Image Secret Sharing - Visual Cryptography and Secret Image Sharing - page 374

2. The secret key s cannot be restored from k 1 (or less) shares.
3. The size of each share is not more than the size of the secret key s.
Such a scheme is referred to as a (k;n) threshold cryptography scheme
or a secret sharing system[2][17]. It provides a backup mechanism to the se-
cret key and it provides protection against the loss of a key. Secret sharing is
also regarded as a mechanism to transfer secret information by public chan-
nels in cryptography [4]. Blakley based his secret sharing scheme on hyper-
planes [17] and Shamir provided a solution based on the Lagrange interpo-
lation [2]. Asmuth and Bloom scheme is based on the Chinese Remainder
Theorem [5]. The details of these methods are available in [1] [12]. These tra-
ditional secret sharing schemes primarily concentrate on bit strings and do
not take the specific content of these bits into account. However, with the
increasing emphasis on security and digital rights management of multime-
dia data, the connection between multimedia and cryptography is becoming
stronger. In this context, we present our novel ideas on color image sharing in
which we utilize the concept of secret sharing from cryptography and employ
it to protect a secret color image. As we shall see, the ideas cannot be directly
applied so we need to take into account that the data under consideration
describes color images and is not any generic bit stream. In our scheme, a
secret color image is divided into n shares. Each share is an innocuous image
totally unrelated to the secret image. We utilize k (or more) shares in order
to perfectly reconstruct the secret image. However, having access to k1 (or
less) shares will not reveal the secret color image.
We envisage several useful applications for a color image sharing scheme.
Suppose we have a secret color image that we desire to protect. If we employ
traditional cryptographic techniques, then we need to encrypt the image and
store the image on a secure server. We then need to pay attention on the
security of the key used for encryption. This server would then become a single
focus of attack from a potential adversary. However, with an image sharing
scheme, we can divide the information in the image into several shares and
keep them on separate servers. This would allow for a lot more redundancy
in the protection since breaking one server will not reveal the secret image.
Another application would be that of data hiding. Suppose we would like to
transmit a secret image over a noisy and insecure channel. We could divide
the image information into several shares that are basically innocuous images.
These images could be transmitted and at the other end, the secret image
could be reconstructed from the threshold number of shares. Another useful
application would be that of a military command and control system based on
the Clark-Wilson security model [11]. Suppose we want the battlefield plans to
be made only if k out of n commanders agree. In which case, we could divide
the battle terrain map into n shares and distribute it to the commanders. Only
if k of them get together can they restore the terrain map and agree to a battle
plan. In general, our scheme would be advantageous in any situation where a