# Optimal (2, n) visual cryptographic schemes

@article{Bose2006OptimalN, title={Optimal (2, n) visual cryptographic schemes}, author={Mausumi Bose and Rahul Mukerjee}, journal={Designs, Codes and Cryptography}, year={2006}, volume={40}, pages={255-267} }

In (2,n) visual cryptographic schemes, a secret image(text or picture) is encrypted into n shares, which are distributed among n participants. The image cannot be decoded from any single share but any two participants can together decode it visually, without using any complex decoding mechanism. In this paper, we introduce three meaningful optimality criteria for evaluating different schemes and show that some classes of combinatorial designs, such as BIB designs, PBIB designs and regular graph…

## 18 Citations

### Optimal (k, n) visual cryptographic schemes for general k

- MathematicsDes. Codes Cryptogr.
- 2010

It is shown how block designs can be used to construct VCS which achieve optimality with respect to the average and minimum relative contrasts but require much smaller pixel expansions than the existing ones.

### Results on (2, n) Visual Cryptographic Scheme

- MathematicsSSCC
- 2014

A construction on an ideal contrast VCS using combined XOR and OR operations with less amount of transparencies than ideal contrast (2, n) VCS with reversing using OR and NOT operations is proposed.

### Threshold visual secret sharing by random grids with improved contrast

- Computer ScienceJ. Syst. Softw.
- 2013

### Number theory based { k , n } Visual Cryptography Scheme For Color Images

- Computer Science, Mathematics
- 2007

The proposed secret sharing scheme ideal for transmitting color images over un-trusted, bandwidth limited communication channels and any subset of k or more participants can perfectly reconstruct the original image using their shares.

### Construction of General （k, n） Probabilistic Visual Cryptography Scheme

- Computer Science, Mathematics
- 2011

This paper shows another construction of (k, n)-PVCS by extending the ( k, k-DVCS), which is a secure method that encrypts a secret image by subdividing it into shadow images.

### On the Pixel Expansion of Visual Cryptography Scheme

- Mathematics, Computer ScienceInt. J. Digit. Crime Forensics
- 2017

This paper generalizes Ateniese et al.'s method of comparing the optimal pixel expansion of VCSs with two different access structures and derives constructive upper bounds derived by the graph decomposition technique.

### A Probabilistic Model of $(t,n)$ Visual Cryptography Scheme With Dynamic Group

- Computer ScienceIEEE Transactions on Information Forensics and Security
- 2012

The maximal contrasts with t = 2 to 6 are explicitly solved in this paper and an equation derived from the fundamental definitions of the (t, n) VC scheme achieving maximal contrast can be designed by using the derived equation.

### K out of K Extended Visual Cryptography Scheme by Random Grids

- Mathematics, Computer ScienceSignal Process.
- 2014

### A Probabilistic Model of Visual Cryptography

- Computer Science
- 2013

An extended VC scheme based on basis matrices and a probabilistic model is proposed, and an equation derived from the fundamental definitions of the VC scheme achieving maximal contrast can be designed by using the derived equation.

### On the Equivalence of Two Definitions of Visual Cryptography Scheme

- Computer ScienceISPEC
- 2012

The study shows that the above two definitions of basis matrix (k,n)-VCS are actually equivalent, and generalize the equivalence relation to general access structure basis matrix VCS and generalAccess structure size invariant VCS.

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