Grayscale-Based Image Encryption Considering Color Sub-sampling Operation for Encryption-then-Compression Systems

Grayscale-Ba sed Image Encryption Con sidering Color Sub-sampling Operation for Encryption-then-Compression Systems W arit Sirichotedumrong, T atsuya Chuman and Hit oshi Kiya T okyo Metropolitan University , Asahigaok a, Hino-shi, T okyo, 191-0065 , Japan Abstract —A new graysc ale-based block scrambling image encryption scheme is p resented to enhance the security of Encryption-then-Compression (EtC) system s, wh ich are used to securely transmit images through an untrusted chann el pro vider . The p roposed scheme enables the use of a smaller block size and a larg er number of blocks than the con ventional scheme. Images encrypted using the proposed scheme include less color in fo rma- tion due to the use of grayscale images e ven wh en the original image h as three color ch annels. These features enhance security against various attacks, su ch as jigsa w puzzle solver and brute- fo rce attacks. Moreo ver , it allo ws the u se of color sub -sampling, which can impr ov e the compression perf ormance, although the encrypted i mages hav e no color inf ormation. In an experiment, encrypted i mages were up loaded to a nd then downloaded from Fac ebook and T witter , and the r esults demonstrated that the proposed scheme is effectiv e f or EtC systems, while maintaining a high compre ssion perfo rmance. Index T erms —Compression, encryption, EtC systems I . I N T RO D U C T I O N The use of images and video sequences has gr eatly in- creased because of rapid growth of the I n ternet and m u ltimedia systems. A lot of studies on secur e , efficient and flexible commun ications have been r eported [1]–[3]. For securing mul- timedia data, full encryp tion with provable security (like RSA, AES, etc) is the most secur e optio ns. Ho wev er , many multi- media ap plications have been seek ing a trade-off in secur ity to en a b le other requ irements, e .g., low proc essing demands, retaining bitstream comp liance, and signal pro cessing in th e encryp ted do m ain. Encryp tion-then - Compression (EtC) systems with JPEG compression [3]–[6] h av e been propo sed to be app lied to Social Network Services (SNS) and Clou d Photo Storag e Services (CPSS). Ho wev er , th e color-based image encryptio n schemes fo r EtC systems [7]–[ 10] cannot provid e th e robust- ness ag ainst color sub-samp ling used f or JPEG comp r ession because an encrypte d image is a f u ll-color image. In o rder to solve this issue, the gray scale-based images encry ption has been prop osed [1 1], [ 12] to encryp t a fu ll- color imag e as a grayscale-b ased imag e. Even if the g r ayscale-based image encryp tio n [1 1] c an a void th e effect of co lor sub-sampling, it is impo ssible to co nsider color sub-samplin g ope ration because the g rayscale-based ima g e is generated from RGB This work wa s partia lly supported by Grant-in -Aid for Scienti fic Re- search(B) , No.17H03267, from the Japan Society for the Promotion Scienc e. Fig. 1: EtC system compon ents. Moreover , compa red to the color-based image encryp tio n [7]–[ 10], the compression performan ce is strongly degraded. Accordin g to [12], the g rayscale-based image en - cryption gen e rated from YCbCr co mpon e n ts and the quan ti- zation table f or gray scale-based im ages have been p roposed to provid e th e better compression performan ce. Howev e r, the color sub-sam pling o peration has no t been consider ed. This paper discusses and co nsiders the color sub-sampling operation for grayscale-b ased imag e encr yption. Instead of generating the grayscale- based image from RGB componen ts, a fu ll-color imag e in RGB color spac e is firstly transformed to YCbCr color space. Hence, c o lor sub-sampling o peration can be perfo rmed to g enerate grayscale-based images. Moreover , we describe scen a rio and r equiremen ts tha t image encryption have to satisfy . The