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!