Feng Liu, Weiqi Yan, Peng Li and Chuankun Wu
Transcript of Feng Liu, Weiqi Yan, Peng Li and Chuankun Wu
![Page 1: Feng Liu, Weiqi Yan, Peng Li and Chuankun Wu](https://reader030.fdocuments.us/reader030/viewer/2022012505/61804baeabb5c51f3f40d59a/html5/thumbnails/1.jpg)
Feng Liu, Weiqi Yan, Peng Li and Chuankun Wu
February 4, 2021
![Page 2: Feng Liu, Weiqi Yan, Peng Li and Chuankun Wu](https://reader030.fdocuments.us/reader030/viewer/2022012505/61804baeabb5c51f3f40d59a/html5/thumbnails/2.jpg)
Background
Preliminaries
Our work
February 4, 2021
![Page 3: Feng Liu, Weiqi Yan, Peng Li and Chuankun Wu](https://reader030.fdocuments.us/reader030/viewer/2022012505/61804baeabb5c51f3f40d59a/html5/thumbnails/3.jpg)
Visual Cryptography (VC) has the advantage of “stacking to see”, but suffers from large pixel expansion and low information rate.
Aim of this work: How to let the VC scheme carry more secrets?
Our approach: Embed the output of a private-key system into the input random numbers of VC.
February 4, 2021
![Page 4: Feng Liu, Weiqi Yan, Peng Li and Chuankun Wu](https://reader030.fdocuments.us/reader030/viewer/2022012505/61804baeabb5c51f3f40d59a/html5/thumbnails/4.jpg)
Background
Preliminaries
Our work
February 4, 2021
![Page 5: Feng Liu, Weiqi Yan, Peng Li and Chuankun Wu](https://reader030.fdocuments.us/reader030/viewer/2022012505/61804baeabb5c51f3f40d59a/html5/thumbnails/5.jpg)
A (2,2)-VCS
Original secret image Stacked secret image
Share 1
Share 2
February 4, 2021
PRNG
![Page 6: Feng Liu, Weiqi Yan, Peng Li and Chuankun Wu](https://reader030.fdocuments.us/reader030/viewer/2022012505/61804baeabb5c51f3f40d59a/html5/thumbnails/6.jpg)
Definition 1. Let k, n, m, l and h be non-negative integers satisfying 2≤ k≤n and 0 ≤ l < h ≤m. The two sets of n ∗ m Boolean matrices (C0, C1) constitute a (k, n)-VCS if the following properties are satisfied:
1. (Contrast) For any s ∈ C0, the OR of any k out of the n rows of s, is a vector v that, satisfies w(v) ≤ l.
2. (Contrast) For any s ∈C1, the OR of any k out of the n rows of s, is a vector v that, satisfies w(v)≥h.
3. (Security) For any i1< i2<…<it in {1, 2,…, n} with t < k, the two collections of t ∗ m matrices F0 and F1 obtained by restricting each n ∗ m matrix in C0and C1to rows i1, i2,…,it, are indistinguishable in the sense that they contain the same matrices with the same frequencies.
February 4, 2021
![Page 7: Feng Liu, Weiqi Yan, Peng Li and Chuankun Wu](https://reader030.fdocuments.us/reader030/viewer/2022012505/61804baeabb5c51f3f40d59a/html5/thumbnails/7.jpg)
f(x) = (a0 + a1x + ...+ at-1xt-1) mod p, where
a0 is the secret from GF(p) and a1,... ,at-1 are randomly drawn element from GF(p).
Encoding: The n shares can be calculated by f(1) , f(2) , ..., f(n) .
Decoding: f(x) can be reconstructed from any t of n shares, and hence the secret f(0) can be computed.
