A Review on Visual Secret Sharing Schemes

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International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 7, Issue 11, November 2017)

223

A Review on Visual Secret Sharing Schemes

Javvaji V.K. Ratnam

1

, T. Sreenivasulu Reddy

2

, P. Ramana Reddy

3

1,3

Department of Electronics and Communication Engineering, Jawaharlal Nehru Technological University Anantapur, Ananthapuramu, India

2_{Department of Electronics and Communication Engineering, Sri Venkateswara University, Tirupati, India}

Abstract— It is important to secure images while

transmitting over the internet or other communication channels to avoid unauthorized access. Visual secret sharing scheme is a powerful technique to encode the original secret into two or more shadow images or share images. These shares are distributed to different participants. These share images are printed on transparencies and stacked to recover original secret by the human eye (human visual system). Various techniques are reviewed in this paper with latest developments since its inception. Various secret sharing schemes such as visual cryptography based schemes, random grid based schemes, polynomial based schemes and Boolean operation based schemes are discussed. This paper outlines main research topics along with future work to be examined.

Keywords—Boolean operations, Lagrange Polynomial,

random grid, security, visual cryptography, visual secret sharing scheme.

I. INTRODUCTION

The increase in usage of the internet and advancements in the network technologies makes the communication becomes more crucial in many application areas. In multimedia communication, images are the most preferred source. They may cause certain risk from unauthorized sources. Hence there is a demand in information security to protect secret images or important data from being tampered or grabbed. Secret sharing scheme has turn into an important concept in information protection and security. The Visual Secret Sharing (VSS) schemes encode original image into a number of share images. The original image can be recovered by superimposing collected shares. The Visual Cryptography (VC) is a secret sharing method that encodes original image into n shadow or share images and circulated among participants. Original image can be reconstructed by the human visual system (HVS) while superimposing or stacking k (k ≥ n) or more share images and fewer than k shares never give information about the original secret.

The motivation behind VSS schemes is the generation of share images to distribute securely secret image to overcome high transmission risk. Because each shared image is separate, the secret is completely incoherent.

The traditional cryptographic methods allow each party to maintain portion of the original data and provide a way to remember some part of the original secret whereas visual secret sharing methods avoid it.

Adi Shamir [1] in 1979 published an article with title “How to share a secret”. Shamir formulated (k, n) threshold scheme. The technique is briefed as follows: “Let D be the secret data to be shared among n participants. A (k, n) threshold scheme divides secret data D into n pieces D1, . . . , Dn in such a way that:

1. Knowledge of any k or more Di pieces makes D easily

computable;

2. Knowledge of any k-1 or fewer Di pieces leaves D completely undetermined (in the sense that all its possible values are equally likely).”

Visual secret sharing scheme represents mechanism for reconstruction of the secret and perfect secrecy (with one-time pad). VSS scheme is perfect secure whereas cryptographic schemes are conditionally secure. This survey paper covers the evolution of different secret sharing schemes along with present trends and various research topics in this area.

The rest of this survey paper is organized in the following pattern: Section II briefs polynomial based scheme. Section III concentrates on visual cryptography based visual secret sharing schemes. Section IV elaborates random grid based schemes. Boolean operation based schemes are analyzed in Section V. Section VI gives research topics in this area. The conclusion and future work is given in Section VII.

II. POLYNOMIAL BASED VISUAL SECRET SHARING SCHEME

In Shamir’s [1] (k, n) secret sharing scheme, the polynomial interpolation is applied to spilt the original data A into distinct shares or shadows D1, D2,. . . ,Dn. The

secret A cannot be reconstructed for shares less than k. To partition secret data A into n shares or shadows, choose randomly k-1 degree polynomial and prime number p as,

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International Journal of Emerging Technology and Advanced Engineering

224 where a0 = A, and remaining coefficients a1, a2, . . . ., a

k-1 are chosen in random from an integer within the range from 0 to p-1.

Next, calculate for shares as

D1 = q(1) (2a)

D2 = q(2) (2b)

. . . . . .

Di = q(i) (2i)

. . . . . .

Dn = q(n) (2n)

By Lagrange’s interpolation, the coefficients a1, a2, . . . .

, ak-1 are found with any k pairs out of n generated pairs {(i,

Di)}i=1 to n. Therefore the original data A = a0 is recovered.

