Digital key chaos-communication systems with delay time concealment

Chaos-based optical communications has no clear counterpart of the digital key in algorithmic cryptography. Typically the chaotic carrier is generated using delayed optical or electro-optical systems. Confidentiality relies on hardware parameters that should be kept secret. Unfortunately, the delay time in itself cannot be a key parameter since it can be identified using autocorrelation function or delayed mutual information (DMI). We propose a scheme based on a double opto-electronic feedback system which allows on one hand to integrate a digital key required for decoding and on the other to conceal the delay time so that it cannot be identified from the time series using the typical methods. The scheme we propose is based on high speed phase chaos [1], with constant intensity and an essentially featureless power spectrum, and includes a send delay line in which a key random bit sequence (RBS) is included. The emitter dynamics is given by the dimensionless variables x(t) and y(t) equation equation where du 1 /dt = x, du 2 /dt = y, m(t) is the message and R(t) the RBS. The parameters are the MZI static phases φ 1 = π/4 and φ 2 = π/8, the feedback strengths β 1 = β 2 = 5, the time delays T 1 = 17 ns and T 2 = 15 ns, the fast (low) filter response times τ 1 = 20 ps (θ 1 = 1.6 µs) and τ 2 = 12.2 ps (θ 2 = 1.6 µs) and the MZI imbalanced time delays δT 1 = 510 ps and δT 2 = 400 ps. Figures. 1 b) and c) display DMI of the chaotic carrier as function of the delay without and with RBS, respectively. It is seen that without RBS, clear peaks appear at time-delays T, T + δT 1 , T + δT 2 and T + δT 1 + δT 2 . However, when RBS is employed, time-delays cannot be identified anymore. Similar results were obtained from the computation of the autocorrelation function. Figures 1 d) and e) show the effects of mismatch η in the key by measuring the root-mean-square synchronization error σ and quality factor, respectively. Considering 10 Gb/s message with amplitude of 0.6 for Fig 1 e), it appears that even 4% of key-mismatch is enough to considerably degrade the synchronization quality. Thus, we have shown that RBS can be an efficient way to both provide further security and conceal the time delays in some electro-optic systems.