Abstract

$(n,n)$ secret sharing is a procedure for splitting the key into several pieces so that no subset is sufficient to read the encrypted message except the entire one. In this paper, we propose a novel, to the best of our knowledge, secret sharing scheme based on spread spectrum ghost imaging (SSGI). In the scheme, a dealer divides a secret key, which is obtained by a modulo 2 addition over $n$ sequences from a Hadamard matrix, into $n$ pieces to $n$ participants, and then the dealer uses the secret key as a direct sequence code to encrypt an image using the SSGI method. The resultant bucket signal, as the ciphertext, is then shared with $n$ participants, and the modulated speckle patterns in SSGI are also transmitted to $n$ participants by private channels for preventing eavesdropping. An independent signal is used as a protective signal to prevent the information leakage in SSGI. In the decryption process, only if all participants are honest and cooperative, the secret key can be obtained; thus, the ciphertext can be decrypted to the correct image using the second-order correlation algorithm. Otherwise, the image information cannot be extracted. The theoretical analysis shows that the probability of finding out others’ pieces for successfully reconstructing the image for one dishonest participant is ${({1/{2^N}})^{n - 1}}$, where $N$ is the length of the secret key, and $n$ is the number of participants. The simulation and experimental results demonstrate that the proposed scheme has a stronger data security capacity in optical information encryption.

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