Article Reversible Dual-Image-Based Hiding Scheme Using Block Folding Technique

Artcle Reversble Dual-Image-Based Hdng Scheme Usng Block Foldng Technque Tzu-Chuen Lu, * and Hu-Shh Leng Department of Informaton Management, Chaoyang Unversty of Technology, Tachung 4349, Tawan Department of Mathematcs, Natonal Changhua Unversty of Educaton, Changhua 50058, Tawan; lenghs@cc.ncue.edu.tw * Correspondence: tclu@cyut.edu.tw; Tel.: +886-4-333000 (ext. 4558) Receved: 9 September 07; Accepted: 9 October 07; Publshed: October 07 Abstract: The concept of a dual-mage based scheme n nformaton sharng conssts of concealng secret messages n two cover mages; only someone who has both stego-mages can extract the secret messages. In 05, Lu et al. proposed a center-foldng strategy where each secret symbol s folded nto the reduced dgt to reduce the dstorton of the stego-mage. Then, n 06, Lu et al. used a frequency-based encodng strategy to reduce the dstorton of the frequency of occurrence of the maxmum absolute value. Because the foldng strategy can obvously reduce the value, the proposed scheme ncludes the foldng operaton twce to further decrease the reduced dgt. We use a frequency-based encodng strategy to encode a secret message and then use the block foldng technque by performng the center-foldng operaton twce to embed secret messages. An ndcator s needed to dentfy the sequence number of the foldng operaton. The proposed scheme collects several ndcators to produce a combned code and hdes the code n a pxel to reduce the sze of the ndcators. The expermental results show that the proposed method can acheve hgher mage qualty under the same embeddng rate or hgher payload, whch s better than other methods. Keywords: dual stego-mages; nformaton hdng; center-foldng strategy; block foldng. Introducton Informaton hdng s a technque that conceals secret messages n dgtal meda. The sender embeds secret messages n a cover mage to generate a stego-mage and then sends t to the recever. The recever can extract the secret messages from the stego-mage (Fgure ). Fgure. Dagram of the nformaton hdng process. Symmetry 07, 9, 3; do:0.3390/sym9003 www.mdp.com/journal/symmetry

Symmetry 07, 9, 3 of 5 In general, nformaton hdng schemes can be classfed nto two categores,.e., reversble data hdng and rreversble data hdng, as shown n Fgure. The most commonly used rreversble data hdng methods nclude the least sgnfcant bt (LSB) substtuton method, the pxel-value dfferencng (PVD) method, and the explotng modfcaton drecton method (EMD) [ 4]. The LSB method s a well-known rreversble data hdng technque because of ts hgh payload and low dstorton. It drectly replaces the bts of the cover pxel wth secret bts for embeddng. Melkanen (006) proposes a modfcaton to the LSB method called LSB matchng []. In hs method, the secret bts are embedded by usng the bnary functon and four embeddng rules. Fgure. Informaton hdng categores. LSB: least sgnfcant bt substtuton method, PVD: the pxelvalue dfferencng method, EMD: the explotng modfcaton drecton method, DE: dfference expanson, HS: hstogram shftng, PVO: pxel-value orderng method. Wu and Tsa (003) proposed the PVD method []. In ther method, the dfference of two pxels n the cover mage s calculated to determne the number of bts to be embedded n these two pxels and a pre-defned range table. The technque can embed a large number of secret bts nto the cover mage wth hgh mperceptblty as t makes use of the characterstc of human vson senstvty. Chang and Tseng (004) utlzed the dfference of the predcted value and the target pxels to estmate the degree of smoothness or contrast of pxels to determne the number of bts to be embedded n the target pxels [3]. Zhang and Wang (006) proposed the EMD method [4]. The EMD method provdes a good mage qualty for the stego-mage wth a peak sgnal-to-nose rato (PSNR) of more than 5 db, snce, at most, only one pxel n each pxel group needs to be ncreased or decreased by one. Keu and Chang (0) mproved the EMD method by explotng eght modfcaton drectons to embed several secret bts nto a cover par at a tme [5]. Compared wth rreversble data hdng schemes, reversble data hdng schemes can recover the cover mage wthout any dstorton from the stego-mage after the secret messages have been extracted. The most commonly used reversble data hdng methods nclude the dfference expanson (DE) method, hstogram shftng (HS) method, and pxel-value orderng (PVO) method. Tan (003) proposed the DE method [6] that embeds a secret bt nto the LSB of the expanded dfference of each pxel par of the cover mage. The scheme provdes a hgh payload; however, the dstorton caused by the DE s sgnfcant. Alattar (004) mproved Tan s scheme wth double the respectve dfferences between four neghborng pxels and acheved more secret bts wth the expanded dfference [7]. N et al. (006) proposed the HS method n 006 [8]. Ther method s to frstly generate the hstogram by the pxel ntensty value and shft the bns between the zero and peak pont to create empty bns for data embeddng. The advantage of the HS method s ts low dstorton; however, ts drawback s a low payload, because the embeddng capacty s determned by the number of ponts

Symmetry 07, 9, 3 3 of 5 n the peak pont of the bn. L et al. and Gu et al. proposed an adaptve embeddng technque that dvdes pxels nto dfferent types to enhance the embeddng capacty of a predcton error [9,0]. L et al. (03) proposed the PVO method []. In ther method, for each block, the pxels are reordered nto a pxel vector, then the smallest pxel s predcted by the second smallest pxel, and the largest pxel s predcted by the second largest pxel. It uses predcton errors and to embed data, whereas predcton error 0 s unchanged. Peng et al. (04) mproved the PVO method to use larger blocks for embeddng and take better advantage of mage redundancy to yeld a hgher PSNR []. Qu and Km (05) modfed the PVO method so that each pxel s predcted usng ts sorted context pxels to acheve a better embeddng capacty n smooth mage regons [3]. Wang et al. (05) used a dynamc blockng strategy to dvde the cover mage adaptvely nto varous-szed blocks. Thus, the flat mage areas are preferentally dvded nto smaller blocks to retan a hgh embeddng capacty and the rough areas are dvded nto larger blocks to avod decreasng PSNR value [4]. The dual-mage-based hdng scheme s a new technology n the nformaton hdng feld. The concept of dual-mage, based on nformaton sharng, conssts of concealng secret messages n two of the same cover mages; only someone who has both stego-mages can extract the secret messages. A dagram of the dual-mage based hdng scheme s shown n Fgure 3. There are many advantages to usng dual-mage n data hdng, such as a hgh payload, reversblty, and strong robustness. (a) (b) Fgure 3. Dual-mage based hdng scheme. (a) Embed secret messages nto two of the same cover mages; (b) Extract secret messages from the two stego-mages. In the dual-mage-based hdng scheme, mage qualty and payload are affected by embeddng rules [5 ]. Chang et al. (007) combned the EMD method wth the dual-mage technque to

