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

Transcription

1 S S symmetry Artcle Reversble Dual-Image-Based Hdng Scheme Usng Block Foldng Technque Tzu-Chuen Lu Tzu-Chuen Lu 1, 1, * and Hu-Shh Leng * ID and Hu-Shh Leng 1 Department Informaton Management, Chaoyang Unversty Technology, Tachung 41349, Tawan Department Informaton Management, Chaoyang Unversty Technology, Tachung 41349, Tawan Department Mamatcs, Natonal Changhua Unversty Educaton, Changhua 50058, Tawan; Department Mamatcs, Natonal Changhua Unversty Educaton, Changhua 50058, Tawan; lenghs@cc.ncue.edu.tw lenghs@cc.ncue.edu.tw * Correspondence: tclu@cyut.edu.tw; Tel.: (ext. 4558) Correspondence: tclu@cyut.edu.tw; Tel.: (ext. 4558) Receved: 19 September 017; Accepted: 9 October 017; Publshed: 1 October 017 Receved: 19 September 017; Accepted: October 017; Publshed: 1 October 017 Abstract: The concept a dual-mage based scheme n nformaton sharng conssts concealng secret messages n ntwo twocover mages; mages; only only someone someone who who has both has both stego-mages stego-mages can extract can extract secret secret messages. messages. In 015, InLu 015, et al. Luproposed et al. proposed a center-foldng a center-foldng strategy strategy where each where secret eachsymbol secret symbol s folded s folded nto nto reduced reduced dgt to dgt reduce to reduce dstorton dstorton stego-mage. stego-mage. Then, n Then, 016, nlu 016, et al. Lu used et al. a used frequency-based a frequency-based encodng encodng strategy strategy to reduce to reduce dstorton dstorton frequency frequency occurrence occurrence maxmum maxmum absolute absolute value. value. Because Because foldng foldng strategy strategy can can obvously reduce value, proposed scheme ncludes foldng operaton twce twce to to furr furr decrease decrease reduced reduced dgt. dgt. We use We use a frequency-based a encodng encodng strategy strategy to to encode encode a secret a secret message and andn use block foldng technque by performng center-foldng operaton twce to embed secret messages. An ndcator s needed to dentfy sequence number foldng operaton. The proposed scheme collects several ndcators to toproduce a acombned code codeand andhdes hdes code code n n a pxel a pxel to reduce to reduce sze sze ndcators. ndcators. The The expermental results results show showthat that proposed method can canacheve hgher mage qualty under same embeddng rate or hgher payload, whch s better than or methods. Keywords: dual stego-mages; nformaton hdng; center-foldng strategy; block foldng 1. 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 n sends tto recever. The recever can extract secret messages from stego-mage (Fgure 1). Fgure 1. Dagram nformaton hdng process. Fgure 1. Dagram nformaton hdng process. Symmetry 017, 9, 3; do: /sym91003 Symmetry 017, 9, 3; do: /sym

2 Symmetry 017, 9, 3 5 Symmetry 017, 9, 3 5 In general, nformaton hdng schemes can be classfed nto two categores,.e., reversble data hdng andin rreversble general, nformaton data hdng, asschemes showncan n Fgure be classfed. The nto most two commonly categores,.e., used reversble rreversble data data hdng hdng methods and rreversble nclude data least hdng, sgnfcant as shown bt n (LSB) Fgure substtuton. The most method, commonly used pxel-value rreversble dfferencng data (PVD) hdng method, methods and nclude explotng least modfcaton sgnfcant drecton bt (LSB) method substtuton (EMD) method, [1 14]. The pxel-value LSB method dfferencng (PVD) method, and explotng modfcaton drecton method (EMD) [1 14]. The LSB s a well-known rreversble data hdng technque because ts hgh payload and low dstorton. method s a well-known rreversble data hdng technque because ts hgh payload and low It drectly replaces bts cover pxel wth secret bts for embeddng. Melkanen (006) dstorton. It drectly replaces bts cover pxel wth secret bts for embeddng. Melkanen proposes (006) a modfcaton proposes a modfcaton to LSB to method LSB method called LSB called matchng LSB matchng [1]. In [1]. hs In method, hs method, secret secret bts are embedded bts are byembedded usng by bnary usng functon bnary and functon fourand embeddng four embeddng rules. rules. Fgure. Informaton hdng categores. LSB: least sgnfcant bt substtuton method, PVD: pxelvalue dfferencng method, EMD: explotng modfcaton drecton method, DE: dfference Fgure. Informaton hdng categores. LSB: least sgnfcant bt substtuton method, PVD: pxel-value dfferencng method, EMD: explotng modfcaton drecton method, DE: dfference expanson, HS: hstogram shftng, PVO: pxel-value orderng method. expanson, HS: hstogram shftng, PVO: pxel-value orderng method. Wu and Tsa (003) proposed PVD method []. In r method, dfference two pxels Wu n andcover Tsa mage (003) s proposed calculated to determne PVD method number []. In r bts method, to be embedded dfference n se two two pxels pxels n cover and mage a pre-defned s calculated range table. to determne The technque number can embed a bts large tonumber embedded secret nbts se nto two cover pxels and mage wth hgh mperceptblty as t makes use characterstc human vson senstvty. a pre-defned range table. The technque can embed a large number secret bts nto cover mage Chang and Tseng (004) utlzed dfference predcted value and target pxels to estmate wth hgh mperceptblty as t makes use characterstc human vson senstvty. Chang degree smoothness or contrast pxels to determne number bts to be embedded n and Tseng target (004) pxels [3]. utlzed dfference predcted value and target pxels to estmate degree Zhang smoothness and Wang or contrast (006) proposed pxels toemd determne method [4]. number The EMD method bts toprovdes be embedded a good n targetmage pxels qualty [3]. for stego-mage wth a peak sgnal-to-nose rato (PSNR) more than 5 db, snce, Zhang at most, and only Wang one pxel (006) n each proposed pxel group EMD needs method to be ncreased [4]. The or EMD decreased method by one. provdes Keu and achang good mage qualty(011) for mproved stego-mage EMD wth method a peak by explotng sgnal-to-nose eght modfcaton rato (PSNR) drectons moreto than embed 5several db, snce, secret at most, bts nto a cover par at a tme [5]. only one pxel n each pxel group needs to be ncreased or decreased by one. Keu and Chang (011) Compared wth rreversble data hdng schemes, reversble data hdng schemes can recover mproved EMD method by explotng eght modfcaton drectons to embed several secret bts cover mage wthout any dstorton from stego-mage after secret messages have been nto a extracted. cover par The atmost a tme commonly [5]. used reversble data hdng methods nclude dfference expanson Compared (DE) method, wth hstogram rreversble shftng data (HS) hdng method, schemes, and pxel-value reversble orderng data(pvo) hdng method. schemes Tan can (003) recover cover proposed mage wthout DE method any[6] dstorton that embeds from a secret bt stego-mage nto LSB after expanded secretdfference messages have each been extracted. pxel The par most commonly cover mage. used The scheme reversble provdes data hdng a hgh payload; methodshowever, nclude dstorton dfference caused expanson (DE) method, by DE hstogram sgnfcant. shftng Alattar (HS) (004) method, mproved and Tan s pxel-value scheme wth orderng double (PVO) respectve method. dfferences Tan (003) proposed between DE four method neghborng [6] that pxels embeds and acheved a secret more bt secret nto bts LSB wth expanded expanded dfference dfference [7]. each N et al. (006) proposed HS method n 006 [8]. Ther method s to frstly generate pxel par cover mage. The scheme provdes a hgh payload; however, dstorton caused by hstogram by pxel ntensty value and shft bns between zero and peak pont to create DE empty s sgnfcant. bns for data Alattar embeddng. (004) The mproved advantage Tan s scheme HS method wth s double ts low dstorton; respectve however, dfferences ts between drawback four neghborng s a low payload, pxels because and acheved embeddng morecapacty secret bts s determned wth expanded by number dfference ponts [7]. N et al. (006) proposed HS method n 006 [8]. Ther method s to frstly generate hstogram by pxel ntensty value and shft bns between zero and peak pont to create empty bns for data embeddng. The advantage HS method s ts low dstorton; however, ts drawback s a low payload, because embeddng capacty s determned by number ponts

