How to Secretly Share the Treasure Map of the Captain?

摘要

In this paper we present a new approach for sharing a secret image between l users exploiting additive homomor-phic property of Paillier algorithm. With a traditional approach, when a dealer wants to share an image between l players, the secret image must be sequentially encrypted l + 1 times using l + 1 keys (secret or public keys). When the dealer and the l players want to extract the secret image, they must decrypt sequentially, keeping the same order of the encryption step, by using l + 1 keys (secret or private). With the proposed approach, during the encryption step, each player encrypts his own secret image using the same public key given by the dealer, the dealer encrypts the secret image to be shared with the same key and then the l secret encrypted images plus the encrypted image to be shared are multiplied between them to get a scrambled image. After this step, the dealer can securely use the private key to decrypt this scrambled image to get a new scrambled image which corresponds to the addition of the l +1 original images because of the additive homomorphic property of Paillier algorithm. When the l players want to extract the secret image, they do not need the dealer and to use keys. Indeed, with our approach, to extract the secret image, the l players need only to subtract their own secret image from the scrambled image. In this paper we illustrate our approach with an example of a captain who wants to share a secret treasure map between l pirates. Experimental results and security analysis show the effectiveness of the proposed scheme.