February 4, 2021
![Page 8: Feng Liu, Weiqi Yan, Peng Li and Chuankun Wu](https://reader030.fdocuments.us/reader030/viewer/2022012505/61804baeabb5c51f3f40d59a/html5/thumbnails/8.jpg)
Background
Preliminaries
Our work
February 4, 2021
![Page 9: Feng Liu, Weiqi Yan, Peng Li and Chuankun Wu](https://reader030.fdocuments.us/reader030/viewer/2022012505/61804baeabb5c51f3f40d59a/html5/thumbnails/9.jpg)
⚫ k: the VCS threshold
⚫ t: the covert data threshold
⚫ n: the number of participants
(C0, C1) require that any t rows can uniquely determine a share matrix
Generally, it is required that t≥k
February 4, 2021
![Page 10: Feng Liu, Weiqi Yan, Peng Li and Chuankun Wu](https://reader030.fdocuments.us/reader030/viewer/2022012505/61804baeabb5c51f3f40d59a/html5/thumbnails/10.jpg)
February 4, 2021
![Page 11: Feng Liu, Weiqi Yan, Peng Li and Chuankun Wu](https://reader030.fdocuments.us/reader030/viewer/2022012505/61804baeabb5c51f3f40d59a/html5/thumbnails/11.jpg)
February 4, 2021
![Page 12: Feng Liu, Weiqi Yan, Peng Li and Chuankun Wu](https://reader030.fdocuments.us/reader030/viewer/2022012505/61804baeabb5c51f3f40d59a/html5/thumbnails/12.jpg)
The sets of share matrices of a (2, 2, 2)-ESSVCS are as follows:
The principle of choosing a share matrix is that: if the random input is 0, we choose the 1st share matrix in C0
or C1; if the random input is 1, we choose the 2nd share matrix.
From another hand, we also can get to know the random input: if the first share matrix is chosen then the random input is 0, and if the second share matrix is chosen then the random input is 1
February 4, 2021
![Page 13: Feng Liu, Weiqi Yan, Peng Li and Chuankun Wu](https://reader030.fdocuments.us/reader030/viewer/2022012505/61804baeabb5c51f3f40d59a/html5/thumbnails/13.jpg)
February 4, 2021
213 bits
![Page 14: Feng Liu, Weiqi Yan, Peng Li and Chuankun Wu](https://reader030.fdocuments.us/reader030/viewer/2022012505/61804baeabb5c51f3f40d59a/html5/thumbnails/14.jpg)
Bandwidth of the ESSVCS is defined by the maximum amount of covert data it carries.
Theoretically, the amount of covert data carried by a pixel i is log2|Ci|
Denote columns in the basis matrix Mi as c1,…,ceand multiplicities of these columns as a1,…, ae.The number of share matrices in Ci is:
Considering the canonical basis matrices of threshold scheme constructed by Droste, we have the following table:
February 4, 2021
![Page 15: Feng Liu, Weiqi Yan, Peng Li and Chuankun Wu](https://reader030.fdocuments.us/reader030/viewer/2022012505/61804baeabb5c51f3f40d59a/html5/thumbnails/15.jpg)
February 4, 2021
![Page 16: Feng Liu, Weiqi Yan, Peng Li and Chuankun Wu](https://reader030.fdocuments.us/reader030/viewer/2022012505/61804baeabb5c51f3f40d59a/html5/thumbnails/16.jpg)
February 4, 2021
![Page 17: Feng Liu, Weiqi Yan, Peng Li and Chuankun Wu](https://reader030.fdocuments.us/reader030/viewer/2022012505/61804baeabb5c51f3f40d59a/html5/thumbnails/17.jpg)
Theorem 4. For a secret image SI which consists of nw white pixels and nb black pixels, the bandwidth W of the ESSVCS is W = ⌊nw log2 |C0| + nb log2 |C1|⌋, and it is achieved when using the qa-pixel encryption model where qa = nw + nb.
February 4, 2021
![Page 18: Feng Liu, Weiqi Yan, Peng Li and Chuankun Wu](https://reader030.fdocuments.us/reader030/viewer/2022012505/61804baeabb5c51f3f40d59a/html5/thumbnails/18.jpg)
February 4, 2021
![Page 19: Feng Liu, Weiqi Yan, Peng Li and Chuankun Wu](https://reader030.fdocuments.us/reader030/viewer/2022012505/61804baeabb5c51f3f40d59a/html5/thumbnails/19.jpg)
Any questions?
February 4, 2021