Objective

2

Conventional multi-carrier secret image sharing scheme based on error diffusion and recovery function can be used to hide secret image in multiple same size carriers. In these carriers

the error diffusion method leads to low visual quality and the recovery function is only designed for specific gray scale images

such as 1-bit binary images or 8-bit gray scale images. This scheme can only provide limited security by using simple Arnold scrambling or XOR encryption in which Arnold mapping is usually employed for special resolution images

such as square images. However

the security of Arnold mapping is poor due to its dependence on iteration numbers

and its scrambling coefficients are only 1

1

1

2. In addition

Arnold mapping cannot change its mapping type and form by multiple iterations. To address these problems and further improve the visual qualities of carriers and security

a multi-carrier secret image sha

ring scheme with EMD-

c

l

embedding is proposed in this study.

Method

2

In sharing phase

the double hash function values (MD5 and SHA-1 values) are first used to randomly generate scrambling. Iteration variables of secret images and related user keys are used to change every carrier pixel position by 2D bi-scale rectangular mapping. Vectors composed of same position pixels in scrambled carriers are then randomly allocated to the weights of EMD-

c

l

basis vector using extended Josephus mapping where the start position and count termination value

count gap

and count direction sequences are added to increase the number of permutations and the kinds of variations in Josephus mapping. Afterward

EMD-

c

l

embedding strategy is used to embed secret image pixels into multiple carriers to verify the high visual qualities of stego carriers. Finally

both user keys and the double hash function values of secret image are distributed to

N

participant sharing information by Lagrange (

N

N

) under module

p

where each participant sharing information is kept by one participant and the MD5 and SHA-1 values of each participant sharing information are known to the third trust party to guarantee that every participant sharing information cannot be faked. In recovering phase

all participant sharing information is verified by checking their MD5 and SHA-1 values known to the third trust party. This information is used to recover the related variables

such as the MD5 and SHA-1 values of secret image and the user keys by Lagrange (

N

N

) under module

p

. These related variables are used to generate groups of scrambling and iteration variables of a 2D bi-scale rectangular mapping and variables of extended Josephus mapping. Scrambling and iteration variables are used to find the mapping relationship

s between each secret pixel and

N

carrier pixels. Extended Josephus mapping variables are used to find the weights of EMD-

c

l

and EMD-

c

l

is adopted to embed the secret image pixels. In recovering phase

if all participant sharing information passes the third trust party checking and the related variables are the same as those of the sharing phase

then the secret image can be recovered correctly.

Result

2

Unlike in conventional methods

the visual qualities of all stego carriers are enhanced because EMD-

c

l

only makes slight modifications

and the most modification for any non-overflow pixel is only

$$ \pm \left\lfloor {c/2} \right\rfloor $$

. The proposed scheme need not design any recovery function and can be easily applied in different resolutions or gray scale images. The following are the improved securities:1) The proposed strategy uses different 2D bi-scale rectangular mappings to scramble distinct carrier with varying iteration numbers to avoid the fixed relationship of carrier pixels. 2) A 2D bi-scale rectangular mapping can be used to scramble images in different resolution

and its multiple iterations differ in transform type and form

so this mapping is more complex and secure than Arnold mapping. 3) By introducing the double hash function values

that is

the MD5 and SHA-1 values of the secret image

the proposed strategy easily overcomes the conflict brought by the single hash value (MD5 or SHA-1 value). 4) The proposed strategy uses extended Josephus mapping to scramble weights of EMD-

c

l

basis vector

guaranteeing high steganography security. 5) All key variables in the proposed strategy

that is

the MD5 and SHA-1 values of the secret image

and the user keys are closely binded where only the correct user keys and MD

5 and SHA-1 values can be used to recover the secret image but not vice versa. 6) To avoid tricks

the MD5 and SHA-1 values of key related variable sharing information are known to the third trusted party to provide authentication. 7) The total key space is 1.193 6×10

118

which can resist brute-force attack. Experimental results show that

by EMD-

c

l

embedding

the proposed multi-carrier secret image sharing scheme has enhanced visual qualities in stego carriers. The NC value is close to 1. The PSNR values of all stego carriers are close to 50 dB by EMD-3

l

embedding strategy. In EMD-5

l

embedding strategy

the PSNR values of all stego carriers are close to 45 dB

and the PSNR values of all stego carriers are close to 42 dB for the EMD-7

l

method. However

in conventional multi-carrier secret image sharing schemes

the best results of the PSNR values of all stego carriers are only approximately 42 dB. The proposed strategy can share different resolutions or different gray scale secret images

so it boasts high universality. Everyone can verify the facticity of any key sharing information provided by other participants. Moreover

the strategy is extremely sensitive to any slight modification in the user keys and hash function values:MD5 and SHA-1 or both of them. Therefore

the security of the proposed strategy is higher than that of conventional multi-carrier secret image sharing schemes.

Conclusion

2

The proposed method has low complexity and high security and universality

and it provides several authentication capabilities. Thus

the overall performance of the proposed method is superior to that of conventional multi-carrier secret image sharing schemes in terms of error diffusion and recovery function. The proposed method is suitable for multi-carrier secret image sharing schemes that need the high visual qualities of stego carriers and require sharing of secret images in different resolutions or gray scale secret.