Evaluation of True Random Number Sequences Generated by Utilizing Timing Jitters in Superconducting Integrated Circuits

<jats:title>Abstract</jats:title> <jats:p>A Hardware Random Number Generator (HRNG), which generates true random number sequences, is studied. In superconducting Single Flux Quantum (SFQ) circuitry, HRNGs that utilized timing jitters in trigger signals have been demonstrated. In this paper, we propose an HRNG with two oscillators to enhance stability against variation of oscillator frequencies. We investigate the characteristics of random numbers generated with the proposed HRNG not only by numerical simulation but also by experiments using Nb test circuits. In the numerical simulation, the probability of “1” in random number sequences has a local minimum of “1” output probability at conditions where <jats:italic>f<jats:sub>clk</jats:sub> </jats:italic> (the clock oscillator frequency) and <jats:italic>f<jats:sub>gate</jats:sub> </jats:italic> (the gate oscillator frequency) are approximately equal (<jats:italic>f<jats:sub>clk</jats:sub> </jats:italic> ≈ <jats:italic>f<jats:sub>gate</jats:sub> </jats:italic>) for <jats:italic>f<jats:sub>clk</jats:sub> </jats:italic> ≤ 60 GHz. It is also found that pass rates for the FIPS140-2 random number tests are little affected by variations of <jats:italic>f<jats:sub>clk</jats:sub> </jats:italic> at <jats:italic>f<jats:sub>gate</jats:sub> </jats:italic> = 69.2 GHz. The random number generation rate for <jats:italic>f<jats:sub>clk</jats:sub> </jats:italic> = 60 GHz and <jats:italic>f<jats:sub>gate</jats:sub> </jats:italic> = 43 GHz reaches 3.98 GHz. In experimental measurements, random numbers of 1 Mbits generated by a test circuit pass the SP800-22 random number tests at <jats:italic>f<jats:sub>clk</jats:sub> </jats:italic> = 48.79 GHz and <jats:italic>f<jats:sub>gate</jats:sub> </jats:italic> = 19.81 GHz.</jats:p>