Hiding data in images by simple LSB substitution

Transcription

1 Pattern Recognton 37 (004) Hdng data n mages by smple LSB substtuton Ch-Kwong Chan, L.M. Cheng Department of Computer Engneerng and Informaton Technology, Cty Unversty of Hong Kong, Hong Kong Receved 17 May 00; receved n revsed form 11 July 003; accepted 11 August 003 Abstract In ths paper, a data hdng scheme by smple LSB substtuton s proposed. By applyng an optmal pxel adjustment process to the stego-mage obtaned by the smple LSB substtuton method, the mage qualty of the stego-mage can be greatly mproved wth low extra computatonal complexty. The worst case mean-square-error between the stego-mage and the cover-mage s derved. Expermental results show that the stego-mage s vsually ndstngushable from the orgnal cover-mage. The obtaned results also show a sgncant mprovement wth respect to a prevous work.? 003 Pattern Recognton Socety. Publshed by Elsever Ltd. All rghts reserved. Keywords: Data hdng; LSB substtuton 1. Introducton Data hdng s a method of hdng secret messages nto a cover-meda such that an unntended observer wll not be aware of the exstence of the hdden messages. In ths paper, 8-bt grayscale mages are selected as the covermeda. These mages are called cover-mages. Cover-mages wth the secret messages embedded n them are called stego-mages. For data hdng methods, the mage qualty refers to the qualty of the stego-mages. In the lterature, many technques about data hdng have been proposed [1 5]. One of the common technques s based on manpulatng the least-sgncant-bt (LSB) planes by drectly replacng the LSBs of the cover-mage wth the message bts. LSB methods typcally acheve hgh capacty. Wang et al. [6] proposed to embed secret messages n the moderately sgncant bt of the cover-mage. A genetc algorthm s developed to nd an optmal substtuton matrx for the embeddng of the secret messages. They also proposed to use a local pxel adjustment process (LPAP) to mprove the mage qualty of the stego-mage. Unfortunately, Correspondng author. E-mal address: kwong.chan@alumn.ctyu.edu.hk (C.-K. Chan). snce the local pxel adjustment process only consders the last three least sgncant bts and the fourth bt but not on all bts, the local pxel adjustment process s obvously not optmal. The weakness of the local pxel adjustment process s ponted out n Ref. [7]. As the local pxel adjustment process modes the LSBs, the technque cannot be appled to data hdng schemes based on smple LSB substtuton. Recently, Wang et al. [8] further proposed a data hdng scheme by optmal LSB substtuton and genetc algorthm. Usng the proposed algorthm, the worst mean-square-error (WMSE) between the cover-mage and the stego-mage s shown to be 1 of that obtaned by the smple LSB substtuton method. In ths paper, a data hdng scheme by smple LSB substtuton wth an optmal pxel adjustment process (OPAP) s proposed. The basc concept of the OPAP s based on the technque proposed n Ref. [7]. The operatons of the OPAP s generalzed. The WMSE between the cover-mage and the stego-mage s derved. It s shown that the WMSE obtaned by the OPAP could be less than 1 of that obtaned by the smple LSB substtuton method. Expermental results demonstrate that enhanced mage qualty can be obtaned wth low extra computatonal complexty. The results obtaned also show better performance than the optmal substtuton method descrbed n Ref. [8] /$30.00? 003 Pattern Recognton Socety. Publshed by Elsever Ltd. All rghts reserved. do: /j.patcog

