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Added readme analysis.

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Signed-off-by: Pol Henarejos <pol.henarejos@cttc.es>
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Pol Henarejos
2022-08-22 13:13:49 +02:00
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README.md
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@@ -1,5 +1,7 @@
# Raspberry Pi Pico Random Number Generator
** This fork includes an enhanced RNG to produce a true RNG. **
A basic random number generator that generates numbers from enviromental noise with the onboard DAC of the Raspberry Pi Pico. The project uses the Raspberry Pi Pico USB dev_lowlevel as a starting point. The Pico RNG is not meant to be FIPS 140-2 compliant as a stand-alone device by any means. However it does supply the Linux Kernel with random bits that is used with the appropriate entropy to achieve FIPS 140-2 compliant random numbers. Maybe one day the next gen Pico's will include an onboard crypto module.
## Project Goals
@@ -8,13 +10,13 @@ A basic random number generator that generates numbers from enviromental noise w
* Driver can transmit random numbers on demand to the system and/or user processes via a character device.
### Prerequisites
## Prerequisites
* Raspberry Pi Pico development environment. See [Raspberry Pi Pico Getting Started Documentation](https://www.raspberrypi.org/documentation/pico/getting-started/)
* Linux Kernel development headers
### Building
## Building
The entire project uses CMake to keep with Rasberry Pi Pico's development environment and project setup instructions.
```bash
@@ -31,7 +33,7 @@ cmake ..
make
```
### Install
## Install
The driver can be installed from the build directory using the traditional insmod command.
@@ -50,25 +52,360 @@ The Pico firmware is installed thorugh the normal process as outlined in the Ras
* Copy the uf2 file to the Pico ```sudo cp firmware/pico_rng.uf2 /mnt```.
* Umount the pico ```sudo umount /mnt```.
### Testing
## Testing
You can test Pico RNG firmware with the [pico_rng_test.py](firmware/pico_rng_test.py) script.
```bash
# Running with --performance will measure the devices' KB/s.
# if the kernel module has been installed, then the test tool will use /dev/pico_rng otherwise python's libusb implementation will be used.
sudo firmware/pico_rng_test.py [--performance]
sudo firmware/pico_rng_test.py [--performance] [--size] [--endless]
```
You can also test the Kernel's random number pool that contains random numbers from the Pico
![Pico Random Numbers](pico-rng.gif)
## Analysis
# Remove
A set of random samples can be analyzed with the [pico_rng_analyze.py](firmware/pico_rng_analyze.py) script.
For generating a set of samples, the following code can be executed:
```bash
$ python3 firmware/pico_rng_test.py --size 1073741824 > sample.rng
```
will produce a 1 GB file containing random bytes.
Then
```bash
$ python3 firmware/pico_rng_analyze.py sample.rng
```
will produce two figures:
Fig. 1 depicts the distribution of the bytes, from `0` to `255`. Ideally, it must be a uniform distribution, with mean equal to `127.5`.
Fig. 2 depicts the distribution of chi square tests and excess percentages. Ideally, the distribution of chi square tests must follow a chi square distribution with mean at `255`. Excess percentage distribution must follow a uniform distribution.
Pico-rng is also tested with `ent`, `rngtest` and `dieharder` tests. These are the results obtained with pico-rng:
```
$ ent sample.rng
Entropy = 7.999999 bits per byte.
Optimum compression would reduce the size
of this 1073741824 byte file by 0 percent.
Chi square distribution for 1073741824 samples is 839.56, and randomly
would exceed this value less than 0.01 percent of the times.
Arithmetic mean value of data bytes is 127.4993 (127.5 = random).
Monte Carlo value for Pi is 3.141625006 (error 0.00 percent).
Serial correlation coefficient is 0.000006 (totally uncorrelated = 0.0).
```
- Entropy test should produce an ideal result of `8`, as each byte has `8` bits.
- Optimum compression test should produce an ideal result of 0 percent.
- Chi square should be called with different sample tests and produce a chi square distribution.
- Arithmetic mean should produce an ideal result of `127.5`.
- Pi test should be equal to pi number.
- Serial correlation should be `0`.
These results show that pico-rng is pretty random.