Symmetry 07, 9, 3 4 of 5 acheve a hgh payload and reduce dstorton [5]. Lee et al. (009) used combnatons of pxel orentaton locatons wth dual-mage to enhance embeddng capacty and preserve good vsual qualty [6]. Lee and Huang (03) converted secret messages nto qunary-based secret symbols and combned every two secret symbols as a set embedded n the dual-mage [7]. Chang et al. (03) converted secret messages nto decmal-based secret symbols, then embedded secret symbols n a rght dagonal lne [8]. Qn et al. (04) embedded secret messages n the frst mage usng the EMD method and n the second mage usng other rules that were dependent on the frst mage [9]. Lu et al. (05) used the LSB matchng method and modfed the non-reversble stego-pxels based on a rule table to restore the cover mage [0]. They proposed the center-foldng strategy to reduce the value of the secret symbols. Then, they embedded secret symbols n two stego-mages through an averagng method []. Lu et al. (06) proposed a frequency-based encodng method to reduce the dstorton derved by the maxmum secret dgt []. In [], Lu et al. propose a center-foldng strategy n whch each secret symbol s folded nto the reduced dgt before the embeddng procedure to reduce the dstorton of the stego-mage. The foldng strategy s smple and effectve, to the extent that the mage qualty of the stego-mage s very good. Because the foldng strategy can obvously reduce the value, the proposed scheme performs the foldng operaton twce to further decrease the reduced dgt. Furthermore, n [], Lu et al. use a frequency-based encodng strategy to reduce the dstorton of the frequency of occurrence of the maxmum absolute value. The re-encoded technque also can be used to reduce the number of the secret dgt and narrow down the dstance between the stegopxel and the orgnal pxel. Therefore, the proposed scheme frst uses a frequency-based encodng strategy to encode the secret message and then uses the block foldng technque by ncludng the center-foldng operaton twce to embed secret messages. In addton, several steganalyss technques are used to prove the strong robustness of the proposed scheme, ncludng hstogram steganalyss, Regular and sngular groups (RS) steganalyss [3], prmary sets, Ch square, sample pars RS analyss, and fuson detecton [4]. The rest of ths paper s organzed as follows. Secton descrbes related works. Secton 3 ntroduces the proposed scheme. Secton 4 summarzes the experment results. The conclusons are presented n Secton 5.. Related Works In ths secton, we brefly ntroduce Lee et al. s scheme, the center-foldng strategy, and the frequency-based encodng strategy... Lee et al. s Methods Lee et al. [6,7] proposed a drecton-based dual-mage method. In ther scheme, two pxels P and P are used to conceal four secret bts and a drecton map s used to represent the embeddng rules. Fgure 4 shows the drecton map. Suppose that two pxels are P = 5, P = 0 and the secret bts are 00. The drecton map ndcates that P = P + = 5 + = 6 and P = 0 for embeddng 00 n the frst stego-mage. If the next two secret bts are 0, then the stego-pxels are P = P = 5 and P = P + = 0 + = for the second stego-mage.

Symmetry 07, 9, 3 5 of 5 Fgure 4. Drecton-based embeddng rules. However, n some cases, the method cannot conceal secret data n the second stego-mage. Therefore, only the frst mage s modfed to embed the frst two secret bts. In 03, Lee and Huang mproved the above method by ncreasng the number of drecton rules from four drectons to fve drectons and redesgned the embeddng rule to ncrease the embeddng payload. The drecton map s shown n Fgure 5... Center-Foldng Strategy Fgure 5. Data embeddng method usng fve drectons. In [], Lu et al. proposed a center-foldng strategy where each secret symbol s folded nto the reduced dgt before the embeddng procedure to reduce the dstorton of the stego-mage. For example, K bts of secret data were taken as a set and converted nto the secret symbol d. The centerfoldng strategy changed the range of secret symbols from ={0,,,, } to = {, +,,,0,,,, }. The formula s as follows: d = d K, () where s a folded secret symbol and s an ntermedate value. After the foldng, the value range of the secret symbol changed to [, ]. Fgure 6 shows an example where s set to be 3. The maxmum value of the value range s 7. Assume that a pxel value s 38. If the secret symbol d = 7 s added drectly to the pxel to get the stego-pxel 38

Symmetry 07, 9, 3 6 of 5 + 7 = 45, then the mage dstorton nflcted s (45 38) =7 =49. However, n Lu et al. s scheme, the symbol s folded as = 7 = 3. The folded symbol =3 nstead of the orgnal symbol 7 s added wth the pxel 38 to get the stego-pxel 38 + 3 = 4. The mage dstorton caused by Lu et al. s method s (4 38) =3 =9. The mage dstorton s reduced from 49 to 9. Fgure 6. Example value range of the central-foldng strategy wth = 3. It s obvous that the center-foldng strategy s smple and effectve; t can reduce the dstorton of the stego-mage after the embeddng procedure. Therefore, n the proposed scheme, we perform the foldng operaton twce to further decrease the reduced dgt..3. Frequency-Based Encodng Strategy In [], Lu et al. used a frequency-based encodng strategy to reduce the dstorton of the frequency of occurrence of the maxmum absolute value. For example, suppose that the secret bt stream s 0 0 0 0 00 0. Frst, the scheme converts each three bts (K = 3) as a group to a decmal dgt stream as 7 3 7 3 5 6 7. Next, t uses the center-foldng strategy to reduce the dgt stream as 3 3 3. Then, the frequency table can be made as Table, whch records the rank of each reduced dgt and map number of ts new ndex n descendng order by occurrence frequency. Table. Example of the frequency-based encodng table (K = 3). Decmal Dgt Reduced Dgt Occurrence Frequency Order Indces 0 4 0 5 3 3 0 6 3 3 4 0 0 7 4 5 3 6 4 7 3 3 0 0 Compared wth embeddng the re-encoded secret dgt and the orgnal secret dgt, the frequency-based encodng strategy can be used to reduce the number of the secret dgt and narrow down the dstance between the orgnal pxel and the stego-pxel..4. Proposed Method In Lu s scheme, each secret symbol s reduced to the reduced dgt usng the center-foldng strategy. A dagram of Lu s center-foldng strategy s shown n Fgure 7. In the fgure, the center value 5 s subtracted from each decmal message to generate the reduced dgt. The value range of Fgure 7 can be seen as a band. The maxmum value of the band s 7 n Fgure 7. After the foldng, the band s separated nto two sub-bands. The maxmum absolute value of the two sub-bands s 4.