enhancem ents of com p ression p erforma nce and robustness ag ainst colo r sub -sampling are ev alua te d in terms of Rate-Distor tio n (R-D) curves. I I . S C E NA RI O A N D R E QU I R E M E N T S According to the image manipu lation on Social Network Services (SNS) and Cloud Photo Storage Ser vices (CPSS) [13], almost all providers manipu late every up loaded image as illustrated in Fig. 1. Because of such scenarios, the grayscale- based im age en cryption schem es f or E tC system have been propo sed [11], [12] as th e e x tension of th e color-based EtC systems [7]–[1 0]. There are three requir e ments that image encryp tion schemes have to satisfy: co mpression per forman ce, security level, and robustness against image manipulatio n. I g I e K 1 K 3 K 2 Grayscale-based Image Generation Block Scrambling Negative-Positive Transformation Block Rotation and Inversion Key Block Scrambling Steps I RGB Fig. 2: Con ventiona l g rayscale-based b lock scr a mbling image encryp tio n 1) Compres sion P erformance: In order to apply an imag e encryp tio n scheme to SNS and CPS S, it is necessary for encryp ted JPEG images to have almost the same compre s- sion perfor mance as the non-enc rypted ones. The color-based encryp tio n scheme [7]–[1 0 ] can provide almost the same compression perf ormanc e as the n on-encr ypted JPEG images. Howe ver, it cannot be achieved by the co nventional gray scale- based image encryption [11] because a grayscale-based ima g e is gen erated from RGB comp onents a s sho wn in Fig. 2 2) Security Level: In this paper , w e con sider security against br ute-forc e attack and jigsaw puzzle solver attacks as ciphertext-on ly attacks. It has been confir m ed th at the key space o f b lo ck scramb ling-based imag e encryp tion for EtC systems is huge eno ugh against bru te-force attack [9] an d has the r o bustness ag ainst jigsaw puzzle d solver attack s [11], [14]– [17]. This paper considers the extended jigsaw puzzle solver [16], [17] as cip hertext-only attacks. There are three metr ics using fo r evaluating the ro bustness against jigsaw p uzzle solver attacks [15], [1 8] which are descr ib ed as follows: • Direct c omparison ( D c ) is the ratio between the n umber of pieces wh ich are placed in the correct position an d the total num ber of pieces. • Neighbor co mparison ( N c ) expresses the ratio of the number of pieces tha t are joined with the correct p attern and the to tal number of pieces. • Largest components ( L c ) refers to the ra tio between the nu mber of the largest joined blo cks that are corre ctly adjacent and the n umber of pieces. Note that D c , N c , L c ∈ [0 , 1] and a larger v alu e means a higher com patibility . As imag es encry pted using the g rayscale-ba sed image en- cryption contain only o ne co lor chann el [11], th e smallest block size ( B x × B y ) of the g r ayscale-based image enc r yption is 8 × 8 . Mo reover , since th e block size is smaller, a n d the number o f blocks is larger than the color-based encryption scheme. As a r esult, gra yscale-based en c rypted imag es h av e stronger security and ro bustness again st jig saw puzzled solver attacks [17] than th ose with the co lor-based o ne. 3) Robustness against Image Ma nipulatio n: It is known that almost all SNS and CPS S provide r s manipu la te ev er y u p- loaded image when it satisfi es their conditio ns [1 3]. Uploaded JPEG image s are decom pressed an d sequen tially r ecompr e ssed with new com pression parameters based on th eir algorithm s. In recom p ression, as the color sub-sampling is usually carried out, th e image encry p tion which has rob ustness against colo r sub-samplin g is requ ired. Howe ver, this req uirement canno t be I g I e K 1 K 3 K 2 Grayscale-based Image Generation Method Block Scrambling Negative-Positive Transformation Block Rotation and Inversion Key Block Scrambling Steps I Color Space Transformation CT I RGB Fig. 3: Proposed grayscale- based block