29-03-2014, 04:53 PM
An Introduction to Visual Cryptography
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Abstract
In this paper we give a tutorial introduction to visual secret sharing scheme (VSSS). VSSS is a secret sharing scheme that uses human visual system to decrypt secret image without performing any cryptographic computation. A k-out-of-n VSSS, VSSS, is to encrypt a secret image into shadow images called shares. To decrypt the secret image, we simply xerox k shares onto transparencies, and then stacking them. We can “visually” decrypt the secret image, but any shares gain no information about it.
Introduction
In this section, we review the idea of traditional secret sharing scheme that was invented by Shamir [1] and Blakley [2] independently. Here is an example to illustrate the idea. Assume that a bank has a vault that must be opened by a secret key. The bank employs three senior tellers, but the bank does not want to trust any of them individually. Hence, they would like to design a system such that any two of the three senior tellers can open the vault together. This problem can be viewed as a secret sharing scheme.
Visual Secret Sharing Scheme
Naor and Shamir [3] proposed a visual secret sharing scheme (VSSS) that uses human visual system to decrypt the secret image without performing any cryptographic computation. The difference between a VSSS and a traditional secret sharing scheme is in how the secret is decrypted. Usually, the traditional secret sharing scheme requires computation over a finite field. In a VSSS, however, the computation is simply performed by the human visual system of the users.
It is important to realize that the construction of a secure VSSS is difficult. Suppose that a particular pixel on a share is black. Whenever a set of shares (including ) is stacked together, the result must be black. It means that in the secret image, the pixel must be black. In other words, we gain “some” information about the secret image be examining one of the shares, and the security condition does not allow this. Naor and Shamir [3] proposed a VSSS that solved this problem by splitting each original pixel into m subpixels. In this section, we will introduce this idea and explain how to decrypt “visually”.
General Access Structure Scheme
Ateniese, Blundo, Santis and Stinson [4] extend the VSSS to a general access structure VSSS. Here is an example to illustrate the idea. Assume that a bank has a vault. In this time, the bank employs three senior tellers and a manager. They would like to design a system such that one of the three senior tellers together with the manager can open the vault. However, two of the three senior tellers can not obtain the permission. This problem can be viewed as a general access structure scheme.
CONCLUSION
Ateniese, Blundo, Santis and Stinson [4] extend the VSSS to a general access structure VSSS. Here is an example to illustrate the idea. Assume that a bank has a vault. In this time, the bank employs three senior tellers and a manager. They would like to design a system such that one of the three senior tellers together with the manager can open the vault. However, two of the three senior tellers can not obtain the permission. This problem can be viewed as a general access structure scheme.