Symmetry 07, 9, 3 7 of 5 Fgure 7. Dagram of Lu s center-foldng strategy. Because the foldng strategy can obvously reduce the value, the proposed scheme ncludes the foldng operaton twce to further decrease the reduced dgt. The concept of the proposed scheme s shown n Fgure 8. In the fgure, the value range of s frst dvded nto two sub-bands SB and SB. Each sub-band performs a one-tme center-foldng strategy. For example, the value range of subband SB s shown n Fgure 8a. The center value of SB s. The center value s subtracted from the values n SB to generate the reduced dgt. We can see that the maxmum absolute value of the two sub-bands s, whch s smaller than the value 4 n Fgure 8. Fgure 8. Dagram of the proposed block foldng technque. However, the sub-bands SB and SB have the same reduced values. We cannot dstngush the orgnal value from. Hence, an ndcator s needed to dentfy whch sub-band the reduced value s located n. If the reduced value s located n the sub-band SB, then the ndcator s set to be 0, where =0. In contrast, f the reduced value s located n the sub-band SB, then the ndcator s set to be, where =. The orgnal value s mapped to a code par (, ) to reduce the mage dstorton. For example, the decmal value = 7 s mapped to the code par (, ) = (, ). However, the ndcator s extra nformaton that also needs to be concealed n the cover mage and wll decrease the hdng capacty. To solve ths problem, the proposed scheme collects several ndcators to produce a combned code and hdes the code n a pxel. In the proposed scheme, the cover mage s dvded nto several blocks. Each block has pxels n t. The last pxel n the block s used to embed the combned code. The other pxels are used to conceal the reduced dgt. Furthermore, the proposed scheme consders the occurrence frequency of the decmal dgt to reassgn proper code to the reduced dgt that can sgnfcantly shrnk the mage dstorton..5. Embeddng Procedure In the proposed scheme, a cover mage s dvded nto several blocks. Each block has pxels n t. Let = {,,, } be the block. A secret mage s formed as a bnary strng. The strng s separated nto several substrngs the sze of. Each substrng s transformed nto a decmal dgt. The scheme computes the occurrence frequency of each decmal dgt to generate a hstogram and sort the hstogram n descendng order. The dgt wth the maxmum frequency s I ', d ˆ'. encoded wth the smallest dstorton code par ( )

Symmetry 07, 9, 3 8 of 5 Each block can be used to hde ( ) code pars. The scheme conceals the reduced dgt n the pxel by usng an averagng method to generate the stego-pxels and, where. The ndcators are collected to form a combned code, and the code s concealed nto the last pxel of the block to generate and. Fgure 9 shows the nformaton hdng dagram of the proposed method. More detals of the procedures are gven below. Fgure 9. Informaton hdng dagram of the proposed scheme. Step : Transform a set of K secret bts nto a decmal dgt. Let d be the decmal dgt that s computed by d = where d [0, K ] and s j denotes the jth secret bt n the set. K j j s, () j= Step : Compute the occurrence frequency of each decmal dgt. Let F ( d ) be the occurrence frequency of each decmal dgt. These frequences are sorted n descendng order, and the ndex of sorted results s denoted as O ( d ). Step 3: Compute the reduced code d ˆ for each decmal dgt. In Fgure 6, the decmal dgt d has been folded twce to generate the reduced code dˆ and the ndcator I. Table shows the reduced codes and ndcators wth K = 3. The decmal dgts are reduced effectvely from [0, K ] to [ K, K ]. Table. Example code pars of Fgure 6 wth K = 3. d 0 3 4 5 6 7 I 0 0 0 0 dˆ 0 0 ( I, d ˆ ) (0, ) (0, ) (0, 0) (0, ) (, ) (, ) (, 0) (, ) However, the reduced dgts n Table do not show the feature of the secret mage. In Table, the absolutely reduced code d ˆ = s the maxmum reduced code, whch causes maxmum dstorton when drectly concealed nto the pxel. If the maxmum reduced code s occurrence

Symmetry 07, 9, 3 9 of 5 frequency s hgh, then drectly embeddng t n the mage wll decrease the vsual qualty. Hence, the proposed scheme further re-encodes the reduced code and ndcator code accordng to the order ˆ s computed by of O ( d ). The re-encoded code d where ˆ O( d) = sgn( O( d)), 4 d (3), ( v) =, f v s an odd number, sgn. (4) otherwse. Step 4: Compute the re-encoded ndcator I ' by 0, f O( d) = 0, I =, f mod( ( O( d) + ),4) = 0 or mod( O( d),4) = 0, (5) 0, otherwse. The above procedure re-encodes the reduced dgts and ndcators, whch occurs most frequently as the mnmum absolute value. The re-encoded code pars of Table are shown n Table 3. Table 3. The re-encoded code pars of Table. O ( d ) 0 3 4 5 6 7 I' 0 0 0 0 0 d ˆ 0 ( I',d' ˆ ) (0, 0) (0, ) (0, ) (, ) (, ) (0, ) (0, ) (, ) Step 5: Generate a mappng table for further embeddng and recovery processes. Integrate the reencoded code pars ( I ', d ˆ' ) wth the ndces d to form a mappng table. The mappng relatonshp must be recorded for use n the recovery phases. Table 4 shows an example mappng table wth K = 3. Table 4. Example mappng table wth K = 3. d F ( d) ( d) O I d ˆ ( I,dˆ ) 0 787,558 0 (0, ) 90,36 5 0 (0, ) 33,73 7 (, ) 3 90,853 3 (, ) 4 90,36 4 (, ) 5 34,03 6 0 (0, ) 6 90,853 0 (0, ) 7 879,3 0 0 0 (0, 0) Step 6: Step 7: Dvde a cover mage nto server blocks. Let = {,,, } be a block. Pck ( ) code pars,,,,,, to embed nto the block. () Conceal the re-encoded reduced dgt n the pxel by usng and BK = BK ˆd +, (6)