```bash
$ cat sample.rng | rngtest
rngtest 2-unofficial-mt.14
Copyright (c) 2004 by Henrique de Moraes Holschuh
This is free software; see the source for copying conditions. There is NO warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
rngtest: starting FIPS tests...
rngtest: entropy source exhausted!
rngtest: bits received from input: 8589934592
rngtest: FIPS 140-2 successes: 429141
rngtest: FIPS 140-2 failures: 355
rngtest: FIPS 140-2(2001-10-10) Monobit: 42
rngtest: FIPS 140-2(2001-10-10) Poker: 41
rngtest: FIPS 140-2(2001-10-10) Runs: 138
rngtest: FIPS 140-2(2001-10-10) Long run: 136
rngtest: FIPS 140-2(2001-10-10) Continuous run: 0
rngtest: input channel speed: (min=9661835.749; avg=23078154805.083; max=0.000)bits/s
rngtest: FIPS tests speed: (min=5.699; avg=239.429; max=261.281)Mibits/s
rngtest: Program run time: 34612429 microseconds
```
In these results, we have a total number of trials `429496 (429141+355)`.
- The acceptable result of Monobit test is `1` failed trial for every `9662` trials. For `429496` trials, the number of failed trials should be less than `429496/9662=44.45`.
- The acceptable result of Poker test is `1` failed trial for every `10078` trials. For `429496` trials, the number of failed trials should be less than `42.62`.
```bash
$ dieharder -a -g 201 -k 2 -Y 1 -m 2 -f sample.rng
#=============================================================================#
# dieharder version 3.31.1 Copyright 2003 Robert G. Brown #
#=============================================================================#
rng_name | filename |rands/second|
file_input_raw| batch1.rng| 3.57e+07 |
#=============================================================================#
test_name |ntup| tsamples |psamples| p-value |Assessment
#=============================================================================#
diehard_birthdays| 0| 100| 200|0.17739498| PASSED
diehard_operm5| 0| 1000000| 200|0.97387049| PASSED
# The file file_input_raw was rewound 1 times
diehard_rank_32x32| 0| 40000| 200|0.37394022| PASSED
# The file file_input_raw was rewound 2 times
diehard_rank_6x8| 0| 100000| 200|0.09038266| PASSED
# The file file_input_raw was rewound 2 times
diehard_bitstream| 0| 2097152| 200|0.71785604| PASSED
# The file file_input_raw was rewound 4 times
diehard_opso| 0| 2097152| 200|0.37146068| PASSED
# The file file_input_raw was rewound 5 times
diehard_oqso| 0| 2097152| 200|0.35763562| PASSED
# The file file_input_raw was rewound 5 times
diehard_dna| 0| 2097152| 200|0.01889729| PASSED
# The file file_input_raw was rewound 5 times
diehard_count_1s_str| 0| 256000| 200|0.63258197| PASSED
# The file file_input_raw was rewound 6 times
diehard_count_1s_byt| 0| 256000| 200|0.65359815| PASSED
# The file file_input_raw was rewound 6 times
diehard_parking_lot| 0| 12000| 200|0.83176205| PASSED
# The file file_input_raw was rewound 6 times
diehard_2dsphere| 2| 8000| 200|0.64543002| PASSED
# The file file_input_raw was rewound 6 times
diehard_3dsphere| 3| 4000| 200|0.01258942| PASSED
# The file file_input_raw was rewound 8 times
diehard_squeeze| 0| 100000| 200|0.67578527| PASSED
# The file file_input_raw was rewound 8 times
diehard_sums| 0| 100| 200|0.23981668| PASSED
# The file file_input_raw was rewound 8 times
diehard_runs| 0| 100000| 200|0.77427455| PASSED
diehard_runs| 0| 100000| 200|0.08390099| PASSED
# The file file_input_raw was rewound 9 times
diehard_craps| 0| 200000| 200|0.59348655| PASSED
diehard_craps| 0| 200000| 200|0.23828837| PASSED
# The file file_input_raw was rewound 24 times
marsaglia_tsang_gcd| 0| 10000000| 200|0.15517856| PASSED
