Public key based bidirectional shadow image authentication without pixel expansion in image secret sharing

Image secret sharing(ISS)is gaining popularity due to the importance of digital images and its wide application to cloud-based distributed storage and multiparty secure computing.Shadow image authentication generally includes shadow image detection and identification,and plays an important role in ISS.However,traditional dealer-participatory methods,which suffer from significant pixel expansion or storing auxiliary information,authenticate the shadow image mainly during the decoding phase,also known as unidirectional authentication.The authentication of the shadow image in the distributing(encoding)phase is also important for the participant.In this study,we introduce a public key based bidirectional shadow image authentication method in ISS without pixel expansion for a(k,n)threshold.When the dealer distributes each shadow image to a corresponding participant,the participant can authenticate the received shadow image with his/her private key.In the decoding phase,the dealer can authenticate each received shadow image with a secret key;in addition,the dealer can losslessly decode the secret image with any k or more shadow images.The proposed method is validated using theoretical analyses,illustrations,and comparisons.