Symmetry 07, 9, 3 0 of 5 K = BK d ˆ B, (7) where, B K denotes the th pxel of the frst stego-block and B K denotes the th pxel of the second stego-block. Fgure 0 shows that the proposed ˆd method can control the dstorton wthn. () Collect the ndcators to form a combned code () = (,,, ). The combned code s computed by B = ID = (8) I (3) Embed the combned code n the pxel Step 8: BK = BK ID + B B, and (9) BK = BK ID Repeat Step 6 untl all blocks have been processed. B B (0) Fgure 0. Dagram of the averagng embeddng method. Fgure shows an example to llustrate the embeddng process. Fgure a s a secret strng wth 4 secret bts. Let K = 3, and the frst three secret bts 0 are transformed nto a decmal dgt 3 3 d = s = + + 0 = 6. The scheme maps the decmal dgt d to the = mappng table as shown n Table 4 to obtan the re-encoded code par, = (0, ). The transformaton of the other secret bts follows the same procedure descrbed above. Assume a cover mage s dvded nto several blocks szed B = 3. Each block can be used to hde ( ) = (3 ) = code pars. In Fgure a, the code pars are,,, = {(0, ), (,)}. Fgure 8b shows a cover mage. The frst block s = {05, 49,3 }. The reduced dgts = and = are concealed nto = 05 and = 49, respectvely. The stegopxels of the frst cover pxel = 05 are computed by B K = BK + = 05 + ( ) = 04 and B K = BK = 05 0 = 05. The stego-pxels of the second cover pxel = 49 are computed by B K = 49 + = 49 and B K = 49 = 48. Then, the scheme collects the ndcators to form a combned code = ( ) = (0) = (). The combned code s embedded n the pxel = 3 by B K 3 = BK3 + = 3 + 0 = 3 and B K 3 = BK3 = 3 = 3. Two stego-blocks are shown n Fgure b.

Symmetry 07, 9, 3 of 5 The embeddng procedure s executed repeatedly untl all code pars are embedded. The fnal stego-mages, along wth the mappng table, are sent to the recever for extracton and recovery. (a) (b) Fgure. Example of the proposed method. (a) Secret encodng; (b) Embeddng example..6. Overflow/Underflow Problem In the embeddng process, an underflow/overflow problem mght occur as a result of the reduced code. For example, f the pxel s BK = 54 and ˆd = 3, then the two together would cause the overflow problem. In the proposed scheme, the range of dˆ s [ K, K ]. If a pxel s larger than 55 ( K ) = 56 K, then the overflow problem mght occur because of the addton of K. If a pxel that s less than K, then t mght cause the underflow problem because of the addton of K. For example, assume K = 4, and the range of dˆ s [ 4, 3]. Suppose that dˆ = 3, and ˆd 3 = =. Then, the stego-pxel s BK ˆd BK = 0, =, and there s an underflow problem. Hence, the embeddable pxel s defned as beng n the range of K and 56 K. In the embeddng process, the proposed scheme determnes whether the pxel BK s n the range of [ K,

Symmetry 07, 9, 3 of 5 56 K ] or not. If the pxel s wthn the range, then t could be classfed nto a block. However, the pxel mght cause an underflow/overflow problem and the pxel s non-embeddable. For the nonembeddable pxel, the stego-pxels are set to equal the value of the orgnal pxels. For example, assume that K = 4 and a pxel n the range of [ 4, 56 4 ] = [4, 5] s embeddable. In Fgure, the pxel 54 s out of the range, whch means t s non-embeddable. The stego-pxels are set to equal ts orgnal pxel. The next pxels 3 and 05 are embeddable. However, the next pxel s nonembeddable and cannot be classfed nto a block. So, the next pxel 50 s gathered wth pxels 3 and 05 to form block BK ={3,05,50}, and the embeddng process s performed..7. Extracton and Recovery Fgure. Example of a block wth three embeddable pxels. In ths secton, we descrbe the extracton and recovery processes by whch re-encoded reduced dgts and secret bts are extracted from the stego-mage as well as the process of cover mage recovery. There are ( ) code pars concealed n an embeddable block. Hence, the recever dvdes the stego-mages nto several blocks the sze of B. The re-encoded reduced dgts dˆ can be extracted by computng the dfferences between two stego-pxels, where d ˆ = BK BK and. The combned code s extracted from the last pxels of the stego-blocks by ID = BK B BK. B Then, the recever transforms the combned code ID nto ( ) bnary bts. Each bt represents an ndcator I. One ndcator I along wth one re-encoded reduced dgt d ˆ forms the code par ( I, d ˆ ). After the code par s obtaned, t s then mapped to the mappng table to obtan the orgnal decmal dgt d. Each decmal dgt d s transformed nto K secret bts. In the recovery process, the cover pxel BK can be recovered by the average between two stegopxels,.e., BK + BK BK =. Fgure 3 shows the data extracton and recovery procedure of the proposed method. Fgure 3. Dagram of the extracton and recovery processes.

