A holographic optical communication system based on RSA algorithm and quaternion function

A facile encryption way was successfully applied to the holographic optical encryption system with high speed, multi-dimensionality, and high capacity, which provided a better security solution for underwater communication. The reconstructed optical security system for information transmission was based on wavelength <italic>λ</italic> and focal length <italic>f</italic> that were keys to encryption and decryption. To finish the secure data transmission (<italic>λ</italic>, <italic>f</italic>) between sender and receiver, an extended Rivest-Shamir-Adleman(ERSA) algorithm for the encryption was achieved based on three-dimension quaternion function. Therein, the Pollard’s rho method was used for the evaluation and comparison of RSA and ERSA algorithms. The results demonstrate that the message encrypted by the ERSA algorithm has better security than that by RSA algorithm in the face of unpredictability and complexity of information transmission on the unsecure acoustic channel.