2 470 C.-K. Chan, L.M. Cheng / Pattern Recognton 37 (004) The rest of the paper s organzed as follows. Secton brey descrbes the smple LSB substtuton. In Secton 3, the optmal pxel adjustment process s descrbed and the performance s analyzed. Expermental results are gven n Secton 4. Fnally, Secton 5 concludes ths paper. Table 1 Worst PSNR for k = 1 5 by smple LSB substtuton k PSNR Data hdng by smple LSB substtuton In ths secton, the general operatons of data hdng by smple LSB substtuton method s descrbed. Let C be the orgnal 8-bt grayscale cover-mage of M c N c pxels represented as C = {x j 0 6 M c; 0 6 j N c; x j {0; 1;:::;55}}: (1) M be the n-bt secret message represented as M = {m 0 6 n; m {0; 1}}: () Suppose that the n-bt secret message M s to be embedded nto the k-rghtmost LSBs of the cover-mage C. Frstly, the secret message M s rearranged to form a conceptually k-bt vrtual mage M represented as M = {m 0 6 n ;m {0; 1;:::; k 1}}; (3) where n M c N c. The mappng between the n-bt secret message M = {m } and the embedded message M = {m } can be dened as follows: k 1 m = m k+j k 1 j : j=0 Secondly, a subset of n pxels {x l1 ;x l ;:::;x ln } s chosen from the cover-mage C n a predened sequence. The embeddng process s completed by replacng the k LSBs of x l by m. Mathematcally, the pxel value x l of the chosen pxel for storng the k-bt message m s moded to form the stego-pxel x l as follows: x l = x l x l mod k + m : (4) In the extracton process, gven the stego-mage S, the embedded messages can be readly extracted wthout referrng to the orgnal cover-mage. Usng the same sequence as n the embeddng process, the set of pxels {x l 1 ;x l ;:::;x l n } storng the secret message bts are selected from the stego-mage. The k LSBs of the selected pxels are extracted and lned up to reconstruct the secret message bts. Mathematcally, the embedded message bts m can be recovered by m = x l mod k : (5) Suppose that all the pxels n the cover-mage are used for the embeddng of secret message by the smple LSB substtuton method. Theoretcally, n the worst case, the PSNR of the obtaned stego-mage can be computed by 55 PSNR worst =10 log 10 WMSE 55 =10 log 10 db: (6) ( k 1) Table 1 tabulates the worst PSNR for some k = 1 5. It could be seen that the mage qualty of the stego-mage s degraded drastcally when k Optmal pxel adjustment process In ths secton, an optmal pxel adjustment process (OPAP) s proposed to enhance the mage qualty of the stego-mage obtaned by the smple LSB substtuton method. The basc concept of the OPAP s based on the technque proposed n Ref. [7]. Let p, p and p be the correspondng pxel values of the th pxel n the cover-mage C, the stego-mage C obtaned by the smple LSB substtuton method and the re- ned stego-mage obtaned after the OPAP. Let = p p be the embeddng error between p and p. Accordng to the embeddng process of the smple LSB substtuton method descrbed n Secton, p s obtaned by the drect replacement of the k least sgncant bts of p wth k message bts, therefore, k k : (7) The value of can be further segmented nto three ntervals, such that Interval 1: k 1 k ; Interval : k k 1 ; Interval 3: k k 1 : (8) Based on the three ntervals, the OPAP, whch mod- es p to form the stego-pxel p, can be descrbed as follows: Case 1( k 1 k ): If p k, then p = p k ; otherwse p = p ; Case ( k k 1 ): p = p ; Case 3( k k 1 ): If p 56 k, then p = p + k ; otherwse p = p.