Symmetry 07, 9, 3 3 of 5 Followng the same example presented n Fgure b. The stego-blocks are = {04, 49, 3} and B K ={05,48,3}. The re-encoded reduced codes are d ˆ = BK BK = 04 05 = and d ˆ = BK BK = 49 48 =, and the combned code s ID = BK 3 BK 3 = 3 3=. The combned code s transformed nto (3 ) = bnary bts ID = ( 0), where I = 0 and I =. The code pars are ( I, d ˆ ) = (0, ) and ( I, d ˆ ) = (, ). The orgnal decmal dgts d = 6 and d = 3 can be derved by mappng them nto the mappng table as shown n Fgure a. Fnally, the decmal dgts d = 6 and d = 3 are transformed nto three secret bts,.e., 0 and 0. Furthermore, the orgnal pxel can be recovered by the average between B K and B K,.e., BK + BK 04 + 05 BK = = = 05, 49 + 48 BK = = 49, and 3 + 3 BK 3 = = 3. In the extracton process, the proposed scheme determnes whether the two stego-pxels are both outsde the range [ K, 56 ]. If so, then the pxels are non-embeddable. If the two stego-pxels are not equal and more than one pxel s wthn the range, then the pxels are embeddable and data are concealed wthn. The secret nformaton can be extracted, and the pxels can be restored followng the extracton procedure..8. Re-Encodng of the Combned Code In the embeddng process, the combned code s used to ndcate the number of sub-bands of the re-encoded code. The value range of ID s [0, () ]. For example, assume that the block sze s set to be = 5. The value range of ID s [0, () ] = [0, 5]. The maxmum value of the range s 5. The value s drectly added to the last pxel of the block to generate the stego-pxel. However, f the maxmum value occurrence frequency s hgh, then drectly embeddng t n the pxel wll decrease the vsual qualty. Therefore, the proposed scheme selectvely re-encodes the combned code accordng to ts occurrence frequency and generates a mappng table to record the relatonshp between the combned code and the re-encoded combned code. The re-encodng procedure s the same as the re-encodng procedure of the reduced code. 3. Results In the proposed scheme, the block sze B and the hdng bt K are key factors that nfluence the hdng performance. To fnd out proper values of B and K, eght schemes wth dfferent values are mplemented. They are BlockFoldng (B = 3, K = 3, RE = 0), BlockFoldng (B = 3, K = 3, RE = ), BlockFoldng (B = 3, K = 4, RE = 0), BlockFoldng (B = 3, K = 4, RE = ), BlockFoldng (B = 5, K = 3, RE = 0), BlockFoldng (B = 5, K = 3, RE = ), BlockFoldng (B = 5, K = 4, RE = 0), and BlockFoldng (B = 5, K = 4, RE = ). The parameters B and K are the block sze and the hdng bts, respectvely. The parameter RE ndcates whether the combned code s re-encoded or not. RE = 0 means the combned code s the orgnal value wthout re-encodng. In contrast, RE = means the combned code s re-encoded accordng to ts occurrence frequency. Fve related methods are also mplemented for a comparson wth the proposed schemes. These are Lee s dual steganographc scheme (Lee009), Lee s orentaton combnaton scheme (Lee03), Chang s magc matrx scheme (Chang03), Lu et al. s center-foldng scheme (Lu05), and Lu s scheme wthout the center-foldng strategy (NonFoldng). Two measurements are used to measure the performance of the hdng methods, the embeddng rate and the mage qualty. The embeddng rate R s calculated by C E R = (bpp), () h w

Symmetry 07, 9, 3 4 of 5 where C s the total hdng capacty of the two stego-mages, E s the sze of the mappng table, and h w s the sze of the mage. A hgh embeddng rate means that the proposed scheme has great embeddng ablty. Image qualty s calculated by usng the PSNR gven by PSNR_z = 0 log0 55 (db), MSE_z () where PSNR_z s the PSNR value of the zth stego-mage, db represents the decbels, and MSE_z s the mean squared error between the cover mage and the stego-mage, and s obtaned by MSE = (P P), hw (3) where P s the cover pxel and P s the stego-mage. The PSNR values n the expermental results are the average values of all PSNR_z, whch can be computed by PSNR_avg = PSNR_z (db). z (4) In general, t s very dffcult to determne the dfference between the cover mage and the stegomage by human eyes when the PSNR value s greater than 30 db. Sx grayscale mages were used to test the hdng performance. Fgure 4 shows the mages Lena, Mandrll, Arplane, Peppers, Lake, and Tffany. The sze of the mage s 5 5. Four secret mages, namely, random (5 5), Dolphn (375 35), Bran (40 35), and TffanySec (5 5) are shown n Fgure 5. (a) Lena (b) Mandrll (c) Arplane (d) Peppers (e) Lake (f) Tffany Fgure 4. Sx test mages.

Symmetry 07, 9, 3 5 of 5 (a) random (5 5) (b) Dolphn (75 35) (c) TffanySec (5 5) (d) Bran (40 35) Fgure 5. Four secret mages. In the frst experment, we tested the performance of the proposed scheme wth varous B, K, and RE. Fgure 6 shows the expermental results. BlockFoldng s the proposed scheme. Under the same embeddng rate, BlockFoldng (B = 3, K = 3, RE = 0) can acheve the hghest mage qualty. BlockFoldng (B = 5, K = 4, RE = ) can get the hghest hdng payload. When B = 3 and K = 3, the mage qualty wth RE = 0 s hgher than that wth RE =. However, when B = 5 and K = 4, the mage qualty wth RE = s hgher than that wth RE = 0. The reason s that f the block sze s small, then the combned code s small enough that t does not need to be re-encoded. However, for a block wth a large sze, the combned code s usually large enough that t needs to be re-encoded. For example, f the value range of the combned code wth B = 5 s [0, ( ) ] = [0, 5], the maxmum value 5 wll cause great mage dstorton. The re-encodng process can effectvely narrow down the dstorton.

