A temporal phase-truncated double random phase encoding cryptosystem in the temporal skew Fourier transform domain

Abstract

A temporal phase-truncated double random phase encoding cryptosystem is proposed to be improved by replacing the temporal Fourier transformers (TFTs) of the dispersion-time lens-dispersion structure with temporal skew Fourier transformers (TSFTs). A TSFT is similar to a TFT except for the time lens (TL) replaced by a skew time lens (STL). A STL is a temporal analog of a spatial cylindrical lens with the in-plane rotational asymmetry mapping to a front–back asymmetry. The front–back asymmetry is achieved by adding the chirp factor C of a TL by +ϵ⋅C and −ϵ⋅C respectively along the positive and negative half axis of the local time coordinate. The skew coefficients ϵ1 and ϵ2 of the two TSFTs involved in the encryption stage are dimensionless and ideally unbounded, serving as additional secret keys. By mathematical analysis, STLs are proven to have complex-value modulations on low frequency components of input signals of TSFTs, which cannot be removed by phase truncations (PTs) in the legal decryption stage. The plain/cipher-text-independent and non-removability features of STLs make phase retrieval attacks unable to exempt eavesdroppers from brute-force trials of STLs. A STL is implemented by an electrical arbitrary waveform generator (AWG) driven electro-optic phase modulator (EOPM). By numerical simulations, the using of STLs is proven to increase the difficulty of phase retrieval attacks in terms of the time consuming required for convergence. Even if phase retrieval attacks converge, the plaintext signal cannot be recovered without the knowledge of ϵ1,2 in the encryption stage. The total key space of ϵ1,2 is also evaluated as 217 at AWG bandwidth Bm=20 GHz, and as 237 at Bm=100 GHz. The fidelity robustness of our optical cryptosystem against possible noise and occlusion penalties on the communication channels and networks of optical cipher-text signals is also proven.