IEEE SIGNAL PROCESSING LETTERS, VOL. 16, NO. 8, AUGUST 2009 659

Region Incrementing Visual CryptographyRan-Zan Wang

Abstract—This letter presents a novel visual cryptographyscheme, called region incrementing visual cryptography (RIVC),for sharing visual secrets with multiple secrecy levels in a singleimage. In the proposed -level RIVC scheme, the content ofan image S is designated to multiple regions associated withsecret levels, and encoded to � � shares with the followingfeatures: (a) each share cannot obtain any of the secrets in S,(b) any �� � �� shares can be used to reveal �levels of secrets, (c) the number and locations of not-yet-revealedsecrets are unknown to users, (d) all secrets in S can be disclosedwhen all of the � � shares are available, and (e) the secrets arerecognized by visually inspecting correctly stacked shares withoutcomputation. The basis matrices for constructing the proposed

-level RIVC with small values of � �, 3, 4 are introduced, andthe results from two experiments are presented.

Index Terms—Image sharing, secret sharing, visual cryptog-raphy, visual secret sharing.

I. INTRODUCTION

V ISUAL cryptography (VC), invented by Noar and Shamir[1], is a method for protecting image-based secrets that

has a computation-free decoding process. In the VCscheme, the input image is transformed into noise-like sharesto ensure that the contained secret is unreadable. These sharescan be printed on transparent slides and distributed to theparticipants. Any subset of or more shares can decrypt thesecret in the original image, but no information about the secretcan be obtained from fewer shares. The decryption processin a VC scheme involves inspecting the stacked shares withthe unaided eye without computation. The ciphering model ofVC is similar to a one-time pad in the sense that each imageis decrypted with a different set of shares, and provides highsecurity to the protected secrets.

Following the pioneering research of Noar and Shamir, Ate-niese et al. [2] extended the VC scheme to general ac-cess structures where the dealer can specify all qualified andforbidden subsets of participants, with participants in a quali-fied subset being able to reveal the secret in the image and thosein a forbidden subset not being able to do so. In general, thereare two important parameters for a VC scheme: 1) the pixel ex-pansion, which refers to the number of pixels in a share used to

Manuscript received January 15, 2009; revised March 29, 2009. Current ver-sion published May 28, 2009. This work was supported by the National ScienceCouncil of Taiwan under Grant NSC96-2221-E-155-073. The associate editorcoordinating the review of this manuscript and approving it for publication wasProf. H. Vicky Zhao.

The author is with the Department of Computer Science & Engineering, YuanZe University, Chung-Li, Taoyuan 320, Taiwan (e-mail: rzwang@saturn.yzu.edu.tw).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/LSP.2009.2021334

encode a pixel of the secret image and 2) the contrast, which isthe luminance difference between black and white pixels in thereconstructed image. For a VC scheme, a smaller pixel expan-sion benefits the printing out and storage of shares, and a highcontrast makes the revealed secret easier to recognize by the un-aided eye. The conditions of maximum contrast and minimumpixel expansion for a VC scheme have been discussed previ-ously [3]–[6]. Proposed progressive VC schemes using moreflexible decryption effects to produce higher quality images [7],[8] stack increasing numbers of shares. There have also beensome VC schemes proposed [9]–[12] for sharing non-bilevelsecrets. Other VC schemes for generating shares with naturalimage appearances have been designed with the aim of furtherconcealing the existence of the secret in the shares [13], [14].

VC schemes reported in the literature usually process the con-tent of an image as a single secret; that is, all of the pixels in thesecret image are shared using a single encoding rule. This typeof sharing policy reveals either the entire image or nothing, andhence limits the secrets in an image to have the same secrecyproperty. A method for recursively hiding secrets in VC wasproposed by hierarchically embedding multiple secrets of dif-ferent sizes at various levels of an image [15]. There have alsobeen efforts to share multiple secrets in two images [16]–[18].All of these methods are based on superimposing the two sharesat different angles. In this paper, we consider the content of a se-cret image with multiple regions, where each region has a cer-tain level of secrecy. In this scheme, the secrets in the originalimage are hidden in such a way that more levels of secrets are re-vealed when more shares are obtained in the decoding process.This property of incremental disclosure of the number of secretsin an image widens the possible applications of VC schemes.

