Identification of the delay time in semiconductor lasers with optical feedback

Semiconductor lasers (SLs) with optical feedback have attracted a lot of attention in the chaos cryptography community due to its capability to develop broadband chaos within which gigabit messages can be encoded [1]. The security of laser-based chaos communications relies mainly on the difficulty of identifying the emitter parameters necessary to build an adequate receiver, which can synchronize with it. In chaos communication schemes based on SLs with delayed optical feedback, the delay time can be identified from time series using standard techniques in most parameter regimes. However, the efforts to enhance the security in these schemes have led to the characterization of a regime in which the delay time appears to be concealed, namely when it is close to the relaxation oscillation period of the laser operating with moderate feedback [2]. These results were obtained exclusively by computing the quantifiers from intensity time series. Taking into account that, in addition to the intensity, the phase information is also transmitted through the public channel, it is mandatory to check if the delay time can be concealed when computing different quantifiers from the phase of the field [3].