| Summary: | 碩士 === 國立東華大學 === 資訊工程學系 === 107 === Shamir’s secret sharing divides the secret message into n shares. The secret can be reconstructed by using any k shares, but (k-1) or less than k shares have no information about the secret. When applying secret sharing on digital image is called as secret image sharing (SIS). A (k, n)-SIS has the threshold property of secret sharing and meantime deals with image processing to achieve image security. However, most (k, n)-SIS schemes may degrade the visual quality of recovered secret image. Therefore, how to achieve security and high image quality of secret image deserve studying.
In general, when secret sharing extended to secret image sharing, we have choose a finite field and cause the less distortion in recovered image. In polynomial based (k, n)-SIS, the GF(251) finite field is often used. The operation of GF(251) is a simple modular function, and can be easily finished. However, in GF(251), we can only deal with the pixel values from 0 to 250. Thus, the grayness 251~255 should be truncated to 250, and this result in image distortion. If we want to recover a distortion-less secret image, a polynomial based GF(2^8) finite field should be adopted. But, the operation of GF(2^8) is more complicated than the simple modular function.
A (k, n)-SIS based on simple modular arithmetic is proposed, which we use bit-wise operation instead of pixel-wise operation. We process N bits every time to enhance the recovered image quality. Because our method using simple modular arithmetic still has efficient computation. In this thesis, we theoretically give analysis to figure out the optimal values of
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