3 Symmetry 017, 9, Symmetry 017, 9, n peak pont bn. L et al. and Gu et al. proposed an adaptve embeddng technque that dvdes pxels nto dfferent types to enhance embeddng capacty a predcton error [9,10]. L et al. (013) proposed PVO method [11]. In r method, for each block, pxels are reordered nto a pxel vector, n smallest pxel pxel s s predcted by by second second smallest smallest pxel, pxel, and and largest largest pxel pxel s predcted s predcted by by second second largest largest pxel. pxel. It uses It predcton uses predcton errors errors 1 and1 1 and to 1 embed to embed data, whereas data, whereas predcton predcton error 0error s unchanged. 0 s unchanged. Peng et Peng al. (014) et al. (014) mproved mproved PVO method PVO method to use to larger use larger blocks blocks for embeddng for embeddng and take and better take better advantage advantage mage mage redundancy redundancy to yeld to yeld a hgher a hgher PSNR PSNR [1]. [1]. Qu and Qu Km and (015) Km (015) modfed modfed PVO method PVO method so thatso each that pxel each spxel predcted s predcted usng ts usng sorted ts context sorted pxels context topxels acheve to acheve a better a embeddng better embeddng capacty capacty n smooth n mage smooth regons mage [13]. regons [13]. Wang et al. (015) used a dynamc blockng strategy to dvde cover mage adaptvely nto varous-szed blocks. Thus, flat mage areas are preferentally dvded nto smaller blocks to retan a hgh embeddng capacty and rough areas are dvded nto larger blocks to avod decreasng PSNR value [14]. The dual-mage-based hdng scheme s s a new a newtechnology n n nformaton hdng hdng feld. feld. The The concept concept dual-mage, based based on on nformaton sharng, conssts concealng secret messages n two same cover mages; only someone who has both stego-mages can extract secret messages. A dagram dual-mage based hdng scheme s s shown n n Fgure There are are many advantages to to usng usng dual-mage n data n data hdng, such such as as a hgh a hgh payload, reversblty, and and strong strong robustness. (a) (b) Fgure Fgure Dual-mage Dual-mage based based hdng hdng scheme. scheme. (a) (a) Embed Embed secret secret messages messages nto nto two two same same cover cover mages; mages; (b) (b) Extract Extract secret secret messages messages from from two two stego-mages. stego-mages. In dual-mage-based hdng scheme, mage qualty and payload are affected by embeddng rules [15 1]. Chang et al. (007) combned EMD method wth dual-mage technque to

4 Symmetry 017, 9, In dual-mage-based hdng scheme, mage qualty and payload are affected by embeddng rules [15 1]. Chang et al. (007) combned EMD method wth dual-mage technque to acheve a hgh payload and reduce dstorton [15]. Lee et al. (009) used combnatons pxel orentaton locatons wth dual-mage to enhance embeddng capacty and preserve good vsual qualty [16]. Lee and Huang (013) converted secret messages nto qunary-based secret symbols and combned every two secret symbols as a set embedded n dual-mage [17]. Chang et al. (013) converted secret messages nto decmal-based secret symbols, n embedded secret symbols n a rght dagonal lne [18]. Qn et al. (014) embedded secret messages n frst mage usng EMD method and n second mage usng or rules that were dependent on frst mage [19]. Lu et al. (015) used LSB matchng method and modfed non-reversble stego-pxels based on a rule table to restore cover mage [0]. They proposed center-foldng strategy to reduce value secret symbols. Then, y embedded secret symbols n two stego-mages through an averagng method [1]. Lu et al. (016) proposed a frequency-based encodng method to reduce dstorton derved by maxmum secret dgt []. In [1], Lu et al. propose a center-foldng strategy n whch each secret symbol s folded nto reduced dgt before embeddng procedure to reduce dstorton stego-mage. The foldng strategy s smple and effectve, to extent that mage qualty stego-mage s very good. Because foldng strategy can obvously reduce value, proposed scheme performs foldng operaton twce to furr decrease reduced dgt. Furrmore, n [], Lu et al. use a frequency-based encodng strategy to reduce dstorton frequency occurrence maxmum absolute value. The re-encoded technque also can be used to reduce number secret dgt and narrow down dstance between stego-pxel and orgnal pxel. Therefore, proposed scheme frst uses a frequency-based encodng strategy to encode secret message and n uses block foldng technque by ncludng center-foldng operaton twce to embed secret messages. In addton, several steganalyss technques are used to prove strong robustness 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 ths paper s organzed as follows. Secton descrbes related works. Secton 3 ntroduces proposed scheme. Secton 4 summarzes experment results. The conclusons are presented n Secton 5.. Related Works In ths secton, we brefly ntroduce Lee et al. s scheme, center-foldng strategy, and frequency-based encodng strategy..1. Lee et al. s Methods Lee et al. [16,17] proposed a drecton-based dual-mage method. In r scheme, two pxels P 1 and P are used to conceal four secret bts and a drecton map s used to represent embeddng rules. Fgure 4 shows drecton map. Suppose that two pxels are P 1 = 15, P = 0 and secret bts are 00. The drecton map ndcates that P 1 = P = = 16 and P = 0 for embeddng 00 n frst stego-mage. If next two secret bts are 10, n stego-pxels are P 1 = P 1 = 15 and P = P + 1 = = 1 for second stego-mage.

5 Symmetry 017, 9, Symmetry 017, 9, Symmetry 017, 9, Fgure Fgure Drecton-based embeddng rules. rules. However, However, n some n nsome cases, cases, method cannot conceal secret data data n n second second stego-mage. stego-mage. Therefore, Therefore, only only frst frst mage mage s s modfed to embed frst frst two two secret secret bts. bts. bts. In In 013, In013, Lee Lee and and Huang Huang mproved mproved above method by by ncreasng ncreasng number number drecton drecton rules rules from four drectons to fve drectons and redesgned embeddng rule to ncrease embeddng from four payload. drectons to fve drectons and redesgned embeddng rule to ncrease embeddng The drecton map s shown n Fgure 5. payload. The drecton map s shown n Fgure 5. Fgure Fgure Data Data embeddng embeddng method method usng usng fve fve drectons. drectons... Center-Foldng Strategy.. Center-Foldng Strategy In [1], Lu et al. proposed a center-foldng strategy where each secret symbol s folded nto In [1], Lu et al. proposed a center-foldng strategy where each secret symbol s folded nto reduced Fgure 5. Data embeddng method usng fve drectons. reduced dgt dgt before before embeddng embeddng procedure procedure to reduce to reduce dstorton dstorton stego-mage. stego-mage. For example, For example, K bts K bts secret data secret were data taken were as taken a set and as a converted set and converted nto secret nto symbol secret d. The symbol centerfoldng strategy Strategy changed range secret symbols from ={0,1,,, } to = d... Center-Foldng {, + 1,, 1,0,1,,, 1}. The formula s as follows: In [1], Lu et al. proposed a center-foldng strategy where each secret symbol s folded nto d = d reduced dgt before embeddng procedure to K reduce 1, (1) dstorton stego-mage. For example, where K bts s a secret folded data secret were symbol taken and as a set s an and ntermedate converted value. nto secret symbol d. The centerfoldng strategy After changed foldng, value range secret symbols changed from to [ ={0,1,,,, 1]. Fgure } 6 to = { shows, an example where s + 1,, 1,0,1,, set to be 3., The maxmum value value range s 7. Assume that 1}. The formula s as follows: a pxel value s 138. If secret symbol d = 7 s added drectly to pxel to get stego-pxel 138