II. PROPOSED SCHEME

Given the input binary image S containing secret messages,the proposed scheme allows the dealer to split the content of Sinto multiple regions and assign a secrecy property to each re-gion. In our -level region incrementing VC (RIVC) scheme,the secrecy level of a region has a value ranging from 1 to ,where the first-level secret is the least significant and the thlevel secret is the most significant. More specifically, the dealercan assign each region of S to a secrecy level according to thespecification of her/his application, which represents the degreeof secrecy of that region. Unlike all previous VC schemes thatadopt a single encoding rule, the basic idea of our RIVC schemeis applying encoding rules called level kernels—one for eachsecrecy level—to encode the secret image. Each level kernel isused to encode the regions belonging to a certain secrecy prop-erty, and hence our RIVC scheme uses the following level ker-nels: a VC encoding rule, a VC encodingrule,…, and an VC encoding rule.

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660 IEEE SIGNAL PROCESSING LETTERS, VOL. 16, NO. 8, AUGUST 2009

Let matrix represent the basis matrixfor encoding a white pixel of the th level kernel, and rep-resent the basis matrix for encoding a black pixel of the th levelkernel. (The requirements of and methods for constructingand are discussed in Section III.) The collection of en-coding matrices and for encoding white and black pixels,respectively, at the th level are all of the matrices obtained bypermuting the columns of and . The following foursteps summarize the procedure for encoding a secret image S to

shares in our -level RIVC scheme.1) Assign a secrecy level to each pixel of S

according to the user’s specification.2) Fetch a not-yet-processed pixel, , from S according to

the scanning order (e.g., from left to right and from top tobottom).

3) Examine secrecy level of , and then proceed with oneof the following substeps:

3.1) If is a white pixel, randomly choose an encodingmatrix from the th level encoding matrices and useit to encode .3.2) If is a black pixel, randomly choose an encodingmatrix from the th level encoding matrices anduse it to encode .

4) Repeat Steps 2 and 3 until all of the pixels in S are pro-cessed. This will yield the shares for our -levelRIVC scheme.

The secret decoding process is as simple as that in the tradi-tional VC scheme. Given a set of shares,carefully stacking and aligning them together will reveal the se-crets to the unaided eye.

III. CONSTRUCTION OF AN -LEVEL RIVC WITH SMALL

The concept of our -level RIVC scheme involves applyinglevel kernels to encode the secret image. In additional to the

basic requirements of the , VCscheme for these level kernels, the level kernels used to gen-erate our -level RIVC should also meet the following two con-straints: 1) the level kernels must have the same degree of pixelexpansion in order to arrange the encoded subpixels of all re-gions within a share and 2) the areas where no secret is revealedin the stacked image should appear visually uniform so as not toreveal the number and regions of not-yet-revealed secrets. Basedon the above requirements, below we provide the basis matricesfor the construction of -level RIVC schemes with , 3, 4.

The two level kernels for our two-level RIVC with fourfoldpixel expansion are

(1)

The same basis matrices are used to encode a white pixel inthe two level kernels, which guarantees that the number and lo-cations of not-yet-revealed secrets remain invisible. Any singlerow in contains two black and two

white pixels, which makes a single share appear with a uniformcontrast so as not to expose the secrets. Stacking any two of thethree shares reveals the first level secret with a contrast of 1/4,and stacking all three shares reveals the secrets at levels 1 and 2with contrasts of 1/2 and 1/4, respectively.

The level kernels for constructing the three-level RIVC withten-fold pixel expansion are

(2)

(3)

Stacking any two of the four shares reveals the first level se-cret with a contrast of 1/5; stacking any three shares reveals thesecrets at levels 1 and 2 with contrasts of 3/10 and 1/10, respec-tively; and stacking all four shares reveals all the secrets at levels1, 2, and 3 with contrasts of 3/10, 1/10, and 1/10, respectively.

