Cryptography Reference
In-Depth Information
1.1 Introduction
Visual cryptography (VC), proposed by Naor and Shamir in [19], is a paradigm
for cryptographic schemes that allows the decoding of concealed images with-
out any cryptographic computation. Particularly in a k-out-of-n visual se-
cret sharing scheme (VSS), a secret image is cryptographically encoded into
n shares. Each share resembles a random binary pattern. The n shares are
then xeroxed onto transparencies respectively and distributed among n par-
ticipants. The secret images can be visually revealed by stacking together
any k or more transparencies of the shares and no cryptographic computa-
tion is needed. However, by inspecting less than k shares, one cannot gain
any information about the secret image, even if infinite computational power
is available. Aside from the obvious applications to information hiding, VC
can be applied to access control, copyright protection [10], watermarking [8],
visual authentication, and identification [18].
1.1.1 Visual Cryptography
The main instantiation of VC realizes a cryptography protocol called secret
sharing (SS). In a conventional SS scheme, a secret image is shared among n
participants in such a way that subsets of qualified participants can pull their
shares and recover the secret but subsets of forbidden participants can obtain
no information about it. Here, both the sharing phase and the reconstruction
phase involve algorithms that are run by computers (specially, a dealer runs a
distribution algorithm and a set of qualified parties can run a reconstruction
algorithm). The surprising novelties of a VSS scheme are in representing data
as images and in an elementary realization of the reconstruction phase, con-
sisting of just viewing the image obtained after stacking transparencies. VSS
schemes inherit all applications of conventional SS schemes; most notably,
access control. As an example, consider a bank vault that must be opened
everyday by five tellers, but for security purposes it is desirable not to en-
trust any two individuals with the combination. Hence, a vault-access system
that requires any three of the five tellers may be desirable. This problem can
be solved using a 3-out-of-5 threshold scheme. In addition to access control,
VSS schemes can be applied to a number of other cryptographic protocols
and applications using conventional SS, such as threshold signatures, private
multiparty function evaluation, electronic cash, and digital elections.
Another quite intriguing instantiation of VC schemes realizes VSS with
innocent-looking images as shares. This version of VSS has applications to
a multiparty variant of steganography. In a steganography scheme, a user A
sends an innocent-looking image to another user B, in such a way that B can
recover some hidden images, but no observer of the communication between A
and B even suspects that the communication contains some hidden images. In
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