IEEE Consumer Electronics Magazine - September 2018 - 42
n + 1 shared images S j j = 1, 2, f, n, n + 1 to get n recovered cover images R i i = 1, 2, f, n and a stego image ST. This
complete process of encryption and decryption using secret
sharing is labeled as level 1. In level 2, the steganography
was used to get recovered secret image G by performing an
additive modulo operation on recovered cover images R i
i = 1, 2, f, n and stego image ST.
The proposed encryption algorithm for n + 1 share generation, S j j = 1, 2, f, n, n + 1, is given in Figure 1. Initially, an
additive inverse modulo operation was performed on secret
image SI and n cover images C i, to get the temporary secret
image, X; X = SI - (1C 1 + 2C 2 + 3C 3 + g + nC n) . The
temporary secret image X was generated to conceal secret
image SI. In the second step, temporary cover image
M i, i = 1, 2, f, n were generated. We initially assigned M 1
equal to C 1 and subsequently performed an additive modulo
operation on M j - 1, j = 2, 3, f, n - 1 and C j, j = 2, 3, f, n,
respectively, to get M j, j = 2, 3, f, n. The generalized
equation for generating temporary cover image M i is
i = 1, 2, f, n; M j = M j - 1 + C j . Thereafter, to get temporary
SI
shared image T, we had to apply additive inverse modulo
on temporary secret image, X with (n + 1 - j) times of
M j, where j = 1, 2, f, n, the generalized equation for T;
T = X (n + 1 - j) M j for j = 1, 2, f, n. Then, to reduce pixel
size, a division operator was performed on T by (n + 1) to get
our first shared image S 1 . In the next step, we generated the
next shared image by using a temporary cover image and a
previously generated shared image, e.g., to generate S 2, we
used T1 and S 1, and similarly for S 3, we used T2 and S 2, which
was generated in the previous step; kept executing this process until we got all of the n + 1 shared images. The generalized equation became S i + 1 = S i + M i for i = 1, 2, f, n, with
S 1 = T/ (n + 1) . After applying the encryption technique, we
got n + 1 shared images S j, j = 1, 2, f, n, n + 1 from n cover
images C i, i = 1, 2, f, n and secret image SI.
The decryption process to recover secret images is different from the encryption process. This also adds a barrier
to prevent an intruder from accessing the secret image from
shared images. Initially, we used a secret-sharing concept to
produce stego image ST and n recovered cover images R i,
C1 + 2C2+ 3C3 + .... +nCn
-
1
2
3
*
*
*
C1
C2
C3
M1
+
....
n
*
....
Cn
X
M2
Mi = i th Temporary Cover Image
T = Temporary Shared Image
Si = Shared Image
+
M3
....
+
Mn
*
*
*
n
n-1
n-2
......
*
1
nM1 + (n -1)M2 + (n -2)M3 + .... + Mn
-
/
n+1
T/(n + 1)
+
+
+
S1
S2
S3
S4
FIGURE 1. The proposed encryption technique.
42 IEEE Consumer Electronics Magazine
^
september 2018
....
- = Additive Inverse Modulo
+ = Additive Modulo
* = Multiplication Operator
/ = Division Operator
SI = Secret Image
X = Temporary Secret Image
Ci = i th Cover Image
+
+
Sn
Sn+1
Table of Contents for the Digital Edition of IEEE Consumer Electronics Magazine - September 2018
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