In this scheme, a0 is chosen as the first pixel gray-scale

value and find the corresponding output value q(1)-q(n). Now a0 is replaced by second pixel gray-scale value. This

process is repeated for all pixels of the original secret. In 2002, C.C. Thien and J.C. Lin [2] proposed a method where shadow images size is smaller than original image. Their method provides benefits like reduced storage space, easier transmission and data hiding. The disadvantage of this scheme is that it requires heavy computational load for retrieving the secret image due to evaluation of polynomials.

III. VISUAL CRYPTOGRAPHY BASED VISUAL SECRET SHARING SCHEMES

Moni Naor and Adi Shamir [3] in 1994 introduced encoding of binary image using threshold visual cryptography technique known as (k, n) visual secret sharing. The original image is divided into n shares. These shares are distributed to n participants and printed on transparencies. The human eyes decrypt the original secret image by stacking or superimposing k or more share images together without any information of encryption process and computation. The fundamental operation of is the logical OR operation and this scheme suffers from disadvantages: lossy, poor contrast, pixel expansion, suitable to binary images, requires basis matrices and more storage.

G. Ateniese, C. Blundo, A. De Santis, and D. R. Stinson [4] extended this scheme to General Access Structure (GAS) to improve security in 1996. A set of n share images is separated into qualified subsets and forbidden subsets.

Any k or more share images from the qualified subset can recover the original secret and less than k share images from the qualified subset of share images cannot reconstruct any secret information. And, k or more number of share images from the forbidden subset cannot reveal the secret information. Hence, general access structure scheme will improve the security of the system. Earlier visual cryptography techniques are limited to binary images. C.C. Lin and W.H. Tsai [5] in 2003 proposed dithering technique for conversion of the gray level image into binary. In 2006, Z. Zhou, G.R. Arce and G.D. Crescezo [6] proposed the halftone visual cryptography. The binary pixel is encoded to a halftone cell having an array of sub pixels. Halftone shares can be obtained by using the halftone cells which maintains good contrast and security of the share images.

E. Verheule and H.V. Tilborg [7] proposed color visual cryptography scheme in 1997. Each pixel is divided into m sub pixels. Each sub pixel is separated to c color regions. There is exactly one color region colored in each sub pixel and remaining regions are black. In 2008, F. Liu, C.K. Wu and X.J. Lin [8] suggested another technique for color visual cryptography scheme. Three approaches are proposed for color image representation: 1. The colors in the original secret can be printed directly on the share images. 2. Separate color channels are used. The additive model uses red, green and blue color channels whereas the subtractive model uses cyan, magenta and yellow color channels. Next secret sharing method is applied to each color channel separately. 3. Binary representation of pixel color and the secret is encoded at bit-level which improves image quality. In traditional schemes, share images are created as random noise-like patterns of pixels. The hackers suspect that secret data may be encoded in these noise-like share images. This becomes security issue. The Extended Visual Cryptography (EVC) scheme, developed by M. Nakajima and Y. Yamaguchi [9] in 2002, generates meaningful shares.

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International Journal of Emerging Technology and Advanced Engineering

225 R.Z. Wang [11] proposed region incrementing VSS scheme in 2009. The secrets are encrypted in such a way that more secret levels are reconstructed when more number of share images used in the decryption process. The original image is encrypted into n+1 share images and n levels of secrets are reconstructed incrementally by n+1 share images.

IV. RANDOM GRID BASED VISUAL SECRET SHARING SCHEMES

Random grid (RG) based VSS is proposed by O. Kafri and E. Keren [12] in 1987 has regained much attention in the research community. Three distinct encryption algorithms to binary images were presented by them. They encoded a secret binary image into two random grids. The information areas in the two grids are intercorrelated. When these two grids are stacked together, the correlated areas are determined by the random background due to the difference in light transmission. Hence the original secret image can be recovered. The decoding operation is same as the traditional visual cryptography scheme, i.e. human visual system.

The random grid is a transparency consisting of two-dimensional pixel array. These pixels are transparent (white, 0) or opaque (black, 1) obtained in random way. The transparent (white) pixels allow the light whereas the opaque (black) pixels stop it. RG encoding process removes the drawbacks of VC based VSS schemes.

S. J. Shyu [13] suggested two schemes in 2007 to encrypt gray level images and color images using random grids. The two generated random grids have identical size as the original image. These algorithms are not applicable multi-users’ environment where more than two participants are involved. In 2009, S. J. Shyu [14] further suggested (2, n) and (n, n) VSS schemes for encoding a secret image to general n (≥ 2) pieces of random grids where the original image can be revealed only if 2 random grids or all the n random grids respectively, are superimposed together. T.H. Chen and K.H. Tsao [15] in 2009 proposed a novel (2, n) VSS technique to encrypt binary images and color images by adopting recursive encoding technique to generate share images without pixel expansion. This method is restricted to threshold access structures and not applicable to general access structures. In 2010, R.Z. Wang, Y.C. Lan, Y.K. Lee, S.Y. Huang, S.J. Shyu and T.L. Chia [16] extended the region incrementing concept using random grids. The proposed technique deals with 2-level RIVSS.

