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# Low Cost and Precise Jitter Measurement Method for TRNG Entropy Assessment
## Background
This repository contains data and source codes (in the form of Python notebooks) as complementary material to the article of the same name published in [TCHES 2024](https://ches.iacr.org/2024/)-1.
We advise the user to read the original paper [here](https://ujm.hal.science/ujm-04220101v2/document).
The original article presents a new jitter measurement method aimed at the evaluation of oscillator-based TRNGs.
The aim of this repository is to help the user understand the new jitter measurement method.
Paper abstract
Random number generators, and specifically true random number generators (TRNGs), are essential in cryptography. TRNGs implemented in logic devices usually exploit the time instability of clock signals generated in freely running oscillators as source of randomness. To assess the performance and quality of oscillator-based TRNGs, accurate measurement of clock jitter originating from thermal noise is of paramount importance. We propose a novel jitter measurement method, in which the required jitter accumulation time can be reduced to around 100 reference clock periods. Reduction of the jitter accumulation time reduces the impact of the flicker noise on the measured jitter and increases the precision of the estimated contribution of thermal noise. In addition, the method can be easily embedded in logic devices. The fact that the jitter measurement can be placed in the same device as the TRNG is important since it can be used as a basis for efficient embedded statistical tests. In contrast to other methods, we propose a thorough theoretical analysis of the measurement error. This makes it possible to tune the parameters of the method to guarantee a relative error smaller than 12% even in the worst cases.
Fig. 1 from our [article](https://ujm.hal.science/ujm-04220101v2/document).
Circuitry of the ERO-TRNG with an additional counter aimed at the jitter measurement.
For more information on how to implement the jitter measurement circuitry in hardware, refer to Section 4 of the original [article](https://ujm.hal.science/ujm-04220101v2/document)).
Note that only a set of 16-bit counter values needs to be acquired from that circuit.
Next, we set the parameters of the measurement method (see Algorithm 1 in the original [paper](https://ujm.hal.science/ujm-04220101v2/document)) as follows:
$N=4\ 096$
$L=65\ 535$
$k \in \[1;255\]$
Each file contains a total of $N \left( k_{max}-k_{min}+1 \right) + 1 = 4\ 096(255 - 1 + 1) + 1 = 1\,044\,481$ counter values.
Let $c_{i,j}$ be the $j$-th acquired counter value from the circuit in Fig. 1 when $k=i$. A binary file contains the counter values, ordered as follows:
```math
[c_{1,1},\ c_{1,2},\ c_{1,3},\ ...\ c_{1,4\ 096},\ c_{2,1},\ c_{2,2},\ c_{2,3},\ ...\ ...\ c_{255,4\ 096},\ c_{65\ 535,1}]
```
The last counter value $c_{65\ 535,1}$ is used to approximate the ratio $T_0/T_1$.
Please note that only one file is sufficient to perform several jitter measurements.
However, to demonstrate the reproducibility of the new jitter measurement method, we offer the user twenty binary files acquired one after the other in 3-minute intervals for each FGPA device.
In order to stabilize the temperature of the board and hence the frequency of the oscillators, the files were acquired after the ring oscillators in the FPGA had been running for 10 minutes.
Repository structure
```
├───📁 src/
│ ├───📄 Error_analysis.ipynb
│ ├───📄 FPGA_measurements.ipynb
│ └───📄 Simulation.ipynb
│
└───📦 data.zip
│
📁 data/
├───📁 CV/
│ └───📄acq_TIMESTAMP_CV.bin...
├───📁 S6/
│ └───📄acq_TIMESTAMP_S6.bin...
└───📁 SF2/
└───📄acq_TIMESTAMP_SF2.bin...
```
Fig. 2 Jupyter interface using Binder.
5. Follow the instructions in the notebook.
### By downloading them and running the project locally
1. Download our project on a PC with Python. For more information on how to install Python, click [here](https://wiki.python.org/moin/BeginnersGuide/Download).
2. Make sure that the following Python modules are installed. If they are not, install them using `pip`. For more information on how to install modules with 'pip', click [here](https://packaging.python.org/en/latest/tutorials/installing-packages/).
