Analysis of Randomness Sources in Transition Effect Ring Oscillator based TRNG

We present a deeper analysis of recently published Transition Effect Ring Oscillator (TERO). TERO is an entropy source suitable for cryptographic True Random Number Generator (TRNG) embedded in FPGAs. We propose new TERO structure with simplified control adopted for the Actel Fusion FPGAs. An original idea behind the principle lies in the randomness extraction on an oscillatory trajectory when a bistable circuit is resolving previous metastable event. Although oscillatory behavior is a well-known issue in the field of synchronization flip-flops, this feature was not yet been used for the TRNG designs. We are able to excite the oscillatory metastability in the TERO reliably. The number of executed oscillations varies after each excitation. The randomness is represented as a least significant bit of the number of oscillations accordingly. The number of generated oscillations is directly related to the intrinsic noise of the TERO components. There are three potential random processes that can affect resulting number of oscillations: 1) The actual noise and circuit parameters when excitation pulse forces entering to the oscillatory metastability phase; 2) The jitter accumulation during the oscillatory metastability phase; and 3) The ability of the last pulse to add one more oscillation can also depend on the actual noise conditions. We analyze all three phases that can possibly bring random contribution to final number of oscillations. We enhance an original mathematical model accordingly in terms of the intrinsic noise composition. We attach experimental results from both Actel and Xilinx FPGAs in order to show TERO-based TRNG suitability for the practical use.