In 2011, another (k, n) RG-based technique is proposed by T. H. Chen and K. H. Tsao [17] for binary images and color images. In 2011, T. H. Chen and K. H. Tsao [18] proposed a novel RGVSS technique by implementing a method to distinguish light transmissions on shares using pixel values in the logo image. This method has advantages of being user-friendly and no pixel expansion.

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International Journal of Emerging Technology and Advanced Engineering

226 Here any t share images (k ≤ t ≤ n) can reveal the secret areas up to t−k+1 levels. R.D. Prisco and A. De Santis [27] in 2014 identified a relation between deterministic and random grid based visual cryptography which allows results of the random grid model can be used to deterministic model and vice versa. A probability allocation method proposed by Y.C. Hou, S.C. Wei and C.Y. Lin [28] in 2014 has best contrast in recovered image.

V. BOOLEAN OPERATION BASED VISUAL SECRET SHARING SCHEMES

In 2007, D. Wang, L. Zhang, N. Ma and X. Li [29] proposed Boolean operation based (2, n) and (n, n) methods for binary images and gray scale images respectively using Boolean XOR and AND operations. In 2011, T.H. Chen and C.S. Wu [30] proposed an (n, n) visual secret image sharing technique by using Boolean operations for encryption of n secret images into n+1 shared images. Their scheme suffers from drawbacks: (1) Generated shares are not completely randomized which results in weak security of shares. (2) Only the n-1 shares can be distributed among n different participants. C.C. Chen and W.J. Wu [31] in 2014 proposed multiple secret images sharing technique which uses random image generating function along with Boolean operations in the sharing scheme to improve security. Exactly n shares can be distributed among n participants and randomness in the generated shares is greatly improved. However, this scheme has inaccuracy due to leakage of partial data from (n-1) or less number of shares. In 2014, S. Kumar and R.K. Sharma [32] proposed Boolean operation based threshold secret image sharing scheme. C.N. Yang, C.H. Chen and S.R. Cai [33] in 2015 proposed threshold (n, n) - multiple secret image sharing technique which does not leak any secret data from (n−1) or less number of shares. This proposed method enhances the randomness of shares. In 2016, C.C. Chen, W.J. Wu and J.L. Chen [34] suggested a novel multi secret image sharing technique using symmetric sharing recovery function which consists Boolean XOR operation, hash function, image synthesis, bit reverse and pixel shift operations. K.M. Faraoun [35] in 2016 proposed new scheme to share secret images known as (n, n) multiple secret images sharing which uses secure stream cipher and hash function in addition to Boolean operations for providing improved security. Y.K. Meghrajani and H.S. Mazumdar [36] proposed another multiple secret images sharing technique to encode n original secret into an universal share image and n meaningless share images in 2016.

C.C. Chen and J.L. Chen [37] in 2017 proposed Partial sensitivity Different sized Symmetric sharing-Recovery (PDSR) algorithm and Full sensitivity Different sized Symmetric sharing-Recovery (FDSR) algorithm to share multiple secret images having different sizes using Boolean operations and hash functions. F. Jiang and B. King [38] proposed a new metric, Quality Based on the Secret object Detection (QBSD) which uses object detection-weight map in 2017 to assess the reconstructed secret image quality.

HVS requires perfect alignment of share images in the decoding process. It is not easy to do the alignment of shares in practice, if superimposing of the share images are deviated from few pixels. The perfect alignment problem is solved by Boolean operation based VSS schemes. These visual secret sharing schemes involve computations in the decoding phase. But, these techniques offer an improved visual quality in the recovered original secret image.

VI. RESEARCH TOPICS IN VISUAL SECRET SHARING SCHEME

The visual secret sharing schemes are proven to be helpful in several applications such as identification, verification, security and authentication. Research topics identified in this area are (1) contrast improvement in the reconstructed image, (2) multi image sharing with different sized images, (3) security improvement, (4) capability to share multiple secrets, and (5) wide range of image types.

VII. CONCLUSION AND FUTURE WORK

The survey paper summarizes the work carried out in the visual secret sharing area. This paper explores many topics to do research in this field. There are several topics worth exploring in VSS to further develop secret image sharing, authentication, identification and image security.

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