[`numpy`](https://pypi.org/project/numpy/)
[`matplotlib`](https://pypi.org/project/matplotlib/)
[`scipy`](https://pypi.org/project/scipy/)
[`progressbar2`](https://pypi.org/project/progressbar2/)
[`plotly`](https://pypi.org/project/plotly/)
[`jupyter`](https://pypi.org/project/jupyter/)
3. Unzip the content of the [`data.zip`](https://src.koda.cnrs.fr/labhc/code4publications/2024-tches-lcpj-measurement-method/-/blob/master/data.zip?ref_type=heads) file in its location.
3. In a command line, go to the downloaded folder of this project on your PC.
4. Start the JupyterLab server from the command line by running:
```
python -m notebook
```
5. You should see a JupyterLab interface open in a tab in your web browser.
6. Go to the `/src` folder. Click on the notebook you wish to use.
Fig. 3 Local JupyterLab interface.
7. Follow the instructions in the notebook.
## Authors
**Arturo Garay1,2, Florent Bernard1, Patrick Haddad2, Natahlie Bochard1, Viktor Fischer1,3**
Affiliations
1Hubert Curien Laboratory, Université Jean Monnet, Member of the Université de Lyon, 42000, Saint-Etienne, France
2STMicroelectronics, Advanced System Technology, 13790 Rousset, France
3Faculty of Information Technologies, Czech Technical University in Prague, 160 41, Prague, Czech Republic
Email addresses
- [arturo.garay@univ-st-etienne.fr](arturo.garay@univ-st-etienne.fr)
- [florent.bernard@univ-st-etienne.fr](florent.bernard@univ-st-etienne.fr)
- [patrick.haddad@st.com](patrick.haddad@st.com)
- [nathalie.bochard@univ-st-etienne.fr](nathalie.bochard@univ-st-etienne.fr)
- [fischer@univ-st-etienne.fr](fischer@univ-st-etienne.fr)
For information regarding other jitter measurement methods
- _Viktor Fischer and David Lubicz. Embedded evaluation of randomness in oscillator based elementary TRNG. In Lejla Batina and Matthew Robshaw, editors, CHES 2014, volume 8731 of LNCS, pages 527–543. Springer, Heidelberg, September 2014_, [link](https://ujm.hal.science/ujm-01010404/document).
- _Bohan Yang, Vladimir Rozic, Milos Grujic, Nele Mentens, and Ingrid Verbauwhede. On-chip jitter measurement for true random number generators. In 2017 Asian Hardware Oriented Security and Trust Symposium, AsianHOST 2017, Beijing, China, October 19-20, 2017, pages 91–96. IEEE Computer Society, 2017_, [link](https://lirias.kuleuven.be/bitstream/123456789/630261/2/OCJMFTRNG.pdf).
- _Boyan Valtchanov, Viktor Fischer, and Alain Aubert. A coherent sampling based method for estimating the jitter used as entropy source for True Random Number Generators. In International Conference on Sampling Theory and Applications - SAMPTA 2009, 2009_, [link](https://hal.science/hal-00451849/document).
For the stochastic model of the jitter-based eRO-TRNG
- _Mathieu Baudet, David Lubicz, Julien Micolod, and André Tassiaux. On the security of oscillator-based random number generators. Journal of Cryptology, 24(2):398–425, April 2011_, [link](https://eprint.iacr.org/2009/299.pdf).
For standards requiring the evaluation of TRNGs using their stochastic model
- _Information technology – Security techniques – Test and analysis methods for random bit generators within ISO/IEC 19790 and ISO/IEC 15408. Technical report, International Organization for Standardization, October 2019_, [link](https://www.iso.org/standard/68296.html).
- _Wolfgang Killmann and Werner Schindler. A proposal for: Functionality classes for random number generators, AIS20/31. Technical report, Bundesamt für Sicherheit in der Informationstechnik (BSI), Bonn, 2011_, [link](https://cosec.bit.uni-bonn.de/fileadmin/user_upload/teaching/15ss/15ss-taoc/01_AIS31_Functionality_classes_for_random_number_generators.pdf).