scrambling image encryp tio n achieved by the co lor-based encryptio n sch eme [7]–[10] while the con ventional grayscale-based image encryption [11], [12] has been p roposed to av o id th e effect o f color sub-sampling. I I I . P RO P O S E D G R A Y S C A L E - B A S E D I M A G E E N C RY P T I O N This sectio n d escribes an encryptio n pro cedure of the pro - posed grayscale- based image encry ption and how the color sub-samplin g operation is con sidered with the encr y ption scheme. Finally , th e qu antization table fo r grayscale-based images is discu ssed. A. Encryption Pr oce d ur e Let us consider a full-colo r imag e ( I RGB ) with M × N pixels. T o encry pt I RGB , th e f ollowing six steps a re carried out as f ollows (See Fig. 3). Step1: I RGB are transform ed into the full-color image in YCbCr color space ( I Y C bC r ), so that I C T = I Y C bC r . Step2: Luminance ( i Y ) and chr o minance ( i C b and i C r ) are concatenate d vertically or hor izontally to gener ate the grayscale-b ased imag e ( I g ) with 3( M × N ) pixels. Step3: I g with M g × N g pixels is di vided into non- overlapping blocks each with B x × B y . The number of d ivided block s, N b , is expressed by N b = ⌊ M g B x ⌋ × ⌊ N g B y ⌋ (1) where ⌊·⌋ is the floor fun ction that r ounds down to th e nearest integer . Step4: Randomly permute the di v id ed b locks based o n a ran dom integer which is gene r ated by a secr et key K 1 . Step5: Rotate and in vert each d ivided block rando mly based on a rand om integer ge n erate by a secret key K 2 . Step6: Perform the negati ve-po sitive transfo rmation to each di- vided bloc k using a ra n dom bina ry integer generate d by a secret key K 3 . A tr ansformed pixel of i th blo ck is represented by p ′ and can be e x pressed as p ′ =  p ( r ( i ) = 0 ) p ⊕ (2 L − 1) ( r ( i ) = 1 ) (2) where r ( i ) is a random binary integer ge n erated b y K 3 and p is the pixel value of an original imag e with L bits per pixel. B. Color sub- sampling for Grayscale-based Images As previously describ ed in Section III-A that I RGB is fir stly transform ed to I Y C bC r , this p aper considers the color sub- sampling operation for the gra y scale-based imag e encry ption. Since human eyes ar e m ore sensiti ve to i Y than i C b and i C r , RGB (3 color channels) YCbCr (3 color channels) YCbCr with 4:2:0 color sub-sampling (3 color channels) i Y Color Sub-sampling Grayscale-based Image (1 color channel) i' Cb Cr i' i Y i' Cb Cr i' i Y i' Cb Cr i' Fig. 4: Grayscale - based image generatio n method we downsample i C b and i C r using 4:2:0 color sub-samplin g operation provided by IJG sof tware [19] as shown in Fig. 4 . The sub-sampled chrominance com ponen ts are represen ted by i ′ C b and i ′ C r . Eventually , i Y , i ′ C b , and i ′ C r are combined to produ ce I g with 3 2 ( M × N ) pixels. The example of I g with 4:2:0 color sub-sampling is shown in Fig. 5(a). As I g has only on e color chann el, the color sub-samp ling operation is not carried ou t. Thus, the prop osed scheme can pr ovide the robustness against co lor sub -sampling and better comp ression perfor mance. C. Quan tization T able for Grayscale-based Images JPEG softwares, such as Inde p endent JPEG Group (IJG) software [19], generally u tilize tw o default quantization tables to quantize i Y , i C b , and i C r of I Y C bC r where i Y is q uan- tized b y the luminan ce quantizatio n table (Y -table), and th e chromin ance quantization table (CbCr-table) is employed to quantize i C b and i C r . Ho wever , users are allowed to use other tables rather than th e default ones. The im a ge-depe n dent qua n - tization tab le h as been proposed to minimize th e distortion of quantization process o f each blo ck [20]. H owever , since I g is generated from i Y , i C b , and i C r , those tables are not designed for I g . Th erefore, the quantization table called G-table has been pro posed to improve th e compression perf ormance of I