Symmetry 07, 9, 3 6 of 5

Symmetry 07, 9, 3 7 of 5 Fgure 6. Results of the frst experment. To compare for a comparson of the proposed scheme wth other related methods, the value of B s set to 3 and 5, the value of K s set to 3 and 4, and RE s set to be 0 and. Tables 5 8 show the results of the comparson among the proposed scheme and the related works wth the cover mage Lena and the secret mages random, TffanySec, Dolphn, and Bran, respectvely. Table 5. Experment results for the secret mage random. Method B K RE PSNR_ PSNR_ PSNR_avg Capacty R Tme 3 3 0 59.98 5.00 55.99 55,3.00 6.99 3 3 59.04 5.5 55.78 55,3.00 6.99 3 4 0 57.30 5.34 54.3 700,46.34 6.96 BlockFoldng 3 4 56.95 5.57 54.6 700,46.34 6.96 5 3 0 50.95 48.65 49.80 63,83. 4.65 5 3 58.3 5.5 54.64 63,83. 4.65 5 4 0 5.64 48.79 50. 843,776.6 4.80 5 4 56.8 50.65 53.46 843,776.6 4.80 Lu05 3 45.0 4.94 43.98 786,43.50.4 4 39.65 39.65 39.65,048,576.00.60 NonFoldng 3 4.69 39.35 40.5 786,43.50.4 Lee009 4 5.4 53.76 5.45 405,498 0.77.3 Lee03 4 50.97 5.9 5.63 54,88.00.5 Chang03 4 39.89 39.89 39.89 786,43.50.54 Table 6. Experment results for the secret mage Tffany. Method B K RE PSNR_ PSNR_ PSNR_avg Capacty R Tme 3 3 0 55.37 49.79 5.58 55,3.00 7.0 3 3 53.5 50.8 5.6 55,3.00 7.0 3 4 0 50.6 47.79 49. 700,46.34 7.47 BlockFoldng 3 4 47.79 45.66 46.7 700,46.34 7.47 5 3 0 46.3 44.57 45.44 63,83. 4.89 5 3 5.55 48.88 50. 63,83. 4.89 5 4 0 43.84 4.69 43.6 843,776.6 4.99 5 4 49.48 47.50 48.49 843,776.6 4.99 Lu05 3 49.65 46.76 48.0 786,43.50.57 4 4.7 4.7 4.7,048,576.00.74 NonFoldng 3 4.93 39.80 40.87 786,43.50.57 Lee009 4 5.4 54.65 5.90 378,980 0.7.7 Lee03 4 50.69 49.39 50.04 54,88.00.8 Chang03 4 39.89 39.89 39.89 786,43.50.79

Symmetry 07, 9, 3 8 of 5 Table 7. Experment results for the secret mage Dolphn. Method B K RE PSNR_ PSNR_ PSNR_avg Capacty R Tme 3 3 0 56.98 53.6 55.07 55,3.00 7.7 3 3 55.53 53.6 54.34 55,3.00 7.7 3 4 0 5.8 48.9 50.37 700,46.34 7.49 BlockFoldng 3 4 5.08 48.78 49.93 700,46.34 7.49 5 3 0 46.95 46.06 46.50 63,83. 5.0 5 3 53.56 5.7 5.36 63,83. 5.0 5 4 0 45.47 44.0 44.83 843,776.6 5.06 5 4 49.9 47.38 48.8 843,776.6 5.06 Lu05 3 47. 43.66 45.44 786,43.50.65 4 4.4 4.4 4.4,048,576.00.75 NonFoldng 3 40.64 38.30 39.47 786,43.50.65 Lee009 4 5.4 5.09 5.6 47,800 0.90.3 Lee03 4 49.0 50.86 49.98 54,88.00. Chang03 4 39.89 39.89 39.89 786,43.50.63 Table 8. Experment results for the secret mage Bran. Method B K RE PSNR_ PSNR_ PSNR_avg Capacty R Tme 3 3 0 6.76 58.73 60.4 55,3.00 6.85 3 3 6.03 59.50 60.6 55,3.00 6.85 3 4 0 50.57 48.3 49.44 700,46.34 7.0 BlockFoldng 3 4 47.63 46.0 46.8 700,46.34 7.0 5 3 0 5.58 50.64 5. 63,83. 4.64 5 3 57.3 55.46 56.39 63,83. 4.64 5 4 0 43.89 4.89 43.39 843,776.6 4.88 5 4 48.38 46.90 47.64 843,776.6 4.88 Lu05 3 43. 4.9 43.0 786,43.50.59 4 36.95 36.95 36.95,048,576.00.99 NonFoldng 3 48.30 46.33 47.3 786,43.50.59 Lee009 4 5.4 63.70 57.4 76,696 0.53.6 Lee03 4 60.84 59.35 60.09 54,88.00.7 Chang03 4 39.87 39.87 39.87 786,43.50.55 In Table 5, wth the secret mage random, the PSNR_avg of the proposed scheme wth B = 5, K = 4, and RE = for the cover mage Lena s 53.46 db, whch s greater than the value of 43.98 db for Lu05. The mage qualty of the proposed scheme s hgher than the value of 9.48 db obtaned by Lu s scheme. At the same tme, the hdng rate of the proposed scheme s.6 bpp, whch s hgher than that of Lu05 s 0. bpp. Under the same hdng capacty, the mage qualty of the proposed scheme wth B = 3, K = 3, and RE = 0 s 55.99 db, whch s hgher than that of Lee03 s 5.63 db. Although Lu05 wth K = 4 acheves the hghest hdng rate,.0 bpp, the mage qualty of Lu05 s decreased to 39.65 db. In Table 6, although Lee009 has hghest mage qualty 5.90 db, the hdng rate of Lee009 s only 0.7 db. The results for dfferent secret mages have the same stuaton. In Table 8, for the secret mage Bran, the mage qualty obtaned by Lee009 s the hghest. However, ts hdng capacty s 0.53 bpp, whch s the lowest among all results obtaned by other methods. The proposed scheme wth B = 3, K = 3, and RE = 0 has the same hdng payloads as those of Lee03. The mage qualty of the proposed scheme s 58.73 db, whch s greater than that of the other methods, thereby ndcatng that the proposed scheme stll exhbts better embeddng performance compared wth the others. From the results of the experment, we can see that the proposed scheme wth a small block sze B = 3 acheves a hgher mage qualty. Because the combned code n the small block sze s small, the code does not need to be re-encoded where RE = 0. In contrast, the proposed scheme wth a large

Symmetry 07, 9, 3 9 of 5 block sze B = 5 has a hgher hdng capacty. The combned code n a large block sze needs to be reencoded, as the value of the code s usually very large. Hence, RE s set to be RE = for B = 5. The second experment compared the proposed scheme wth the other methods. Fgure 7 shows the comparson among all fve related methods and the proposed scheme n terms of embeddng rate and PSNR value. Fgure 7 shows that the mage qualty of BlockFoldng (B = 3, K = 3, RE = 0) s hgher than those of the other methods. Under the same embeddng rate, the proposed method can acheve a greater PSNR value than the related methods. The hdng capacty of BlockFoldng (B = 5, K = 4, RE = ) s hgher than those of the other methods.