6 Symmetry 017, 9, The center-foldng strategy changed range secret symbols from R = { 0, 1,,..., K 1} to R = { K 1, K 1 + 1,..., 1, 0, 1,..., K 1, K 1 1 }. The formula s as follows: d = d K 1, (1) where d s a folded secret symbol and K 1 s an ntermedate value. After foldng, value range secret symbol changed to [ K 1, K 1 1]. Fgure 6 shows an example where K s set to be 3. The maxmum value value range s 7. Assume that Symmetry 017, 9, a pxel value s 138. If secret symbol d = 7 s added drectly to pxel to get stego-pxel = 145, n mage dstorton nflcted s ( ) + 7 = 145, n mage dstorton = 7 = 49. However, n Lu et al. s scheme, symbol s folded as d = 7 nflcted s ( ) =7 =49. However, n Lu et al. s scheme, symbol s folded as = 7 = 3. The = 3. folded The folded symbol symbol d = 3=3 nstead nstead orgnal orgnal symbol 7 s added symbol wth 7 s added pxel wth 138 to pxel get138 to stego-pxel get stego-pxel = = 141. The The mage dstorton caused by Lu et al. s by Lu method al. s method s (141 s 138) (141 = 138) 3 = =3 9. The =9. mage The mage dstorton s reduced from 49 to 9. Fgure Fgure 6. Example 6. value value range central-foldng strategy wth wth = K 3. = 3. It s obvous that center-foldng strategy s smple and effectve; t can reduce dstorton It s obvous that center-foldng strategy s smple and effectve; t can reduce dstorton stego-mage after embeddng procedure. Therefore, n proposed scheme, we perform stego-mage foldng after operaton embeddng twce to furr procedure. decrease Therefore, reduced dgt. n proposed scheme, we perform foldng operaton twce to furr decrease reduced dgt..3. Frequency-Based Encodng Strategy.3. Frequency-Based Encodng Strategy In [], Lu et al. used a frequency-based encodng strategy to reduce dstorton In frequency [], Lu et al. occurrence used a frequency-based maxmum encodng absolute value. strategy For toexample, reduce suppose dstorton that secret frequency bt occurrence stream s 110 maxmum absolute value For Frst, example, scheme suppose converts that each three secret bts bt (K stream = 3) as s a group to a 010 decmal dgt stream Frst, as 7 scheme converts 6 7. Next, each t uses three bts center-foldng (K = 3) as strategy a group to to reduce a decmal dgt stream as Then, frequency table can be made as Table 1, whch dgt stream as Next, t uses center-foldng strategy to reduce dgt stream as records rank each reduced dgt and map number ts new ndex n descendng order by occurrence 1 1 frequency. 3. Then, frequency table can be made as Table 1, whch records rank each reduced dgt and map number ts new ndex n descendng order by occurrence frequency. Table 1. Example frequency-based encodng table (K = 3). Table 1. Example frequency-based encodng table (K = 3). Decmal Dgt Reduced Dgt Occurrence Frequency Order Indces Decmal Dgt Reduced Dgt Occurrence Frequency Order Indces Compared wth embeddng re-encoded secret dgt and orgnal secret dgt, Compared frequency-based wth encodng embeddng strategy can re-encoded be used to reduce secret dgt number and secret orgnal dgt secret and narrow dgt, frequency-based down dstance encodng between strategy orgnal can bepxel usedand to reduce stego-pxel. number secret dgt and narrow down dstance between orgnal pxel and stego-pxel..4. Proposed Method 3. ProposedIn Method Lu s scheme, each secret symbol s reduced to reduced dgt usng center-foldng strategy. A dagram Lu s center-foldng strategy s shown n Fgure 7. In fgure, center value In Lu s scheme, each secret symbol s reduced to reduced dgt usng center-foldng 5 s subtracted from each decmal message to generate reduced dgt. The value range strategy. Fgure A dagram 7 can be seen Lu s as a band. center-foldng The maxmum strategy value s shown band s n 7 Fgure n Fgure In After fgure, foldng, center value 5band s subtracted s separated from nto each two sub-bands. decmal message The maxmum d to generate absolute value reduced two dgt sub-bands d. The value s 4. range

7 Symmetry 017, 9, Fgure 7 can be seen as a band. The maxmum value band s 7 n Fgure 7. After foldng, band s separated nto two sub-bands. The maxmum absolute value two sub-bands s 4. Symmetry 017, 9, Symmetry 017, 9, Fgure 7. Dagram Lu s center-foldng strategy. Fgure 7. Dagram Lu s center-foldng strategy. Because foldng strategy Fgure can 7. Dagram obvously Lu s reduce center-foldng value, strategy. proposed scheme ncludes Because foldng operaton foldng twce strategy to furr can decrease obvously reduced dgt. value, The concept proposed proposed scheme scheme ncludes s foldng shown operaton Because n Fgure twce foldng 8. In to furr strategy fgure, decrease can obvously value range reduced s dgt. frst value, dvded The concept proposed nto two scheme sub-bands proposed ncludes SB1 scheme and s shown foldng SB. Each Fgure operaton sub-band 8. Intwce performs fgure, to furr a one-tme decrease valuecenter-foldng range reduced d sstrategy. dgt. frst dvded The For concept example, nto two proposed sub-bands value range scheme SB1 subband sub-band SB1 n Fgure s performs shown 8. In n a and s SB. Each shown Fgure one-tme fgure, 8a. The center-foldng value range value strategy. SB1 s s frst. For The dvded example, center nto value two value sub-bands s subtracted range SB1 from sub-band SB. values Each sub-band n SB1 to performs generate a one-tme reduced center-foldng dgt. We strategy. can see that For example, maxmum value absolute range value subband two SB1 sub-bands s shown s n, Fgure whch 8a. s smaller The center than value 4 n Fgure 8. SB1 s shown n Fgure 8a. The center value SB1 s. The center value s subtracted from values n SB1 to generate reduced dgt d. ˆ value SB1 s. The center value s subtracted from We can see that maxmum absolute value two values n SB1 to generate reduced dgt. We can see that maxmum absolute value sub-bands two ssub-bands, whch s s, smaller whch s than smaller than value 4 n value Fgure 4 n Fgure Fgure 8. Dagram proposed block foldng technque. However, sub-bands Fgure 8. SB1 Dagram and SB have proposed same block reduced foldng values. technque. We cannot dstngush Fgure 8. Dagram proposed block foldng technque. orgnal value from. Hence, an ndcator s needed to dentfy whch sub-band reduced value s However, located n. If sub-bands reduced SB1 value and SB s located have n same sub-band reduced values. SB1, n We cannot ndcator dstngush set to orgnal However, be 0, where value =0. sub-bands from In. contrast, Hence, SB1 and f ndcator SB reduced have s needed value same to dentfy s reduced located whch n values. sub-band sub-band We cannot reduced SB, dstngush n value orgnal ndcator s value located ds from n. set If to d. ˆ be Hence, reduced 1, where an value =1. ndcator The s located orgnal s needed n value tosub-band dentfy s mapped SB1, whch to n a sub-band code ndcator par (, ) reduced to s set to value d ˆ s located be 0, mage n. where Ifdstorton. =0. reduced In For contrast, example, value f d ˆ s located decmal reduced n value sub-band = s 7 s located mapped SB1, n n to sub-band code ndcator par SB, (, ) In s = (1, set 1). to be 0, where ndcator I = However, 0. Ins contrast, set to ndcator be 1, fwhere s reduced extra =1. nformaton The value orgnal d ˆ s that value located also needs s nmapped to sub-band be to concealed a code SB, par n n (, cover ) to reduce mage ndcator I and mage wll decrease dstorton. For hdng example, capacty. decmal To solve value ths problem, = 7 s mapped proposed to code scheme par collects (, ) = several (1, 1). s set to be 1, where I = 1. The orgnal value d s mapped to a code par (I, d) ˆ to reduce mage ndcators However, to produce ndcator a combned s extra code nformaton and hdes that also code needs n a to pxel. be concealed In proposed n cover scheme, mage dstorton. For example, decmal value d = 7 s mapped to code par (I, d) ˆ = (1, 1). and cover wll mage decrease s dvded hdng nto several capacty. blocks. To solve Each block ths problem, has pxels proposed n t. The scheme last pxel collects n block several s ndcators However, used embed to produce ndcator combned a combned s extra code. code nformaton The or and hdes that pxels are code also needs used n to a conceal pxel. to be In concealed reduced proposed n dgt scheme, cover. mage and wll cover decrease Furrmore, mage s dvded hdng proposed nto several capacty. scheme blocks. Toconsders solve Each block ths problem, has occurrence pxels frequency n proposed t. The last scheme pxel decmal n collects block dgt s several ndcators used reassgn to toembed produce proper code a combned to code. reduced code The dgt or and hdes pxels that can are used sgnfcantly codeto nconceal a pxel. shrnk In reduced mage proposed dgt dstorton.. scheme, cover mage Furrmore, s dvded nto proposed several scheme blocks. consders Each block occurrence has B pxels frequency n t. The lastdecmal pxel ndgt block s used.5. toreassgn embed Embeddng proper Procedure combned code to code. reduced The or dgt pxels that aresgnfcantly used to conceal shrnk reduced mage dstorton. dgt d. ˆ Furrmore, In proposed proposed scheme, a scheme cover mage consders s dvded occurrence nto several frequency blocks. Each block decmal has pxels dgt d to.5. Embeddng Procedure reassgn n t. proper Let code = { to, reduced,, } dgt be d ˆ that block. can A sgnfcantly secret mage s shrnk formed as mage a bnary dstorton. strng. The strng In s separated proposed nto scheme, several a substrngs cover mage s sze dvded. nto Each several substrng blocks. s transformed Each block nto has a decmal pxels 3.1. Embeddng dgt t. Let. The Procedure = scheme {, computes,, } be occurrence block. frequency A secret mage each s formed decmal as dgt a bnary to strng. generate The a strng hstogram separated and sort nto several hstogram substrngs descendng sze order.. Each The dgt substrng wth s transformed maxmum nto frequency a decmal s In proposed scheme, a cover mage s dvded dgt encoded. The wth scheme smallest computes dstorton code occurrence par ( I frequency ', d ˆ' nto several blocks. Each block has B pxels n ). each decmal dgt to generate a t. Let hstogram BK = {BK and 1, sort BK,... hstogram, BK B } be n descendng block. Aorder. secretthe mage dgt s formed wth asmaxmum a bnary strng. frequency The s strng s separated nto several substrngs sze K. I Each ', d ˆ'. substrng s transformed nto a decmal dgt d. encoded wth smallest dstorton code par ( )

