visual secret sharing schemes for plural secret images allowing the rotation of shares kazuki...
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Visual Secret Sharing Schemes for Plural Secret Images
Allowing the Rotation of Shares
Kazuki Yoneyama Wang Lei Mitsugu Iwamoto
Noboru Kunihiro Kazuo Ohta
The University of Electro-Communications
Basic VSS schemes V.S. Our scheme• Basic visual secret sharing schemes (VSS) – By stacking up shares, each secret image is
decrypted.
• VSS schemes for plural secret images with general access structures allowing the rotation (VSS-PI-R)– More secret images can be decrypted compared
with the ordinal VSS. – We can construct any VSS-PI-R scheme for given
access structure.
In the case of (2, 2)-threshold
SharesDecryption
(Stacking up) One secret image
Shares Decryption(Stacking up)
Decryption(180 degrees Rotation and Stacking up)
Two secret images
Basic VSS
VSS-PI-R
Construction of VSS-q-PI schemes
p(1)
p(2)
p(q)
p(1)p(2)……p(q)
Secret images A set of sharesA combination of pixels
in secret images
B
p
A code set
V1
V2
Vn
pm
pp sss 11211 pm
pp sss 22221
pnm
pn
pn sss 21
A matrix representingn pixels with m subpixels
Each code set B p can be obtained from matrix Bp
is called basis matrix s.t. B p= .
pB
• Relation between shares and secret images
The permutation of columns R is used in decryption.
Problem
SL1
SU1 SU2
SL2
Share 1 Rotated Share 2
SU1 SU2 SL1 SL2
SU1 R(SL2) SL1 R(SU2)
Decrypted image 1 Decrypted image 2
R(SL2)
R(SU2)
Share 2
A code set in VSS-q-PI-R schemes cannot be an equivalence class of some matrix .
B p = {vn(B) : B }
Main theorem
• A new operation vn– The inverse of vn coincides with vn.
[Theorem] (informal)Each code set B
p of the VSS-PI-R scheme can be obtained by
pB
Conclusion
• The proposed technique can easily be applied to VSS-PI schemes allowing to reverse the shares besides stacking in decryption.
• We will soon submit the paper corresponding to this talk in Cryptology ePrint Archive!