Applications of Visual Cryptography - Visual Cryptography and Secret Image Sharing - page 331

As shown in Figure 12.8, the trojan on the computer is not able to see the
permutation chosen by Alice on the keys, which was randomly chosen by the
server. Thus, the mouse-clicks of the user cannot be interpreted by the trojan.
This method can be generalized to any alphabet and allows Bob to send short
messages to Alice in a secure way.
Note here that this method becomes insecure if the message contains mul-
tiple occurrences of the same symbol, a PIN should thus be chosen without
repetitions. In case Bob wants to send messages of length l that may con-
tain repetitions, this could still be accomplished in a secure way by extending
the alphabet to [fr 1 ;r 2 ;:::;r l1 g, where r i indicates the repetition of the
symbol at position i. In this way, for example, the message "messages" could
be submitted as "mesr 3 agr 2 r 4 " containing no repetitions in the extended
alphabet.
In order to achieve 2-factor security for transactions, we combine the PIN
method with the confirmation method of Section 12.2 as described in Figure
12.9.
Furthermore, to prevent the attack using the original transaction in an
unencrypted way on the screen as in Section 12.2, we use the refined method
of Figure 12.9.
12.4 Security versus Multiple Use
To achieve information theoretic security for a single use, we can divide the
array into clusters of c pixels (resp. areas), where c is the size of the alphabet
of the encrypted image. Only one pixel in each cluster has a 0 on the slide.
To encrypt a pixel p 2 , place p at the position of the cluster with the 0 on
the slide and ll the rest of the cluster with a random permutation of nfpg.
Since each pixel-value in occurs in each cluster of the encrypted image, each
image is possible from the viewpoint of an a evesdropper.
In the model of a known plaintext attack, we assume that the a evesdropper
Eve may receive the secret image later, then she can find out which position in
each cluster has the o on the slide and thus the slide cannot be used securely
a second time.
Known plaintext is relevant for authentication as considered in [13] as
well as for confirmation as considered in Section 12.2; in both cases Bob has
to be convinced that the message was sent by Alice. The problem of multiple
usability is solved in [13] by dividing the slide in distinct areas, where each has
to be big enough to contain the complete message; here we use an approach
with a different distribution. To achieve information theoretic security use a
slide n times, we propose the following two possibilities:
1. For one pixel use a cluster of nc pixels divided into n subclusters of c pixels