8 Symmetry 017, 9, The scheme computes occurrence frequency each decmal dgt d to generate a hstogram and sort hstogram n descendng order. The dgt d wth maxmum frequency s encoded wth smallest dstorton code par (I, d ˆ Symmetry 017, 9, 3 ). 8 5 Each block BK can be used to hde (B 1) code pars. The scheme conceals reduced dgt n pxel Each BKblock by usng can anbe averagng used to hde method ( 1) to code generate pars. The scheme stego-pxels conceals BK reduced and BK dgt, where 1 n B pxel 1. The ndcators by usng are an averagng collected to method form ato combned generate code, stego-pxels and code and s concealed, where nto 1 1. The are collected last pxel block to generate BK B and to form BK B. a combned code, and code s concealed nto last pxel block to generate Fgure 9 shows nformaton hdng and dagram. proposed method. More detals Fgure 9 shows nformaton hdng dagram proposed method. More detals procedures procedures are gven are gven below. below. Fgure Fgure 9. Informaton 9. hdng dagram proposed scheme. Step 1: Transform a set K secret bts nto a decmal dgt. Let d be decmal dgt that s Step 1: Transform computed a setby K secret bts nto a decmal dgt. Let d be decmal dgt that s computed by K Kj 1 j d = d = s, () j 1 s j, () j= 1 j=1 where d [0, K 1] and s j denotes jth secret bt n set. where d [0, K 1] and s j denotes jth secret bt n set. Step : Compute occurrence frequency each decmal dgt. Let F ( d ) be occurrence Step : Compute occurrence frequency each decmal dgt. Let F(d) be occurrence frequency frequency each decmal dgt. These frequences are sorted n descendng order, and each decmal dgt. These frequences are sorted n descendng order, and ndex sorted ndex sorted results s denoted as O ( d ). results s denoted as O(d). Step 3: Compute reduced code d ˆ for each decmal dgt. In Fgure 6, decmal dgt d has Step 3: Compute reduced code d been folded twce to generate ˆ for each decmal dgt. In Fgure 6, decmal dgt d has been reduced code dˆ and ndcator I. Table shows foldedreduced twce tocodes generate and ndcators reduced wth K code = 3. The d ˆ and decmal ndcator dgts are reduced I. Tableeffectvely shows from reduced [0, codes and K 1] ndcators [ K, wth K 1]. K = 3. The decmal dgts are reduced effectvely from [0, K 1] to [ K, K 1]. Table. Example code pars Fgure 6 wth K = 3. Table. Example code pars Fgure 6 wth K = 3. d I d dˆ I ( I, d ˆ ˆd ) (0, ) 1 (0, 1) 0 (0, 0) (0, 1 1) (1, ) (1, 1) 1 (1, 0) 0 (1, 1) 1 (I, ˆd) (0, ) (0, 1) (0, 0) (0, 1) (1, ) (1, 1) (1, 0) (1, 1) However, reduced dgts n Table do not show feature secret mage. In Table, absolutely reduced code d ˆ = s maxmum reduced code, whch causes maxmum dstorton when drectly concealed nto pxel. If maxmum reduced code s occurrence

9 Symmetry 017, 9, However, reduced dgts n Table do not show feature secret mage. In Table, absolutely reduced code d ˆ = s maxmum reduced code, whch causes maxmum dstorton when drectly concealed nto pxel. If maxmum reduced code s occurrence frequency s hgh, n drectly embeddng t n mage wll decrease vsual qualty. Hence, proposed scheme furr re-encodes reduced code and ndcator code accordng to order O(d). The re-encoded code d ˆ s computed by d ˆ O(d) = sgn(o(d)), (3) 4 where sgn(v) = { 1, f v s an odd number, 1, orwse. (4) Step 4: Compute re-encoded ndcator I by 0, f O(d) = 0, I = 1, f mod((o(d) + 1), 4) = 0 or mod(o(d), 4) = 0, 0, orwse. (5) The above procedure re-encodes reduced dgts and ndcators, whch occurs most frequently as mnmum absolute value. The re-encoded code pars Table are shown n Table 3. Table 3. The re-encoded code pars Table. O(d) I ˆd (I, ˆd ) (0, 0) (0, 1) (0, 1) (1, 1) (1, 1) (0, ) (0, ) (1, ) Step 5: Generate a mappng table for furr embeddng and recovery processes. Integrate re-encoded code pars (I, d ˆ ) wth ndces d to form a mappng table. The mappng relatonshp must be recorded for use n recovery phases. Table 4 shows an example mappng table wth K = 3. Table 4. Example mappng table wth K = 3. d F(d) O(d) I ˆd (I, ˆd ) 0 787, (0, 1) 1 90, (0, ) 33, (1, ) 3 90, (1, 1) 4 90, (1, 1) 5 34, (0, ) 6 90, (0, 1) 7 879, (0, 0) Step 6: Dvde a cover mage nto server blocks. Let BK = {BK 1, BK 1,..., BK B } be a block. Step 7: Pck (B 1) code pars {(I 1, d ˆ 1 ), (I, d ˆ ),..., (I B 1, d ˆ B 1 )} to embed nto block BK. (1) Conceal re-encoded reduced dgt ˆ d n pxel BK by usng BK = BK + ˆd, (6)

