In the field of optical information security, the most attractive work is the so-called double random phase encoding encryption scheme. This encryption method is based on the principle of Fourier transform algorithm and its linearity opens avenues of attacks. Double random phase encoding encryption can be implemented optically or digitally. We demonstrate a new approach to chosen-plaintext attack on double-phase encoding encryption system implemented digitally. With this attack an opponent can access both random phase keys with the help of impulse functions. The expressions of retrieved keys are also given. One of the most apparent advantage of proposed approach is that the decryption process is lossless. Numerical simulations show a good agreement with theoretical analysis.