g [12]. In JPEG comp ression, all pixel values in each b lock of I g are m apped f rom [0 , 255] to [ − 127 , 1 2 8] by subtracting 128, th en ea ch block is tr ansformed using Discrete Cosine T ra nsform (DCT) to ob tain DCT coefficients. The DCT coefficients are employed to gener ating G-tab le. Let D n ( i, j ) be the DCT coefficient of the n th block at the position ( i, j ) where 1 ≤ i ≤ 8 and 1 ≤ j ≤ 8 . Considering ev e ry blo ck of I g , the Euclidean distance between the origin O and D n ( i, j ) is measured , an d the arithmetic mean of th e distance is expr e ssed b y c ( i, j ) = 1 N b N b X n =1 | D n ( i, j ) − O | (3) where I g consists of N b blocks. As a set of grayscale-b ased images which consists of R images is utilized to deter mine G-table, we define c n ( i, j ) as c ( i, j ) of the n th image and calcu late the av erage of every c ( i, j ) fro m R grayscale-based images. The av erage ¯ c ( i, j ) is calculated as fo llow . ¯ c ( i, j ) = 1 R R X n =1 c n ( i, j ) (4) Y i' Cr i' Cb i' (a) Grayscale-based image with 4:2:0 color sub-sampling (b) Image enc rypted by grayscal e-based image encryption consideri ng 4:2: 0 col or sub-sampling Fig. 5: E xample images 17 26 32 40 47 56 70 92 26 36 43 52 59 69 84 110 34 44 52 61 70 80 98 125 43 54 63 72 82 95 113 142 52 65 74 84 95 109 129 159 63 78 88 99 110 126 149 182 79 97 109 119 132 150 176 213 102 124 137 149 164 183 213 254 Fig. 6: G-table fo r grayscale-b ased imag es T o o btain G-tab le, q ( i, j ) represents the quantization step size at ( i, j ) an d is d e r iv e d from the ratio betwe e n ¯ c (1 , 1) and ¯ c ( i, j ) . The step size can be calculated b y q ( i, j ) =  ¯ c (1 , 1) ¯ c ( i, j )  + ǫ (5) where ǫ is set to 16 for ad justing the Y -table step size at (1 , 1) as for IJG sof tware [19]. I V . E X P E R I M E N T S A. Experimenta l Set-up T o ev alu ate the performan ce of the gray scale-based im age encryp tio n con sidering color sub-sampling operation, this pa- per utilizes two datasets a s belo w . (a) 20 images from MI T dataset ( 67 2 × 4 80 ) [15] (b) 1338 images f rom Uncompr essed Color Image Database (UCID) [21] All images in Dataset (a) wer e encrypted using the propo sed scheme and co n ven tional one with B x = B y = 8 . Then, all e ncrypted images were compressed with specific quality factors, Q f ∈ [70 , 100] , using the JPEG standard from IJG software [19]. All images in dataset (b) were com pressed u sing IJG software [19] to obtain com pressed gray scale-based images. Note that DCT coefficients are extracted du ring th is JPEG compression . According to the p rocedur es in section III- C, G- table was designed by usin g the DCT co efficients whereas N b = 4608 , R = 133 8 , and ǫ = 1 6 . As a r esult, G-table is shown in Fig . 6. W e c o nduct two e xperime n ts: witho ut color sub-samplin g (4:4:4) and with c o lor sub-sampling (4:2 :0). All JPEG images were decom pressed an d measure Peak -Signal- to-Noise Ratio (PSNR), respecti vely . 2  31 3  41 4  5    6  0 1 2 3 4   P S N  (d B ) b   U   ncrypted (4:4:4)    ncrypted (4:2:0)  roposed grayscale-based (4:2:0) Con v  ntional Grayscale-based 3 1 3 2 3 3 3 4 3  3  3 7 3 8 3 9 0   0 .  0      0   0  0 ! " 0 # $ 1 % S & R ( d ' ) ( ) * Fig. 7: R-D cu rves of JPEG images B. Results and Discussi ons W e evaluated the compression perf ormance and ro bustness against color sub-samp ling of th e propo sed scheme based on Rate-Distortion (R-D) curves which are the relation between the arithmetic mean PSNR of the imag es an d bits p e r p ixel ( bpp ) of JPEG images. The propo sed grayscale-b ased image encryp tio n was co mpared with the non - encryp ted images. 1) Compres sion P erforman ce of Up loaded Images: Fig- ure 7 shows th at the p roposed scheme h a s almost the same compression perfo rmance as non- encryp te d on es with 4:2:0 color sub-sampling and also outperforms tho se without any color sub - sampling and th e conventional one . The pro posed encryp tio n schem e allows u s to a void the effect of color sub- sampling a n d also improve comp ression perfor mance of JPEG compression . 