10 Symmetry 017, 9, Symmetry 017, 9, d ˆ B K = BK, (7) and Step 8: where 1 1, B K denotes th pxel frst stego-block and B K ˆd BK = BK denotes th pxel second stego-block. Fgure, 10 shows that proposed (7) ˆd method where 1 can control B 1, BK dstorton denotes wthn pxel. frst stego-block and BK denotes th pxel second stego-block. Fgure 10 shows that proposed method can () Collect ndcators to form control dstorton wthn ˆd a combned code (). = (,,, ). The combned code s computed by () Collect ndcators to form a combned code (ID) 10 = (I 1, I,..., I B 1 ). The B 1 combned code s computed by 1 ID = I (8) = 1 (3) Embed combned code n ID pxel = 1 I (8) BK = BK (3) Embed combned codeb ID n B pxel BK, and B (9) BK ID B = BK B ID +, and (9) BK B = BKB (10) BK ID Repeat Step 6 untl all blocks have been processed. B = BK B (10) B 1 =1 ID + Fgure Dagram averagng embeddng method. Fgure 11 shows an example to llustrate embeddng process. Fgure 11a s a secret strng Step 8: Repeat Step 6 untl all blocks have been processed. wth 4 secret bts. Let K = 3, and frst three secret bts 110 are transformed nto a decmal dgt 3 Fgure 11 shows an example to llustrate embeddng process. Fgure 11a s a secret strng wth 4 secret bts. Let K = 3, and frst three secret bts 110 are transformed nto a decmal d = s = = 6. The scheme maps decmal dgt d to = 1 3 dgt mappng d = table 1 as s shown = 1 1 n Table to 1 obtan re-encoded = 6. The code scheme par maps, decmal = (0, 1). dgt The d transformaton =1 or secret bts follows same procedure descrbed above. to mappng table as shown n Table 4 to obtan re-encoded code par (I Assume a cover mage s dvded nto several blocks szed B = 3. Each block 1 can, d ˆ 1 ) = (0, 1). The be used to hde transformaton ( 1) = (3 1) = or code secret pars. bts In follows Fgure 11a, same procedure code descrbed pars are above.,,, = Assume a cover mage s dvded nto several blocks szed B = 3. Each block can be used {(0, 1), (1,1)}. Fgure 8b shows a cover mage. The frst block s {105, 149,13 }. The reduced to hde (B 1) = (3 1) = code pars. In Fgure 11a, code pars are {(I dgts = 1 and =1 are concealed nto = 105 and = 149, respectvely. 1, d ˆ 1 ), (I The, d ˆ stegopxels frst cover pxel = 105 are computed by 1 13 }. The reduced )} = {(0, 1), (1, 1)}. Fgure 8b shows a cover mage. The frst block s BK = {105, 149, B K 1 = BK1 + = ( 1) = 104 and dgts d ˆ 1 = 1 and d ˆ = 1 are concealed nto BK 1 = 105 and BK = 149, respectvely. The stego-pxels frst cover 1 pxel BK 1 = B K 1 = BK1 = = The are stego-pxels computed by BK second 1 = BK cover pxel = 105 = ( 1) are = computed 104 and BK 1 = BK 1 1 = = 105. The stego-pxels second cover pxel BK = 149 are by 1 B K = and 1 computed by BK B K = 149 = 148. Then, scheme collects ndcators to form = = 149 and BK = = 148. Then, scheme collects ndcators a combned to code form a combned = ( ) code = (01) ID = (I (1) 1 I ). The = (01) combned = (1) 10 code. The s combned embedded code n s embedded pxel n = pxel BK 13 by B = 13 by 1BK 3 = BK = = 13 B K 3 = BK3 + = = 13 and 1and BK 3 = BK 3 1 = 13 1 = 131. B K 3 = BK3 = 13 1 = 131. Two stego-blocks are Two stego-blocks are shown n Fgure 11b. shown n Fgure 11b.

11 Symmetry 017, 9, Symmetry 017, 9, The embeddng procedure s executed repeatedly untl all all code pars pars are are embedded. The The fnal fnal stego-mages, along wth mappng table, are sent to to recever for for extracton and and recovery. (a) (b) Fgure Fgure Example Example proposed proposed method. method. (a) (a) Secret Secret encodng; encodng; (b) (b) Embeddng Embeddng example. example Overflow/Underflow Overflow/Underflow Problem Problem In In embeddng embeddng process, process, an an underflow/overflow underflow/overflow problem mght occur as a result problem mght occur as a result reduced code. For example, f pxel s BK = 54 and ˆd ˆd = 3, n two toger would cause reduced code. For example, f pxel s BK = 54 and = 3, n two toger would overflow problem. In proposed scheme, range ˆd s [ K, K 1]. If a pxel s larger than 55 ( K 1) = 56 K, n overflow problem mght occur because addton cause overflow problem. In proposed scheme, range dˆ s [ K, K 1]. If a pxel s K 1. If a pxel that s less than K, n t mght cause underflow problem because larger addton than 55 ( K 1) = 56 K, n overflow problem mght occur because addton K 1. If a K. For example, assume K = 4, and range ˆd s [ 4, 3]. Suppose that BK = 0, pxel that s less than K, n t mght cause underflow problem because ˆd = 3, and ˆd = 3 =. Then, stego-pxel s BK ˆd =, addton K. For example, assume K = 4, and range dˆ and re s an underflow problem. Hence, embeddable pxel s defned as beng n range s [ 4, K 3]. and Suppose 56 that K BK. In = 0, embeddng process, ˆd proposed scheme determnes wher 3 pxel BK s n range or not. If dˆ = pxel 3, and s wthn = range, =. n Then, t could stego-pxel be classfed s nto BKa block. However, =, and re pxel s an mght underflow cause an underflow/overflow problem and pxel s non-embeddable. ˆd For non-embeddable pxel, problem. stego-pxels are set to equal value orgnal pxels. For example, assume that K = 4 and Hence, embeddable pxel s defned as beng n range K and 56 K. In embeddng process, proposed scheme determnes wher pxel BK s n range [ K,

