Networks (CICN), 2010 International Conference on. 2010, pp.449-453. [6] J.K.Mandal, M.Sengupta. Steganographic Technique Based on Minimum Deviation of Fidelity (STMDF). Emerging Applications of Information Technology (EAIT), 2011 Second International Conference on. 2011, pp. 298-301. [7] I.C. Lin, Y.B. Lin, C.M. Wang. Hiding data in spatial domain images with distortion tolerance, Comput. Stand. Inter. Vol.31 (2), 2009, pp.458–464. [8] ZHANG Xin-peng; WANG Shuo-zhong. Steganography using multiple-base notational system and human vision sensitivity, Signal Processing Letters, IEEE, 2005 . Vol. 12(1), pp.67 - 70. [9]W.C. Thomas, S. Pantelimon. Cryptographic Boolean functions and applications. Elsevier: Academic Press, first edition 2009, pp.119-156. [10] S.S. Song, J. Zhang, J. Du, Q.Y. Wen. On the construction of Boolean functions with optimal algebraic immunity and good other properties by concatenation, Progress in Informatics and Computing (PIC), 2010 IEEE International Conference on, Volume 1, pp: 417 – 422. [11] C. Carlet, K. Q. Feng. New balanced Boolean functions satisfying all the main cryptographic criteria [EB/OL]. http://eprint.iacr.org/2008/244.pdf. [12] A. Kerckhoffs. La cryptographie militaire. Journal des Sciences Militaries, Vol.4(1), 1883, pp.5-38. [13] Westfeld A. Detecting Low Embedding Rates. Proc. 5th. Information Hiding Workshop, LNCS，Vol.2578， Berlin: Springer-Verlag, 2003, pp.324-339. [14] Westfeld A, Pfitzmann A. Attacks on Steganographic Systems, Proc. 3rd. Information Hiding Workshop, LNCS,Vol.1768, Berlin: Springer-Verlag, 2000, pp.61-76. [15] Fridrich J, Goljan M, Du R. Detecting LSB steganography in color and gray-scale images. IEEE Multimedia, 2001, Vol.8(4), pp.22-28. [16] ZHANG Xin-peng; WANG Shuo-zhong, ZHANG Kai-wen . Steganalysis Based on the Statistics Method for LSB Insertion . Journal of Applied Sciences, 2004. Vol.22(1), pp.16-19. In Chinese. [17] Ker, Andrew D. Resampling and the detection of LSB matching in color bitmaps. Security, Steganography, and Watermarking of Multimedia Contents VII. Edited by Delp, Edward J., III; Wong, Ping W. Proceedings of the SPIE, 2005, Vol.5681, pp. 1-15.