3 C.-K. Chan, L.M. Cheng / Pattern Recognton 37 (004) Let = p p be the embeddng error between p and. can be computed as follows: Case 1( k 1 k and p k ) p = p p = p k p = k k 1 k k k k 1 0: Case ( k 1 k and p k ) = p p = p p = k 1 k : Case 3( k k 1 ) = p p = p p = k k 1 : Case 4( k k 1 and p 56 k ) = p p = p + k p = + k k + k k 1 + k 0 k 1 : Case 5( k k 1 and p 56 k ) = p p = p p = k k 1 : From the above ve cases, t can be seen that the absolute value of may fall nto the range k 1 k only when p k (Case ) and p 56 k (Case 5); whle for other possble values of p, falls nto the range k 1. Because p s obtaned by the drect replacement of the k LSBs of p wth the message bts, p k and p 56 k are equvalent to p k and p 56 k, respectvely. In general, for grayscale natural mages, when k 6 4, the number of pxels wth pxel values smaller than k or greater than 56 k s nsgnfcant. As a result, t could be estmated that the absolute embeddng error between pxels n the cover-mage and n the stego-mage obtaned after the proposed OPAP s lmted to Combnng Eqs. (6) and (10), we have WMSE = (k 1 ) ( k 1) WMSE = WMSE when k =1; 4 WMSE when k =; 9 16 WMSE when k =3; WMSE when k =4: 5 (11) Eq. (11) reveals that WMSE 1 WMSE, for k ; and WMSE 1 WMSE when k = 4. Ths result also shows 4 that the WMSE obtaned by the OPAP s better than that obtaned by the optmal substtuton method proposed n Ref. [8] n whch WMSE = 1 WMSE. Moreover, the optmal pxel adjustment process only requres a checkng of the embeddng error between the orgnal cover-mage and the stego-mage obtaned by the smple LSB substtuton method to form the nal stego-mage. The extra computatonal cost s very small compared wth Wang s method [8] whch requres huge computaton for the genetc algorthm to nd an optmal substtuton matrx. 4. Expermental results Ths secton presents expermental results obtaned for two cover-mage sets. The rst set of cover-mages conssts of four standard grayscale mages, Lena, Baboon, Jet and Scene, each of pxels, as depcted n Fg. 1. The second set conssts of 1000 randomly k 1 : (9) Let WMSE and WMSE be the worst case mean-squareerror between the stego-mage and the cover-mage obtaned by the smple LSB substtuton method and the proposed method wth OPAP, respectvely. Accordng to Eq. (9) WMSE can be derved by WMSE 1 = M c N c M c N c 1 =0 ( k 1 ) =( k 1 ) : (10) Fg. 1. The rst set cover-mages of sze pxels.

4 47 C.-K. Chan, L.M. Cheng / Pattern Recognton 37 (004) Fg.. Test mage used as the second set of secret message. generated grayscale mages. There are two set of secret messages. The rst set of secret message conssts of 1000 randomly generated message of k bts, where k refers to the number of LSBs n the cover mage pxels that are used to hold the secret data bts. For example, suppose that the last two LSBs of the cover mage pxels are used to hold the secret data, then the secret data s of sze = bts. The second set conssts of the reduced-szed mages of the grayscale mage T as shown n Fg.. The reduced-szed mages are of sze pxels (for 4-bt nserton), pxels (for 3-bt nserton), pxels (for -bt nserton) and pxels (for 1-bt nserton), respectvely. The results of embeddng the rst set of secret messages nto the rst set of cover-mages are lsted n Table. Referrng to Table, the column labeled OPAP s our proposed method wth the optmal pxel adjustment process; the column labeled LSB s the smple LSB substtuton method; and the column labeled OLSB n the optmal LSB substtuton method proposed n Ref. [8]. For the OPAP and LSB methods, the obtaned PSNR values are the average values of embeddng the 1000 sets random messages nto the cover-mages. For the OLSB method, for k =1;, the obtaned PSNR values are the average values of embeddng the 1000 sets random messages nto the cover-mages, for k = 3, the obtaned PSNR values are the average values of embeddng the 10 out of 1000 sets random messages nto the cover-mages whle for k = 4, no experments are conducted due to the large number of searchng space for the optmal substtuton matrx. The results reveal that our proposed method has much better performance than the LSB and OLSB methods for k = 4. The results of embeddng the reduced-szed mage of Fg. nto the rst set of cover-mages are lsted n Table 3. The results also reveal that our proposed method has much better performance than the LSB and OLSB methods for k = 4. Table 4 also shows the percentage of cover mage pxels assocated wth the ve cases: Case 1 ( k 1 k and p k ); Case ( k 1 k and p k ); Case 3 ( k k 1 ); Case 4 ( k k 1 and p 56 k ); Case 5 ( k k 1 and p 56 k ): (1) Table The results of embeddng the random messages nto the rst set of cover-mages Cover mage k OPAP LSB OLSB Lena Baboon Jet Scene

