Avoiding weak parameters in secret image sharing

Secret image sharing is a popular image hiding scheme that typically uses (3, 3, n) multi-secret sharing to hide the colors of a secret image. The use of (3, 3, n) multi-secret sharing, however, can lead to information loss. In this paper, we study this loss of information from an image perspective, and show that one-third of the color values of the secret image can be leaked when the sum of any two selected share numbers is equal to the considered prime number in the secret sharing. Furthermore, we show that if the selected share numbers do not satisfy this condition (for example, when the value of each of the selected share number is less than the half of the value of the prime number), then the colors of the secret image are not leaked. In this case, a noise-like image is reconstructed from the knowledge of less than three shares.