12 56 K ] or not. If pxel s wthn range, n t could be classfed nto a block. However, Symmetry 017, 9, pxel mght cause an underflow/overflow problem and pxel s non-embeddable. For nonembeddable pxel, stego-pxels are set to equal value orgnal pxels. For example, 56 K ] or not. If pxel s wthn range, n t could be classfed nto a block. However, assume that K = 4 and a pxel n range [ Symmetry pxel mght 017, 9, cause 3 an underflow/overflow problem 4, 56 and 4 ] = [4, 5] s embeddable. In Fgure 1, pxel s non-embeddable. For 1non- embeddable pxel, stego-pxels are set to equal value orgnal pxels. For example, 5 pxel 54 s out range, whch means t s non-embeddable. The stego-pxels are set to equal ts orgnal pxel. The next pxels 13 and 105 are embeddable. However, next pxel s nonembeddable and cannot be classfed nto a block. So, next pxel In Fgure 50 s 1, gared pxel wth 54pxels s out13 assume that K = 4 and a a pxel n range [ 4 pxel n, 56 4 range [ ] = [4, 5] 4, 56 s embeddable. 4 ] = [4, 5] s embeddable. In Fgure 1, pxel 54 s out range, whch means t s non-embeddable. The stego-pxels are set to equal ts and range, 105 to whch form means block BK t s={13,105,50 non-embeddable. }, and The embeddng stego-pxelsprocess are set to s equal performed. ts orgnal pxel. The orgnal pxel. The next pxels 13 and 105 are embeddable. However, next pxel s nonembeddable and cannot be classfed nto a block. So, next pxel 50 s gared wth pxels 13 next pxels 13 and 105 are embeddable. However, next pxel s non-embeddable and cannot be classfed nto a block. So, next pxel 50 s gared wth pxels 13 and 105 to form block and 105 to form block BK ={13,105,50}, and embeddng process s performed. BK = {13, 105, 50}, and embeddng process s performed. Fgure 1. Example a block wth three embeddable pxels..7. Extracton and Recovery Fgure 1. Example a block wth three embeddable pxels. In ths secton, we descrbe extracton and recovery processes by whch re-encoded reduced dgts Extracton and secret and Recovery bts are extracted from stego-mage as well as process cover mage recovery. There are ( 1) code pars concealed n an embeddable block. Hence, recever In ths secton, we descrbe extracton and recovery processes by whch re-encoded reduced dgts dvdes and secret stego-mages bts bts are are extracted nto extracted several from from blocks stego-mage stego-mage sze asb. well The as as re-encoded well process as reduced process coverdgts mage cover dˆ recovery. mage can be There recovery. extracted are (B by There computng 1) are code ( 1) pars dfferences concealed code pars between nconcealed an embeddable two n stego-pxels, an embeddable block. where Hence, block. d ˆ recever Hence, dvdes recever = BK stego-mages nto several blocks sze B. The re-encoded reduced dgts dvdes stego-mages nto several blocks sze B. The re-encoded reduced ˆd BK and 1 1. The combned code s extracted from last pxels can be extracted dgts dˆ by can be computng dfferences between two stego-pxels, where extracted by computng dfferences between two stego-pxels, ˆd = BK stego-blocks by BK ID = BK B BK. B where d ˆ and 1 B 1. The Then, recever transforms combned code ID nto ( 1) bnary = bts. BK BK and 1 combned code s extracted from last pxels stego-blocks by ID = BK Each B BK bt represents B. Then, recever 1. an ndcator The transforms combned I. One ndcator code combned s extracted I code along IDfrom wth nto one (B last re-encoded 1) pxels bnary bts. reduced Each stego-blocks dgt bt represents d ˆ forms by an ID = ndcator BK code B Bpar KI B. One Then, ( I ndcator recever I along transforms wth one re-encoded combned reduced code ID dgt nto ˆd ( 1) forms bnary codebts. par Each (I, ˆd bt ). represents After, d ˆ ). After code par s obtaned, t s n mapped to mappng table to obtan orgnal code an ndcator par s obtaned, I. One ndcator t s n mapped I along towth one mappng re-encoded table to reduced obtandgt orgnal d ˆ forms decmal code dgt par d. decmal dgt d. Each decmal dgt Each decmal dgt d s transformed nto d s transformed nto K secret bts. K secret bts. ( I, In d ˆ ). After recovery code process, par s obtaned, cover pxel t s n mapped to mappng table to obtan orgnal In recovery process, cover pxel BK can be recovered by average between two stegopxels,.e., BK can be recovered by average between two decmal dgt d stego-pxels,.e., BK. Each BK decmal dgt d s transformed nto K secret bts. = + BK BK = +BK. Fgure. Fgure 13 shows 13 shows data data extracton extracton and and recovery recovery procedure procedure In recovery process, cover pxel BK can be recovered by average between two stegopxels,.e., BK + proposed proposed method. method. BK BK =. Fgure 13 shows data extracton and recovery procedure proposed method. Fgure 13. Dagram extracton and recovery processes. Fgure 13. Dagram extracton and recovery processes. Followng samefgure example 13. Dagram presented n Fgure extracton 11b. and Therecovery stego-blocks processes. are BK = {104, 149, 13} and BK = {105, 148, 131}. The re-encoded reduced codes are ˆd 1 = BK 1 BK 1 = = 1 and ˆd = BK BK = = 1, and combned code s ID = BK 3 BK 3 = = 1. The combned code s transformed nto (3 1) = bnary bts ID = (01), where

13 Symmetry 017, 9, I 1 = 0 and I = 1. The code pars are (I 1, ˆd 1 ) = (0, 1) and (I, ˆd ) = (1, 1). The orgnal decmal dgts d = 6 and d = 3 and can be derved by mappng m nto mappng table as shown n Fgure 11a. Fnally, decmal dgts d = 6 and d = 3 are transformed nto three secret bts,.e., 110 and 011. Furrmore, orgnal pxel can be recovered by average between BK and BK,.e., BK 1 = BK 1+BK 1 = = 105, BK = = 149, and BK 3 = = 13. In extracton process, proposed scheme determnes wher two stego-pxels are both outsde range [ K, 56 1 ]. If so, n pxels are non-embeddable. If two stego-pxels are not equal and more than one pxel s wthn range, n pxels are embeddable and data are concealed wthn. The secret nformaton can be extracted, and pxels can be restored followng extracton procedure Re-Encodng Combned Code In embeddng process, combned code s used to ndcate number sub-bands re-encoded code. The value range ID s [0, (B 1) 1]. For example, assume that block sze s set to be B = 5. The value range ID s [0, (5 1) 1] = [0, 15]. The maxmum value range s 15. The value s drectly added to last pxel block to generate stego-pxel. However, f maxmum value occurrence frequency s hgh, n drectly embeddng t n pxel wll decrease vsual qualty. Therefore, proposed scheme selectvely re-encodes combned code accordng to ts occurrence frequency and generates a mappng table to record relatonshp between combned code and re-encoded combned code. The re-encodng procedure s same as re-encodng procedure reduced code. 4. Results In proposed scheme, block sze B and hdng bt K are key factors that nfluence hdng performance. To fnd out proper values 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 = 1), BlockFoldng (B = 3, K = 4, RE = 0), BlockFoldng (B = 3, K = 4, RE = 1), BlockFoldng (B = 5, K = 3, RE = 0), BlockFoldng (B = 5, K = 3, RE = 1), BlockFoldng (B = 5, K = 4, RE = 0), and BlockFoldng (B = 5, K = 4, RE = 1). The parameters B and K are block sze and hdng bts, respectvely. The parameter RE ndcates wher combned code s re-encoded or not. RE = 0 means combned code s orgnal value wthout re-encodng. In contrast, RE = 1 means combned code s re-encoded accordng to ts occurrence frequency. Fve related methods are also mplemented for a comparson wth proposed schemes. These are Lee s dual steganographc scheme (Lee009), Lee s orentaton combnaton scheme (Lee013), Chang s magc matrx scheme (Chang013), Lu et al. s center-foldng scheme (Lu015), and Lu s scheme wthout center-foldng strategy (NonFoldng). Two measurements are used to measure performance hdng methods, embeddng rate and mage qualty. The embeddng rate R s calculated by R = C E (bpp), (11) h w where C s total hdng capacty two stego-mages, E s sze mappng table, and h w s sze mage. A hgh embeddng rate means that proposed scheme has great embeddng ablty.

14 Symmetry 017, 9, where C s total hdng capacty two stego-mages, E s sze mappng table, and h w s017, 9,sze Symmetry 3 mage. A hgh embeddng rate means that proposed scheme has14great 5 embeddng ablty. Image qualty s calculated by usng PSNR gven by Image qualty s calculated by usng PSNR gven by 55 (db), PSNR_z = 10 log10 55 PSNR_z = 10 log10mse_z (db), (1) (1) 1 MSE = 1 (P P ), 0 MSE = hw ( P P), (13) (13) MSE_z where PSNR_z s PSNR value zth stego-mage, db represents decbels, and MSE_z where PSNR_z s PSNR value zth stego-mage, db represents decbels, and MSE_z s s mean squared error between cover mage and stego-mage, and s obtaned by mean squared error between cover mage and stego-mage, and s obtaned by hw where P s cover pxel and P s stego-mage. where P spsnr cover pxel andexpermental P0 s stego-mage. The values n results are average values all PSNR_z, whch can be The PSNR values n expermental results are average values all PSNR_z, whch can be computed by computed by 1 PSNR_avg = = 1 PSNR_z (14) PSNR_avg PSNR_z ((db). db) (14) zz In general, ttssvery very dffcult determne dfference between cover and In general, dffcult to to determne dfference between cover magemage and stegostego-mage by human eyes when PSNR s greater than mage by human eyes when PSNR value value s greater than 30 db.30 db. Sx grayscale mages were used to test hdng performance. Fgure shows shows mages mages Lena, Lena, Sx grayscale mages were used to test hdng performance. Fgure Mandrll, 51. Four Four secret secret mages, mages, Mandrll, Arplane, Arplane, Peppers, Peppers, Lake, Lake, and and Tffany. Tffany.The Thesze sze mage mage s s namely, random (51 51), Dolphn (375 35), Bran (40 315), and TffanySec (51 51) namely, random (51 51), Dolphn (375 35), Bran (40 315), and TffanySec (51 51) are are shown shown n n Fgure Fgure (a) Lena (b) Mandrll (c) Arplane (d) Peppers (e) Lake (f) Tffany Fgure 14. Sx test mages. Fgure 14. Sx test mages.