5 C.-K. Chan, L.M. Cheng / Pattern Recognton 37 (004) Table 3 The results of embeddng the reduced-szed mage of Fg. nto the rst set of cover-mages Cover mage k OPAP LSB OLSB Lena Baboon Jet Scene Table 4 The percentage of cover mage pxels assocated wth the ve cases (Eq. (1)) when the reduced-szed mages of Fg. are embedded nto the cover-mages Cover mage k Case 1 (%) Case (%) Case 3 (%) Case 4 (%) Case 5 Lena Baboon Jet Scene when the reduced-szed mages of Fg. are embedded nto the cover-mages. For llustratve purpose, Fg. 3 shows a par of stego-mages obtaned by embeddng the reduced-szed mage T of sze pxels nto the cover-mage Lena of sze pxels usng the smple LSB method and the proposed OPAP method. From Fg. 3(a) (stego-mage obtaned by the smple LSB-substtuton method), one can see some false contours appearng on the shoulder of Lena. The unwanted artfacts may arse suspcon and defeat the purpose of steganography. However, there s no such artfacts appearng on the stego-mage (Fg. 3(b)) obtaned by the proposed method. The vsual qualty of stego-mages obtaned by the proposed method are much better than that of obtaned by the smple LSB-substtuton method. To further evaluate the performance of the proposed method, the reduced-szed mage of Fg. are embedded nto 1000 sets randomly generated cover-mages and the obtaned average PSNR values are lsted n Table 5. The

6 474 C.-K. Chan, L.M. Cheng / Pattern Recognton 37 (004) (a) (b) Fg. 3. Stego-mages obtaned by (a) Smple LSB-substtuton method; (b) proposed method, where the secret-mage s of sze pxels (4-bt nserton). Table 5 The results of embeddng the reduced-szed mage of Fg. nto the second set of cover-mages Cover mage k OPAP LSB Random results show that smlar PSNR values can be obtaned for derent type of cover-mages. 5. Concluson In ths paper, a data hdng method by smple LSB substtuton wth an optmal pxel adjustment process s proposed. The mage qualty of the stego-mage can be greatly mproved wth low extra computatonal complexty. Extensve experments show the eectveness of the proposed method. The results obtaned also show sgncant mprovement than the method proposed n Ref. [8] wth respect to mage qualty and computatonal ecency. References [1] A.Z. Trkel, R.G. Van Schyndel, C.F. Osborne, A dgtal watermark, Proceedngs of ICIP 1994, Austn Conventon Center, Austn, Texas, Vol. II, 1994, pp [] W. Bender, N. Mormoto, A. Lu, Technques for data hdng, IBM Syst. J. 35 (3/4) (1996) [3] T.S. Chen, C.C. Chang, M.S. Hwang, A vrtual mage cryptosystem based upon vector quantzaton, IEEE Trans. Image Process. 7 (10) (1998) [4] L.M. Marvel, C.G. Boncelet, C.T. Retter, Spread spectrum mage steganography, IEEE Trans. Image Process. 8 (8) (1999) [5] K.L. Chung, C.H. Shen, L.C. Chang, A novel SVD- and VQ-based mage hdng scheme, Pattern Recognton Lett. (9) (001) [6] Ran-Zan Wang, Ch-Fang Ln, Ja-Chen Ln, Hdng data n mages by optmal moderately sgncant-bt replacement, IEE Electron. Lett. 36 (5) (000) [7] Ch-Kwong Chan, L.M. Cheng, Improved hdng data n mages by optmal moderately sgncant-bt replacement, IEE Electron. Lett. 37 (16) (001) [8] Ran-Zan Wang, Ch-Fang Ln, Ja-Chen Ln, Image hdng by optmal LSB substtuton and genetc algorthm, Pattern Recognton 34 (3) (001) About the Author CHI-KWONG CHAN receved the B.Eng. and M.Phl. degrees n Electronc Engneerng and the Ph.D. degree n Computer Engneerng and Informaton Technology from Cty Unversty of Hong Kong n 1996, 1999, and 003, respectvely. Hs research nterests nclude securty, mage processng, neural networks, and FPGA mplementaton. About the Author L.M. CHENG receved the B.Sc. degree n Physcs and Computer Scence and the Ph.D. degree from Kng s College London (prevously Queen Elzabeth College), Unversty of London n 1979 and 198, respectvely. He had been employed as a research fellow at Kng s College, London, Prncpal Engneer of ERA Technology Ltd. UK, and Project Manager and Senor Consultant at Logca Space and Defence Systems Ltd. UK. He joned Cty Unversty of Hong Kong n 1989 and s now an Assocate Professor at the Cty Unversty of Hong Kong. Hs research nterests nclude mage processng, securty, and neural network.