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 Shares Decryption (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(q) p (1) p (2) ……p (q) Secret images A set of shares A combination of pixels in secret images B pB p A code set V1V1 V2V2 VnVn A matrix representing n pixels with m subpixels Each code set B p can be obtained from matrix B p is called basis matrix s.t. B p =.

Relation between shares and secret images The permutation of columns R is used in decryption. Problem SL1SL1 SU1SU1 SU2SU2 SL2SL2 Share 1Rotated Share 2 S U1 S U2 S L1 S L2 S U1 R( S L2 ) S L1 R( S U2 ) Decrypted image 1 Decrypted image 2 R( S L2 ) R( S U2 ) Share 2 A code set in VSS-q-PI-R schemes cannot be an equivalence class of some matrix.

B p = { v n (B) : B } Main theorem A new operation v n –The inverse of v n coincides with v n. [Theorem] (informal) Each code set B p of the VSS-PI-R scheme can be obtained by

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!