15 Symmetry 017, 9, Symmetry 017, 9, 3 Symmetry 017, 9, (a) random (51 51) (a) random (51 51) (b) Dolphn (75 35) (b) Dolphn (75 35) (c) TffanySec (51 51) (d) Bran (40 315) (c) TffanySec (51 51) (d) Bran (40 315) Fgure 15. Four secret mages. Fgure Fgure Four Foursecret secretmages. mages. In frst experment, we tested performance proposed scheme wth varous B, K, In In frst frstexperment, experment, we we tested tested performance performance proposed proposed scheme scheme wth wth varous varous B, B, K, K, and RE. Fgure 16 shows expermental results. BlockFoldng s proposed scheme. Under and shows expermental expermentalresults. results. BlockFoldng BlockFoldng proposed scheme. Under and RE. RE. Fgure 16 shows s s proposed scheme. Under same embeddng rate, BlockFoldng (B = 3, K = 3, RE = 0) can acheve hghest mage qualty. same embeddng rate, BlockFoldng = 3, RE= =0)0)can canacheve acheve hghest hghest mage qualty. same embeddng rate, BlockFoldng (B (B = 3, KK == 3,3,RE BlockFoldng (B = 5, K = 4, RE = 1) can get hghest hdng payload. When B = 3 and K = 3, mage BlockFoldng 5, KK==4,4,RE RE= = can hghest hdng payload. When = 3Kand = 3, BlockFoldng (B = = 5, 1) 1) can getget hghest hdng payload. When B = 3Band = 3,K mage qualty wth RE = 0 s hgher than that wth RE = 1. However, when B = 5 and K = 4, mage qualty mage wth = 0 s hgher than thatre wth = 1. However, B =K5 =and K =mage 4, qualty mage qualtyqualty wth RE = 0RE s hgher than that wth = 1.RE However, when Bwhen = 5 and 4, wth RE = 1 s hgher than that wth RE = 0. The reason s that f block sze s small, n qualty wth = 1 s hgher thanwth that RE wth = 0.reason The reason s that block s small, n wth RE = 1 RE s hgher than that = RE 0. The s that f f block szesze s small, n combned code s small enough that t does not need to be re-encoded. However, for a block wth a combned code s small enough that t does need re-encoded.however, However,for fora ablock blockwth wtha combned code s small enough that t does notnot need to to bebe re-encoded. large sze, combned code s usually large enough that t needs to be re-encoded. For example, f alarge largesze, sze, combned combnedcode codess usually usually large large enough enough that re-encoded. For For example, example,ff ( ) t needs to be re-encoded. value range combned code wth B = 5 s [0, (5( 1) ) 1] = [0, 15], maxmum value 15 wll 1] value valuerange range combned combnedcode codewth wthbb== 55 s s [0, [0, 1]==[0, [0,15], 15], maxmum maxmumvalue value15 15wll wll cause great mage dstorton. The re-encodng process can effectvely narrow down dstorton. causegreat greatmage magedstorton. dstorton.the There-encodng re-encodngprocess processcan caneffectvely effectvelynarrow narrowdown down dstorton. dstorton. cause Fgure 16. Cont.

16 Symmetry 017, 9, Symmetry 017, 9, Fgure 16. Cont.

17 Symmetry 017, 9, Symmetry 017, 9, Fgure 16. Results frst experment. Fgure 16. Results frst experment. To compare for a comparson proposed scheme wth or related methods, value B s To set compare to 3 and for 5, a comparson value K s set proposed to 3 and 4, scheme and RE wth s set or to be related 0 and methods, 1. Tables 5 8 value show B s results set to 3 and 5, comparson value among K s set to proposed 3 and 4, and scheme RE s set and to be related 0 and 1. works Tables wth 5 8 show cover results mage Lena and comparson secret among mages random, proposed TffanySec, scheme and Dolphn, related and Bran, works respectvely. wth cover mage Lena and secret mages random, TffanySec, Dolphn, and Bran, respectvely. Table 5. Experment results for secret mage random. Table 5. Experment results for secret mage random. Method B K RE PSNR_1 PSNR_ PSNR_avg Capacty R Tme Method 3 B 3 K 0 RE PSNR_ PSNR_ PSNR_avg Capacty 55,31 R 1.00 Tme , ,31 700, , , BlockFoldng , BlockFoldng ,83 63, , , , , , , Lu , Lu ,048, ,048, NonFoldng , NonFoldng , Lee , Lee , Lee013 Lee , , Chang , , Table Experment results for for secret mage Tffany. Method B K K RE RE PSNR_1 PSNR_ PSNR_avg Capacty Capacty R R Tme Tme ,31 55, ,31 55, , , , BlockFoldng , BlockFoldng , ,83 63, ,776 63, , , ,43 843, Lu ,048, , Lu015 NonFoldng , ,048, Lee009 NonFoldng , , Lee009 Lee ,88 378, Lee013 Chang ,43 54, Chang ,

18 Symmetry 017, 9, Table 7. Experment results for secret mage Dolphn. Method B K RE PSNR_1 PSNR_ PSNR_avg Capacty R Tme BlockFoldng Lu , , , , , , , , , ,048, NonFoldng , Lee , Lee , Chang , Table 8. Experment results for secret mage Bran. Method B K RE PSNR_1 PSNR_ PSNR_avg Capacty R Tme BlockFoldng Lu , , , , , , , , , ,048, NonFoldng , Lee , Lee , Chang , In Table 5, wth secret mage random, PSNR_avg proposed scheme wth B = 5, K = 4, and RE = 1 for cover mage Lena s db, whch s greater than value db for Lu015. The mage qualty proposed scheme s hgher than value 9.48 db obtaned by Lu s scheme. At same tme, hdng rate proposed scheme s 1.61 bpp, whch s hgher than that Lu015 s 0.11 bpp. Under same hdng capacty, mage qualty proposed scheme wth B = 3, K = 3, and RE = 0 s db, whch s hgher than that Lee013 s db. Although Lu015 wth K = 4 acheves hghest hdng rate,.0 bpp, mage qualty Lu015 s decreased to db. In Table 6, although Lee009 has hghest mage qualty 5.90 db, hdng rate Lee009 s only 0.7 db. The results for dfferent secret mages have same stuaton. In Table 8, for secret mage Bran, mage qualty obtaned by Lee009 s hghest. However, ts hdng capacty s 0.53 bpp, whch s lowest among all results obtaned by or methods. The proposed scheme wth B = 3, K = 3, and RE = 0 has same hdng payloads as those Lee013. The mage qualty proposed scheme s db, whch s greater than that or methods, reby ndcatng that proposed scheme stll exhbts better embeddng performance compared wth ors. From results experment, we can see that proposed scheme wth a small block sze B = 3 acheves a hgher mage qualty. Because combned code n small block sze s small, code does not need to be re-encoded where RE = 0. In contrast, proposed scheme wth a large block

19 Symmetry 017, 9, Symmetry 017, 9, sze block B sze = 5 has B = a5 hgher has a hgher hdng capacty. hdng capacty. The combned The combned code acode largen block a large szeblock needssze to be needs re-encoded, to be reencoded, value as value code s usually code very s usually large. very Hence, large. RE Hence, s set tore be RE s set = 1to for be B RE = 5. = 1 for B = 5. The second experment compared proposed proposed scheme scheme wth wth or methods. or methods. Fgure 17 Fgure shows17 shows comparson comparson among allamong fve related all fve methods related andmethods proposed and scheme proposed n termsscheme embeddng terms rate and embeddng PSNR value. rate and Fgure PSNR 17 shows value. that Fgure mage 17 shows qualty that BlockFoldng mage qualty (B = 3, BlockFoldng K = 3, RE = 0) s (B hgher = 3, K = as than 3, RE those = 0) s hgher or than methods. those Under or same methods. embeddng Under rate, same proposed embeddng method rate, can proposed acheve amethod greatercan PSNR acheve value than a greater related PSNR methods. value than The hdng related capacty methods. BlockFoldng The hdng (B = capacty 5, K = 4, RE BlockFoldng = 1) s hgher (B = than 5, K those = 4, RE = 1) or s hgher methods. than those or methods. Fgure 17. Cont.

