Secret Image Sharing Based On Chinese Remainder Theorem Over A Polynomial Ring

In recent years,image transmission has become a relatively common phenomenon in information exchange.So how to safely transmit secret images through insecure channels has become an important research content.There are generally three ways to protect the transmission of secret images:image encryption,image hiding and image sharing.Threshold secret image sharing distributes the secret image into n shadow images and stores them in the hands of n participants,and no less than t shadow images can restore the secret image,where t is the threshold.Threshold secret image sharing is an application of threshold secret sharing on images.Compared with image encryption and image hiding,threshold secret image sharing has good scalability and security.The existing threshold secret image sharing schemes are divided into the following two categories:·Threshold secret image sharing based on Shamir scheme.These kinds of thresh-old secret image sharing will be distorted when the secret image is restored.If the secret image needs to be restored without distortion,some additional processing operations are required,for example,pixels in the secret image with pixel val-ues in the[251,255]interval need extra processing operations.Since the largest prime number in the range of[0,255]is 251,the pixel values of each shadow image are randomly distributed in the range of[0,250]instead of in the range of[0,255].·Threshold secret image sharing based on the Chinese remainder theorem over an integer ring.Similarly,if this type of secret image sharing needs to restore the secret image without distortion,some additional processing operations are also required,for example,pre-store the least significant bit of each pixel in the secret image.Due to the value restriction of the modulus over an integer ring,the pixel values of each shadow image cannot be randomly distributed in the range of[0,255].Based on the Chinese remainder theorem over a polynomial ring,this paper pro-poses a threshold secret image sharing scheme based on the Asmuth-Bloom scheme and a threshold secret image sharing scheme based on the Mignotte scheme.Compared with the traditional threshold secret image sharing schemes based on the Chinese re-mainder theorem over an integer ring,the two schemes constructed in this paper can make each shadow image a noise image with a random distribution of pixel values in the range of[0,255]and without additional processing operation can restore the secret image without distortion.In addition,the threshold secret image sharing based on the Mignotte scheme can reduce the size of each shadow image to 1/t of the original secret image size,so the least significant bit replacement algorithm can be added to hide the shadow images in meaningful images.In this way,the scheme is more secure.