Symmetry 07, 9, 3 0 of 5 Fgure 7. Comparson of the proposed and related methods. The thrd experment was amed at provng the vablty of the proposed scheme. Several steganalyss technques such as hstogram steganalyss, RS steganalyss, prmary sets, Ch square, sample pars, RS analyss, and fuson detecton were used to test the performance of the proposed scheme. The hstogram steganalyss method compares the shapes between the cover mage and the stego-mage to detect whether there s a concealed message. Fgure 8 shows hstogram comparsons of Lena wth dfferent parameters. The curve startng wth the symbol * s the hstogram of the stego-mage. We can see that the shape of the stego-mage s almost the same as that of the cover mage.

Symmetry 07, 9, 3 of 5 Fgure 8. Hstogram steganalyss of Lena wth dfferent parameters. RS steganalyss s a knd of attack method proposed by Frdrch et al. In the method, pxels are classfed nto several groups. The method uses a dscrmnaton functon to quantfy smoothness or regularty and uses a flppng functon to defne three groups, regular (R), sngular (S), and unusable

Symmetry 07, 9, 3 of 5 (U). The percentages of each group wth mask M = [ 0 0 ] and M = [ 0 0 ] are represented as R_M_G, R_FM_G, S_M_G, S_FM_G, U_M_G, and U_FM_G, respectvely. The hypotheses are R_M_G R_FM_G, S_M_G S_FM_G, and U_M_G U_FM_G. Fgure 9 shows the RS steganalyss results for Lena wth dfferent parameters. In the fgures, the curve of R_M_G s very smlar to that of R_FM_G. The method judges there s no secret message hdden n the mage. The curves of S_M_G, S_FM_G, U_M_G, and U_FM_G have the same stuatons. Hence, the proposed scheme cannot be detected by the RS steganalyss. Stego Stego Fgure 9. RS-dagram steganalyss of Lena wth the secret mage random.

Symmetry 07, 9, 3 3 of 5 Other tests ncludng prmary sets, Ch square, sample pars, RS analyss, and fuson detecton were appled to examne the proposed scheme. Table 9 shows the experment report. All numbers n the table are very small, whch means the proposed scheme s robust aganst the steganalytc attacks. Table 9. Steganalyss report for StegExpose. Cover B K Stego Prmary Sets Ch Square Sample Pars RS Analyss Fuson (Mean) 3 4 Stego 0.07675 0.00489 0.030703 0.0466 0.083 Stego 0.0305 0.005963 0.0986 0.07787 0.0880 Arplane 5 3 Stego 0.0934 0.004948 0.0735 0.0070 0.08088 Stego 0.0360 0.00569 0.0867 0.07553 0.03763 5 4 Stego 0.0964 0.005567 0.087 0.06658 0.0666 Stego 0.04443 0.004844 0.0066 0.05573 0.068 3 4 Stego 0.050697 0.000000 0.004456 0.07477 0.00658 Stego 0.03 0.00009 0.05046 0.04435 0.0505 Lake 5 3 Stego 0.0449 0.000000 0.0996 0.08785 0.0305 Stego 0.04343 0.000003 0.033 0.0538 0.0470 5 4 Stego 0.043350 0.000000 0.059 0.0905 0.0939 Stego 0.03905 0.000003 0.07985 0.0308 0.058 3 4 Stego 0.005693 0.0096 0.0993 0.005686 0.007967 Stego 0.04598 0.0067 0.060 0.00666 0.00963 Lena 5 3 Stego 0.009356 0.007 0.050 0.0088 0.009004 Stego 0.03644 0.0003 0.08364 0.03555 0.0986 5 4 Stego 0.00998 0.0075 0.040 0.00706 0.005673 Stego 0.0955 0.00 0.0369 0.00865 0.00068 3 4 Stego 0.054084 0.00449 0.09357 0.085073 0.0584 Stego 0.046409 0.00583 0.08333 0.08457 0.059895 Mandrll 5 3 Stego 0.07036 0.00079 0.587 0.5084 0.07856 Stego 0.07760 0.0046 0.070 0.09950 0.0759 5 4 Stego 0.075838 0.0045 0.3048 0.09635 0.074096 Stego 0.053453 0.0049 0.090763 0.08700 0.0584 3 4 Stego 0.080749 0.00956 0.05594 0.06084 0.0507 Stego 0.05870 0.0097 0.05464 0.0796 0.04657 Pepper 5 3 Stego 0.048 0.00355 0.076068 0.063953 0.06797 Stego 0.04876 0.004 0.07476 0.059740 0.08558 5 4 Stego 0.09348 0.0035 0.06543 0.05487 0.0545 Stego 0.08306 0.00894 0.057448 0.063565 0.05734 3 4 Stego 0.04587 0.00567 0.04456 0.046080 0.035357 Stego 0.038765 0.005464 0.04339 0.0400 0.03868 Tffany 5 3 Stego 0.0368 0.005454 0.03673 0.040666 0.0995 Stego 0.0080 0.00570 0.0787 0.03347 0.0076 5 4 Stego 0.04459 0.00590 0.043003 0.04746 0.033799 Stego 0.047008 0.00560 0.04099 0.0337 0.0305 4. Conclusons The dual-mage-based hdng scheme s a new technology n the data hdng feld. The concept of dual-mage, based on nformaton sharng, conssts of concealng secret messages n two of the same cover mages; only someone who has both stego-mages can extract the secret messages. There are many advantages to usng dual-mage n data hdng, such as ts hgh payload, reversblty, and strong robustness. The proposed method mproves Lu s center-foldng strategy by ncludng the foldng operaton twce and usng an ndcator to dentfy the second foldng operaton as a means of dstngushng dfferent sub-bands to further decrease the reduced dgt. In addton, the proposed method effectvely solves the overflow/underflow problem. In order to evaluate the performance of the proposed scheme, eght schemes wth dfferent B and K values were mplemented. Moreover, fve related methods were mplemented for a comparson wth the proposed scheme. The frst experment showed that a small B value acheves hgher mage qualty, a large K value acheves a large payload, and the re-encodng process can effectvely narrow down the dstorton when B s larger. The second experment compared the