2) Compres sion P erformance of Do wnloaded Images: Ac- cording to im age manipulation carried out by SNS providers [13], an u ploaded image is deco ded and comp ressed respec- ti vely based on their specifications when th e u ploaded imag e is satisfied the co nditions of SNS p roviders. In Fig. 8(a ) and (b), th e p erform ance of the colo r-based image encryp tion a nd th e pr o posed schem e was compared in terms of comp ression performanc e of do wn loaded images from T witter an d Facebook, r e spectiv ely . Note th at B x = B y = 16 is used as a block size for the co lor-based im age encryp tio n to a void block distortio n. T witter recomp resses the u ploaded JPEG images with 4:2:0 color sub-sam pling wh en Q f u ≥ 8 5 to the new JPEG images with 4:2:0 sub-sam pling ratio and Q f u = 85 . A s shown in Fig. 8 (a), the pro posed sch eme provided hig her compression perfor mance than those with the color-based image encryption and non - encryp ted ones. In Faceboo k , e very u p loaded JPEG im age is recompressed 30 31 32 33 34 + , - / 1 : 0 ; < = 1 > ? @ 2 A C D E S F G (d H ) I J p K L M ncrypted (4:2:0) Color-based (4:2:0) O roposed grayscale-based (4:2:0) (a) T witter 30 Q S T V 31 W X Z [ 32 \ ] ^ _ 33 ` a c e 34 0 f g h 1 i j k 2 2. l m S NR (d n ) b o q rs t ncrypted (4:2:0) Color-based (4:2:0) u roposed grayscale-based (4:2:0) (b) Facebook Fig. 8: R-D cu rves of do wnloaded JPEG images (a) Color-based image encryption sche m e with B x = B y = 8 and 4:2:0 sub-sampling (PSNR=26.21dB) (b) Proposed scheme with B x = B y = 8 (PSNR=31 .85dB) Fig. 9 : E xample o f de crypted imag e s downloaded from T witter to the new JPEG image with 4:2:0 sub-sampling ratio an d Q f u ∈ [71 , 85] . The images encry pted by the color-based en - cryption we re heavily distor ted by color sub-sam pling carried out by Facebook . I n com parison, the propo sed one provided higher image qua lity compared with the color-based image encryp tio n. Moreover , as sho wn in Fig. 8(b), when bpp > 1 , PSNR values of the non-e ncrypted images wer e high er than those with the propo sed scheme approx imately 0.2 dB. This (a) Color-based image encrypt ion scheme wit h B x = B y = 8 and 4:2:0 sub-sampling (PSNR=2 3.34dB) (b) Proposed scheme with B x = B y = 8 (PSNR=29 .96dB) Fig. 10: Examp le of decrypted imag es downloaded from Facebook is because e very grayscale JPEG ima g e uploaded to Facebook is recompre ssed to the ne w grayscale JPEG image with Q f u = 71 while Facebook r ecompresses JPEG color JPEG images with Q f u ∈ [71 , 85] . Figures 9 an d 10 show the example of de c rypted images downloaded fro m T witter and Facebo ok, respecti vely . Since B x = B y = 8 , the imag es en crypted by using color-based image encryp tion we re strong ly distorted by the colo r sub- sampling carried ou t b y the provid ers. In com parison, th e images encry pted by using the proposed sch e me d id not include any distortion . Considering color sub -sampling o peration to the g rayscale- based image s en cryption does no t affects th e com p ression perfor mance o f JPEG images. The results also proved that the propo sed sch eme can avoid th e effects of color sub- sampling carried out by SNS p roviders. V . C O N C L U S I O N This pape r c o nsidered color sub-samp ling op eration on the grayscale-b ased image encry p tion for EtC systems. Firstly , the scenario and requirem ents of the ima ge encr yption were described. Moreover , we prop osed to gener ate th e grayscale- based image from the luminan ce an d sub -sampled c h romi- nance co m ponen ts. A lot of image s was comp ressed with 4:4:4 and 4:2:0 color sub-samplin g ratio an d decom pressed to ev alu a te the comp ression perfo rmance an d the robustness against color sub-samp ling. 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