Research On Image Sharing Method Of GF Finite Field Lagrangian Interpolation Polynomial

Image sharing is the splitting of a secret image into a series of shadow images and then reconstructing the secret image with a partial distribution of the shadow image.Image sharing provides a higher level of security protection for important secret images.However,the existed image sharing still has many problems:For progressive sharing scheme,the progressive sharing scheme based on image block can't make the overall progressive recovery from blure to clear;the mixed mode based on pixel bit grouping and block grouping can only provides a limited number of progressive recovery and the overall progressive sharing based on the importance of spatial or frequency bit planes have only a limited visual control.For(t,s,k,n)sharing scheme which distinguish important and un important participants,shadow image connection based(t,s,k,n)scheme is prone to different sizes of shadow images and Birkhoff interpolation based(t,s,k,n)scheme avoids unequal sizes of shadow images but leads to low recovery efficiency,while non-equivalent backup and double authentications based self-recovery image sharing scheme has high authentication accuracy,but the recovery capability of the secret image and backup images are very limited.To address these problems,the followings are the finished works:1)Multiple thresholds progressive secret image sharing scheme based on GF(26)galois field is proposed,First the key was shared in combination with the random participation value,the MD5 values corresponding to the sub-keys and participating values were published to prevent participants from cheating,then the secret image was transformed by 8 X 8 DCT where the DCT coefficients are randomly quantified and the binary representation of the assigned code length distribution table was presented to form multiple partition bands by zigzag scanning order and all these bands were reorganized and scrambled to form the band backups;Secondly,bands,band backups and authentication information were shared by multiple thresholds in the GF(26)Galois field,and 2 bit authentication information was added to construct the distribution shadow images.In the process of recovery,first the MD5 values of sub-keys were detected and the rebuild bands combined with multiple thresholds were determined,then the double authentication was used to reconstruct the first and second band backup and to reconstruct the corresponding bands,Finally,the secret image was reconstructed by using the reconstruct bands.The experimental results show that the proposed method can make use of the distributed shadow images for the overall progressive recovery and also improve the visual quality of reconstruction as much as possible,and at the same time also has the self-recovery capability for certain attacks.2)A(t,s,k,n)image sharing sheme with multi-version backups and restricted double authentications was proposed where random participation values were introduced by converting shadow image based(t,s,k,n)scheme into the master key based(t,s,k,n)scheme.The proposed scheme introduced random participation values and generated important and unimportant sub-keys by means of(k,s)and(k-t,n-s)threshold schemes and the MD5 values stored in the third trustable parties are used to prevent participants from cheating.The proposed scheme scrambled the LL(t,s,k,n)of the one layer DWT of the secret image by the master key,and formed the multi-version backup images with different scrambling degrees,where the backup images were equal sizes of the secret image with more backups for significant bits and less backups for non-significant bits.The restricted double authentication strategy can embed as many backup bits as possible while maintaining a certain authentication accuracy by(k,n)sharing scheme over the GF(28)finite field to form the stego carriers.Theoretical and experimental results show,by compared with the existing methods,the proposed master key based(t,s,k,n)scheme can be solved efficiently by Lagrange interpolation and inverse matrix calculation modulus p and avoids shadow image involved in restoration where the large computation and computational complexity were alleviated.Random participation values avoids the disclosure of participant numbers and prevent the malicious participant from tampering self-distributed information and guessing authentication bits of other legitimate participants.The multi-version backup strategy can make full use of the same bits stored in different locations to restore the backup image with high confidence and have good anti-attack ability while the authentication capability of the restricted double authentication strategy is no less than the traditional self-recovery based Galois field image sharing scheme with non-equivalent backup and double authentications.Experiments show the validity of the proposed scheme.