The basis matrices for constructing the four-level RIVC with23-fold pixel expansion are

(4)

(5)

(6)

WANG: REGION INCREMENTING VISUAL CRYPTOGRAPHY 661

Fig. 1. Results of an experiment with the proposed two-level RIVC scheme: (a) Secret image, (b) secrecy-level decomposition, (c)–(e) three encoded shares,(f)–(h) superimposing any two of the three shares, and (i) superimposing all three shares.

Fig. 2. Results of an experiment with the proposed three-level RIVC scheme: (a) Secret image, (b) secrecy-level decomposition, (c)–(f) four encoded shares,(g)–(l) superimposing any two of the four shares, (m)–(p) superimposing any three of the four shares, and (q) superimposing all four shares.

662 IEEE SIGNAL PROCESSING LETTERS, VOL. 16, NO. 8, AUGUST 2009

The minimum contrast between the revealed secret and thebackground is 1/23. The above examples indicate that the pixelexpansion increases and the contrast decreases rapidly in theproposed -level RIVC as increases. This problem resultsfrom the two strict requirements for the generation of the sharesmentioned above, and it limits the applications of our methodin sharing small levels of visual secrets. Future studies shouldtherefore investigate smaller pixel expansion and higher contrastin the RIVC scheme.

IV. EXPERIMENTAL RESULTS

This section presents some experimental results to demon-strate the feasibility of the proposed method. Fig. 1 showsa computer implementation of our two-level RIVC scheme.Fig. 1(a) is an image containing five secrets (“MSL,” “RIVC,”“2009,” “CSE,” and “YZU”) that are divided into two parts, asshown in Fig. 1(b). The level-1 secret contains texts “RIVC”and “2009,” and the level-2 secret contains texts “MSL,” “CSE,”and “YZU.” In this experiment, the level kernels presentedin (1) were used to encode the input image. The three sharesgenerated in this test are shown in Fig. 1(c)–(e)—they allappear noise-like with no secret being obvious. Fig. 1(f)–(h)are the results of superimposing any two of the three shares,revealing the level-1 secrets “RIVC” and “2009.” The result ofsuperimposing all three shares is illustrated in Fig. 1(i), wherethe two secrets at both levels (i.e., “RIVC,” “2009,” “MSL,”“CSE,” and “YZU”) are revealed.

Fig. 2 shows a computer implementation of our three-levelRIVC scheme. Fig. 2(a) is the secret image, in which the se-crets are divided into three parts, as shown in Fig. 2(b). Thelevel-1 secret contains text “RIVC,” the level-2 secret containstexts “MSL” and “2009,” and the level-3 secret contains texts“CSE” and “YZU.” The three level kernels presented in (2) and(3) were used to encode the input image. The four shares gen-erated are shown in Fig. 2(c)–(f). Fig. 2(g)–(l) are the results ofsuperimposing any two of the four shares, revealing the level-1secret. Fig. 2(m)–(p) are the results of superimposing any threeof the four shares, revealing two levels of secrets. The result ofsuperimposing all four shares is illustrated in Fig. 2(q), revealingall three levels of secrets.

V. CONCLUSION

VC can be applied to protect image-based secret informa-tion with the advantage that the decoding process can be per-formed by the unaided eye without computation. This letterhas described the -level RIVC scheme that enables the dealerto specify the content of a secret image to multiple regions,where each region has its own secrecy property. Like traditionalVC schemes, each generated share has a noise-like appearanceand cannot obtain any secret in the secret image. However, anew characteristic of the proposed RIVC scheme is that the

number of secrets that can be revealed is proportional to thenumber of participants engaged in the decoding process. Theidea of sharing multiple secrets based on regions of an image isnovel in the literature, and it could have various applications forsharing multiple weighted messages. For example, it could beused to design a lottery system with three rank prizes in whichthe dealer dispatches a set of transparencies using the proposedthree-level RIVC in such a way that a 10% combination of twostacked transparencies would reveal a symbol representing thethird prize, a 2% combination of three transparencies would re-veal two symbols representing the second prize, and a 0.01%combination of four transparencies would reveal three symbolsrepresenting the first prize. In such a system each transparencywould be considered capable of revealing prizes, which wouldentertain the players when they are stacking the transparencies.

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