20 Symmetry 017, 9, 3 Symmetry 017, 9, Fgure 17. Comparson proposed and related methods. Fgure 17. Comparson proposed and related methods. The thrd experment was amed at provng vablty proposed scheme. Several The thrd experment was at provng vablty proposed scheme. steganalyss technques such as amed hstogram steganalyss, RS steganalyss, prmary sets, ChSeveral square, steganalyss technques such as hstogram steganalyss, RS steganalyss, prmary sets, Ch square, sample pars, RS analyss, and fuson detecton were used to test performance proposed sample pars, RS analyss, and fuson detecton were used to test performance proposed scheme. The hstogram steganalyss method compares shapes between cover mage and scheme. The hstogram steganalyss method compares shapes between cover mage and stego-mage to detect wher re s a concealed message. stego-mage to detect wher re s a concealed message. Fgure 18 shows hstogram comparsons Lena wth dfferent parameters. The curve startng Fgure 18 shows hstogram comparsons Lena wth dfferent parameters. The curve startng wth symbol * s hstogram stego-mage. We can see that shape stego-mage wth symbol * s hstogram stego-mage. We can see that shape stego-mage s almost same as that cover mage. s almost same as that cover mage.

21 Symmetry 017, 9, 3 Symmetry 017, 9, Fgure Hstogram Hstogramsteganalyss steganalysslena Lenawth wthdfferent dfferentparameters. parameters. Fgure RS pxels are RS steganalyss steganalyssssaaknd knd attack attackmethod methodproposed proposedby byfrdrch Frdrchetetal.al.InIn method, method, pxels are classfed nto several groups. The method uses a dscrmnaton functon to quantfy smoothness or 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

22 Symmetry 017, 9, 3 5 regularty Symmetry and 017, uses 9, 3 a flppng functon to defne three groups, regular (R), sngular (S), and unusable 5 (U). The percentages each group wth mask M = [ ] and M = [ ] are represented as (U). The percentages each group wth mask M = [ ] and M = [ ] are represented as R_M_G, R_FM_G, S_M_G, S_FM_G, U_M_G, and U_FM_G, respectvely. The hyposes are R_M_G R_M_G, R_FM_G, = R_FM_G, S_M_G S_M_G, S_FM_G, U_M_G, = S_FM_G, and U_M_G and U_FM_G, respectvely. The hyposes are R_M_G = U_FM_G. Fgure 19 shows RS steganalyss results R_FM_G, S_M_G S_FM_G, and U_M_G U_FM_G. Fgure 19 shows RS steganalyss for Lena wth dfferent parameters. In fgures, curve R_M_G s very smlar to that results for Lena wth dfferent parameters. In fgures, curve R_M_G s very smlar to that R_FM_G. R_FM_G. The method The method judges judges re re s no s no secret secret message message hdden hdden n n mage. mage. The The curves curves S_M_G, S_M_G, S_FM_G, S_FM_G, U_M_G, U_M_G, and and U_FM_G U_FM_G have have same stuatons. Hence, Hence, proposed proposed scheme scheme cannot cannot be be detected detected by by RS RS steganalyss. Stego 1 Stego Fgure 19. RS-dagram steganalyss Lena wth secret mage random. Fgure 19. RS-dagram steganalyss Lena wth secret mage random.

23 Symmetry 017, 9, Or tests ncludng prmary sets, Ch square, sample pars, RS analyss, and fuson detecton were appled to examne proposed scheme. Table 9 shows experment report. All numbers n table are very small, whch means proposed scheme s robust aganst steganalytc attacks. Table 9. Steganalyss report for StegExpose. Cover B K Stego Prmary Sets Ch Square Sample Pars RS Analyss Fuson (Mean) Arplane Lake Lena Mandrll Pepper Tffany Stego Stego Stego Stego Stego Stego Stego Stego Stego Stego Stego Stego Stego Stego Stego Stego Stego Stego Stego Stego Stego Stego Stego Stego Stego Stego Stego Stego Stego Stego Stego Stego Stego Stego Stego Stego Conclusons The dual-mage-based hdng scheme s a new technology n data hdng feld. The concept dual-mage, based on nformaton sharng, conssts concealng secret messages n two same cover mages; only someone who has both stego-mages can extract 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 foldng operaton twce and usng an ndcator to dentfy second foldng operaton as a means dstngushng dfferent sub-bands to furr decrease reduced dgt. In addton, proposed method effectvely solves overflow/underflow problem. In order to evaluate performance proposed scheme, eght schemes wth dfferent B and K values were mplemented. Moreover, fve related methods were mplemented for a comparson wth

24 Symmetry 017, 9, proposed scheme. The frst experment showed that a small B value acheves hgher mage qualty, a large K value acheves a large payload, and re-encodng process can effectvely narrow down dstorton when B s larger. The second experment compared proposed and related methods. The results showed that proposed scheme can acheve hgher mage qualty (B = 3, K = 3, RE = 0), better mage qualty under same embeddng rate, and a hgher payload than or schemes (B = 5, K = 4, RE = 1). The thrd experment used several steganalyss technques to prove strong robustness 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 Scence and Technology (MOST E ). Author Contrbutons: Tzu-Chuen Lu desgned algorthm, conducted all experments, analyzed results, wrote manuscrpt, and conducted lterature revew. Hu-Shh Leng conceved algorthm and wrote manuscrpt. Conflcts Interest: The authors declare no conflct nterest. References 1. Melkanen, J. LSB matchng revsted. IEEE Sgnal Process. Lett. 006, 13, [CrossRef]. Wu, D.-C.; Tsa, W.-H. A steganographc method for mages by pxel-value dfferencng. Pattern Recognt. Lett. 003, 4, [CrossRef] 3. Chang, C.C.; Tseng, H.W. A steganographc method for dgtal mages usng sde match. Pattern Recognt. Lett. 004, 5, [CrossRef] 4. Zhang, X.; Wang, S. Effcent steganographc embeddng by explotng modfcaton drecton. IEEE Commun. Lett. 006, 10, [CrossRef] 5. Keu, T.D.; Chang, C.C. A steganographc scheme by fully explotng modfcaton drectons. Expert Syst. Appl. 011, 38, [CrossRef] 6. N, Z.; Sh, Y.Q.; Ansar, N.; Su, W. Reversble data hdng. IEEE Trans. Crcuts Syst. Vdeo Technol. 006, 16, 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, Tan, J. Reversble data embeddng usng a dfference expanson. IEEE Trans. Crcuts Syst. Vdeo Technol. 003, 13, [CrossRef] 9. L, X.; Yang, B.; Zeng, T. Effcent reversble watermarkng based on adaptve predcton-error expanson and pxel selecton. IEEE Trans. Image Process. 011, 0, [PubMed] 10. Gu, X.; L, X.; Yang, B. A hgh capacty reversble data hdng scheme based on generalzed predcton-error expanson and adaptve embeddng. Sgnal Process. 014, 98, [CrossRef] 11. 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. 013, 93, [CrossRef] 1. Peng, F.; L, X.; Yang, B. Improved PVO-based reversble data hdng. Dgt. Sgnal Process. 014, 5, [CrossRef] 13. Qu, X.; Km, H.J. Pxel-based pxel value orderng predctor for hgh-fdelty reversble data hdng. Sgnal Process. 015, 111, [CrossRef] 14. 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. 015, 310, [CrossRef] 15. Chang, C.C.; Keu, T.D.; Chou, Y.C. Reversble data hdng scheme usng two steganographc mages. In Proceedngs 007 IEEE Regon 10 Internatonal Conference (TENCON), Tape, Tawan, 30 Ocotber November 007; pp Lee, C.F.; Wang, K.H.; Chang, C.C.; Huang, Y.L. A reversble data hdng scheme based on dual steganographc mages. In Proceedngs 3rd Internatonal Conference on Ubqutous Informaton Management and Communcaton (ICUIMC 09), Suwon, Korea, January 009; pp Lee, C.F.; Huang, Y.L. Reversble data hdng scheme based on dual stegano-mages usng orentaton combnatons. Telecommun. Syst. 013, 5, [CrossRef]

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