Emulator

Introduction

The emulator directory includes all Python files dedicated to the emulation of ring oscillators and raw random numbers . These emulators can be executed directly using the provided scripts (refer to the sections below for details).

For detailed information on script parameters, use the -h option

The emulator directory also includes a jupyter notebook named playground.ipynb, providing an interactive environment to explore and utilize the emulator’s internal routines.

Emulate noisy ring oscillators

The emulator, introduced in our CHES 2024 paper, is capable of generating time series for ring oscillators (RO) while incorporating realistic phase noise. Each successive value in the series represents the absolute timing of the rising edge of the RO signal. The phase noise models include both thermal noise (white noise) and flicker noise (colored noise).

To simulate 10,000,000 cycles of a ring oscillator running at 100 MHz, execute the following command:

$ python ro.py -size 10e6 -freq 100e6 ro.txt

Below is an example of the generated file, where each line represents a ring oscillator period in femtoseconds (fs):

The distributions of periods is given in the figure below as an example (see analysis tools for help on distribution plots).

100MHz noisy ring oscillator periods distribution (fs)

By default, the thermal and flicker noise amplitude coefficients, a1 and a2, are calibrated for a ring oscillator operating at 100 MHz on a Xilinx Artix-7 FPGA. Optionally, these coefficients can be customized to define a specific thermal and flicker noise model. For example, using measured coefficients from a 500 MHz ring oscillator fabricated on a 28nm industrial FD-SOI (Fully Depleted Silicon on Insulator) process:

$ python ro.py -size 10e6 -freq 100e6 -a1 1.334e-14 -a2 7.985e-09 ro.txt

Emulate raw random numbers

Raw random numbers (RRN) can be emulated using Python scripts based on the noisy ring-oscillator emulation described in the previous section.

By specifying the frequencies of the target ring oscillators and selecting a sampling architecture — ERO, MURO, or COCOSO — the script will generate a file containing the raw random output.

Elementary RO based TRNG

For instance, to generate a stream of 1,000,000 bits using the ERO architecture, with the first ring oscillator operating at 100 MHz and a divisor of 1,000 sampling the second ring oscillator at 101 Hz, execute the following command:

$ python ero.py -size 1e6 -freq0 100e6 -freq1 101e6 -div 1000 ero.txt

Executing this command produces the following output:

Number of bits to generate: 1.00e+06
Ring-oscillators frequencies:
 - RO0: 1.000e+08 Hz / 1000
 - RO1: 1.010e+08 Hz
Noise amplitude coefficiens:
 - Thermal (a1): 1.421673e-13
 - Flicker (a2): 1.155723e-25
Output bits bias: 0.50

Multi-RO based TRNG

The MURO utilizes multiple ring oscillators. For example, to generate a stream of 1,000,000 bits with a sampling frequency of 100 MHz, divided by 1000, which samples a tuple of ring oscillators operating at frequencies of 99 MHz and 101 MHz, use the following command:

$ python muro.py -size 1e6 -freq 100e6 99e6 101e6 -div 1000 muro.txt

Running this command generates the following output:

Number of bits to generate: 1.00e+06
Number of ring-oscillators: 3 (t=2)
Ring-oscillators frequencies:
 - RO0: 1.000e+08 Hz / 1000
 - RO1-ROt: 9.900e+07, 1.010e+08 Hz
Noise amplitude coefficiens:
 - Thermal (a1): 1.421673e-13
 - Flicker (a2): 1.155723e-25
Output bits bias: 0.50

Coherent Sampling TRNG

In a more straightforward configuration, the COSO only requires two ring-oscillator frequencies as inputs. To generate a stream of 1,000,000 bits with a COSO operating at 99.91 MHz and 100.52 MHz, use the following command:

$ python coso.py -size 1e6 -freq0 121e6 -freq1 122e6 coso.txt

Executing this command produces the following output:

Number of bits to generate: 1.00e+06
Ring-oscillators frequencies:
 - RO0: 9.991e+07 Hz
 - RO1: 1.005e+08 Hz
Noise amplitude coefficiens:
 - Thermal (a1): 1.421673e-13
 - Flicker (a2): 1.155723e-25
Average counter value: 150.28
Output bits bias: 0.51

Below is an illustration of the raw random output for the COSO.

An example of raw binary output for the COSO

Optionnaly, as explained in the previous section, noise amplitudes a1 and a2 can be specified for other hardware target with different thermal and flicker noise model.

The RRN emulators are used as golden model for HDL simulation.