Characteristics of Fast Physical Random Bit Generation Using Chaotic Semiconductor Lasers

Optical Heterodyne Generation of High-Dimensional and Broadband White Chaos

“…Taking the paradigm of a delay system, i.e., an ECL, as an example, the relaxation oscillation of the semiconductor laser dominates the laser intensity chaos and leads to a strong peak projecting from the power spectrum [8]. Additionally, the resonance of the external feedback cavity excites many external-cavity modes (ECMs) in the laser field and leads to a periodically modulated spectrum similar to that of a frequency comb with a spacing equal to the reciprocal of the feedback delay [9,10]. Considerable effort has recently been devoted to expand the power spectrum [8,11] or to depress the external-cavity resonances [12], but it is difficult to completely eliminate the effects of the intrinsic oscillations [3,13].…”

“…Considerable effort has recently been devoted to expand the power spectrum [8,11] or to depress the external-cavity resonances [12], but it is difficult to completely eliminate the effects of the intrinsic oscillations [3,13]. These intrinsic oscillations impose restrictions on random number generation from physical chaos [10] and raise arguments that the extracted numbers are not truly random [14]. Worse yet, the intrinsic oscillations are easily intercepted from time series [9,13] and then pose a risk of cracking to chaos systems [15].…”

“…The periodic spectral pattern means that the chaos has correlation at the delay value and its integer multiples [9,10,13]. Because the two chaotic lasers are independent, the autocorrelation function (ACF) of I bt is …”

Fast random bits generation based on a single chaotic semiconductor ring laser

“…Thus, eliminating the delay signature in the directional mode signals will also lead to the elimination of shared information between the two signals, rendering them therefore independent so that they can contribute to the randomness improvement. Effectively to enhance the randomness of our sequence, the two signals constructed from the CW and CCW mode signals (by including the 4 [6][7][8]. The randomness of the bit sequence is tested using a standard statistical test suite NIST SP 800-22 [29,30].…”

“…In fact, their short internal time scales allow for large bandwidth dynamics, and delayed optical feedback can induce strong diverging chaotic trajectories, thus making rapid bit rates possible. Continuous streams of random bit sequences have been generated at fast rates of up to several Gbit/s in real time by directly sampling the output of two chaotic semiconductor lasers with one-bit analog-digital converters (ADCs) [6][7][8]. Subsequently, the efforts to further increase the bit rate [12] or/and to implement more simplified architectures [9][10][11][12][13] have been reported, by using 8-bit ADCs to sample the chaotic signal and to extract multi-bits in order to form the single random sequence.…”