Symmetry 07, 9, 3 4 of 5 proposed and related methods. The results showed that the proposed scheme can acheve hgher mage qualty (B = 3, K = 3, RE = 0), better mage qualty under the same embeddng rate, and a hgher payload than other schemes (B = 5, K = 4, RE = ). The thrd experment used several steganalyss technques to prove the strong robustness of the proposed scheme, nclude hstogram steganalyss, RS steganalyss, prmary sets, Ch square, sample pars RS analyss, and fuson detecton. Acknowledgments: Ths study was fnancally supported by a research grant from Tawan s Mnstry of Scence and Technology (MOST 05--E- 34-00). Author Contrbutons: Tzu-Chuen Lu desgned the algorthm, conducted all experments, analyzed the results, wrote the manuscrpt, and conducted the lterature revew. Hu-Shh Leng conceved the algorthm and wrote the manuscrpt. Conflcts of Interest: The authors declare no conflct of nterest. References. Melkanen, J. LSB matchng revsted. IEEE Sgnal Process. Lett. 006, 3, 85 87.. Wu, D.-C.; Tsa, W.-H. A steganographc method for mages by pxel-value dfferencng. Pattern Recognt. Lett. 003, 4, 63 66. 3. Chang, C.C.; Tseng, H.W. A steganographc method for dgtal mages usng sde match. Pattern Recognt. Lett. 004, 5, 43 437. 4. Zhang, X.; Wang, S. Effcent steganographc embeddng by explotng modfcaton drecton. IEEE Commun. Lett. 006, 0, 78 783. 5. Keu, T.D.; Chang, C.C. A steganographc scheme by fully explotng modfcaton drectons. Expert Syst. Appl. 0, 38, 0648 0657. 6. N, Z.; Sh, Y.Q.; Ansar, N.; Su, W. Reversble data hdng. IEEE Trans. Crcuts Syst. Vdeo Technol. 006, 6, 354 36. 7. Alattar, A. Reversble watermarks usng a dfference expanson. In Internet and Communcatons Multmeda Securty Handbook; Furht, B, Krovsk, D, Eds.; CRC Press: Boca Raton, FL, USA; 004. 8. Tan, J. Reversble data embeddng usng a dfference expanson. IEEE Trans. Crcuts Syst. Vdeo Technol. 003, 3, 890 896. 9. L, X.; Yang, B.; Zeng, T. Effcent reversble watermarkng based on adaptve predcton-error expanson and pxel selecton. IEEE Trans. Image Process. 0, 0, 354 3533. 0. Gu, X.; L, X.; Yang, B. A hgh capacty reversble data hdng scheme based on generalzed predctonerror expanson and adaptve embeddng. Sgnal Process. 04, 98, 370 380.. L, X.; L, J.; L, B.; Yang, B. Hgh-fdelty reversble data hdng scheme based on pxel-value-orderng and predcton-error expanson. Sgnal Process. 03, 93, 98 05.. Peng, F.; L, X.; Yang, B. Improved PVO-based reversble data hdng. Dgt. Sgnal Process. 04, 5, 55 65. 3. Qu, X.; Km, H.J. Pxel-based pxel value orderng predctor for hgh-fdelty reversble data hdng. Sgnal Process. 05,, 49 60. 4. Wang, X.; Dng, J.; Pe, Q. A novel reversble mage data hdng scheme based on pxel value orderng and dynamc pxel block partton. Inf. Sc. 05, 30, 6 35. 5. Chang, C.C.; Keu, T.D.; Chou, Y.C. Reversble data hdng scheme usng two steganographc mages. In Proceedngs of the 007 IEEE Regon 0 Internatonal Conference (TENCON), Tape, Tawan, 30 Ocotber November 007; pp. 4. 6. Lee, C.F.; Wang, K.H.; Chang, C.C.; Huang, Y.L. A reversble data hdng scheme based on dual steganographc mages. In Proceedngs of the 3rd Internatonal Conference on Ubqutous Informaton Management and Communcaton (ICUIMC 09), Suwon, Korea, 5 6 January 009; pp. 8 37. 7. Lee, C.F.; Huang, Y.L. Reversble data hdng scheme based on dual stegano-mages usng orentaton combnatons. Telecommun. Syst. 03, 5, 37 47. 8. Chang, C.C.; Lu, T.C.; Horng, G.; Huang, Y.H.; Hsu, Y.M. A hgh payload data embeddng scheme usng dual stego-mages wth reversblty. In Proceedngs of the 03 9th Internatonal Conference on Informaton, Communcatons and Sgnal Processng, Tanan, Tawan, 0 3 December 03; pp. 5.

Symmetry 07, 9, 3 5 of 5 9. Qn, C.; Chang, C.C.; Hsu, T.J. Reversble data hdng scheme based on explotng modfcaton drecton wth two steganographc mages. Multmed. Tools Appl. 04, 74, 586 587. 0. Lu, T.C.; Tseng, C.Y.; Wu, J.H. Dual magng-based reversble hdng technque usng LSB matchng. Sgnal Process. 05, 08, 77 89.. Lu, T.C.; Wu, J.H.; Huang, C.C. Dual-mage-based reversble data hdng method usng center foldng strategy. Sgnal Process. 05, 5, 95 3.. Lu, T.C.; Ch, L.P.; Wu, C.H.; Chang, H.P. Reversble data hdng n dual stego-mages usng frequencybased encodng strategy. Multmed. Tools Appl. 06, do:0.007/s04-06-435-. 3. Frdrch, J.; Goljan, M.; Du, R. Relable detecton of LSB steganography n grayscale and color mages. In Proceedngs of the 00 Workshop on Multmeda and Securty, Ottawa, ON, Canada, 5 October 00; pp. 7 30. 4. Boehm, B. StegExpose A Steganalyss Tool for Detectng LSB Steganography n Images. Avalable onlne: http://arxv.org/abs/40.6656 (accessed on 9 September 07). 07 by the authors. Lcensee MDPI, Basel, Swtzerland. Ths artcle s an open access artcle dstrbuted under the terms and condtons of the Creatve Commons Attrbuton (CC BY) lcense (http://creatvecommons.org/lcenses/by/4.0/).