It is an encryption technique, using which we can transform visual data such as
text, pictures into such an encrypted form that it doesn’t lose its original format but
information is encrypted and without keys it can’t be retrieved back.
Moni Naor and Adi Shamir invented a very useful and one of the best methods in
1994 to perform these tasks. A Visual secret sharing scheme was jointly provided
where a picture was split into n shadows(shares) and any individual shadow doesn’t
reveal any information about the picture, that is even n-1 shadows can’t retrieve the
original picture.When these pictures are printed over transparent sheets and stacked
on one another original image is revealed. Generalizations of these methods are
available; one of them is the KN secret sharing scheme where any k of the shadows
can reconstruct the image.
Shamir’s secret sharing scheme
Suppose, our secret number is 334 ( S = 334)
To break the secret number into 5 shares (n = 5) , where any of 3 (threshold)
shares (k = 3) is sufficient to retrieve the original number. Randomly we generate
k − 1 numbers (here 2): 147 and 45.
(a 34, a 147, a 45) , where is a secret 0 = 3 1 = 2 = a 0
So the polynomial to generate the secret shares is thus given by:
f(x) = 334 + 147x + 45x
We generate five points D x, f(x)) from the given f(x), x = ( x ∈ [1, 5]
D 1, 26), D 2, 08), D 3, 180), 1 = ( 5 2 = ( 8 3 = ( 1
D 4, 642), D 5, 194) 4 = ( 1 5 = ( 2
We provide every participant a point from these five points and when any three
(threshold number) of the participants provide their shares then only the original
number can be retrieved.