marsaglia_tsang_gcd| 0| 10000000| 200|0.00447239| WEAK
# The file file_input_raw was rewound 31 times
marsaglia_tsang_gcd| 0| 10000000| 300|0.02554040| PASSED
marsaglia_tsang_gcd| 0| 10000000| 300|0.00100578| WEAK
# The file file_input_raw was rewound 39 times
marsaglia_tsang_gcd| 0| 10000000| 400|0.00299305| WEAK
marsaglia_tsang_gcd| 0| 10000000| 400|0.00008767| WEAK
# The file file_input_raw was rewound 46 times
marsaglia_tsang_gcd| 0| 10000000| 500|0.00201489| WEAK
marsaglia_tsang_gcd| 0| 10000000| 500|0.00004067| WEAK
# The file file_input_raw was rewound 54 times
marsaglia_tsang_gcd| 0| 10000000| 600|0.00028460| WEAK
marsaglia_tsang_gcd| 0| 10000000| 600|0.00000323| WEAK
# The file file_input_raw was rewound 61 times
marsaglia_tsang_gcd| 0| 10000000| 700|0.00004334| WEAK
marsaglia_tsang_gcd| 0| 10000000| 700|0.00000055| FAILED
# The file file_input_raw was rewound 61 times
sts_monobit| 1| 100000| 200|0.11868265| PASSED
# The file file_input_raw was rewound 61 times
sts_runs| 2| 100000| 200|0.55674493| PASSED
# The file file_input_raw was rewound 61 times
sts_serial| 1| 100000| 200|0.99669244| WEAK
sts_serial| 2| 100000| 200|0.46102720| PASSED
sts_serial| 3| 100000| 200|0.44562932| PASSED
sts_serial| 3| 100000| 200|0.84230024| PASSED
sts_serial| 4| 100000| 200|0.98548763| PASSED
sts_serial| 4| 100000| 200|0.57495245| PASSED
sts_serial| 5| 100000| 200|0.77085975| PASSED
sts_serial| 5| 100000| 200|0.56476358| PASSED
sts_serial| 6| 100000| 200|0.45650075| PASSED
sts_serial| 6| 100000| 200|0.05289356| PASSED
sts_serial| 7| 100000| 200|0.27201114| PASSED
sts_serial| 7| 100000| 200|0.76400695| PASSED
sts_serial| 8| 100000| 200|0.62348338| PASSED
sts_serial| 8| 100000| 200|0.57277685| PASSED
sts_serial| 9| 100000| 200|0.38071419| PASSED
sts_serial| 9| 100000| 200|0.07625829| PASSED
sts_serial| 10| 100000| 200|0.47989859| PASSED
sts_serial| 10| 100000| 200|0.11112817| PASSED
sts_serial| 11| 100000| 200|0.92833035| PASSED
sts_serial| 11| 100000| 200|0.69376394| PASSED
sts_serial| 12| 100000| 200|0.84887524| PASSED
sts_serial| 12| 100000| 200|0.97617601| PASSED
sts_serial| 13| 100000| 200|0.65397230| PASSED
sts_serial| 13| 100000| 200|0.56436970| PASSED
sts_serial| 14| 100000| 200|0.51868029| PASSED
sts_serial| 14| 100000| 200|0.92953669| PASSED
sts_serial| 15| 100000| 200|0.85158213| PASSED
sts_serial| 15| 100000| 200|0.93993540| PASSED
sts_serial| 16| 100000| 200|0.35998600| PASSED
sts_serial| 16| 100000| 200|0.20807684| PASSED
# The file file_input_raw was rewound 61 times
sts_serial| 1| 100000| 300|0.19573096| PASSED
sts_serial| 2| 100000| 300|0.85406665| PASSED
sts_serial| 3| 100000| 300|0.06590447| PASSED
sts_serial| 3| 100000| 300|0.45707402| PASSED
sts_serial| 4| 100000| 300|0.44442263| PASSED
sts_serial| 4| 100000| 300|0.52775404| PASSED
sts_serial| 5| 100000| 300|0.40217529| PASSED
sts_serial| 5| 100000| 300|0.06010705| PASSED
sts_serial| 6| 100000| 300|0.08040223| PASSED
sts_serial| 6| 100000| 300|0.00547743| PASSED
sts_serial| 7| 100000| 300|0.24575210| PASSED
sts_serial| 7| 100000| 300|0.28977315| PASSED
sts_serial| 8| 100000| 300|0.36868885| PASSED
sts_serial| 8| 100000| 300|0.49522777| PASSED
sts_serial| 9| 100000| 300|0.40957917| PASSED
sts_serial| 9| 100000| 300|0.09110499| PASSED
sts_serial| 10| 100000| 300|0.77559781| PASSED
sts_serial| 10| 100000| 300|0.19716611| PASSED
sts_serial| 11| 100000| 300|0.80459107| PASSED
sts_serial| 11| 100000| 300|0.44572782| PASSED
sts_serial| 12| 100000| 300|0.20184427| PASSED
sts_serial| 12| 100000| 300|0.60780140| PASSED
sts_serial| 13| 100000| 300|0.76273905| PASSED
sts_serial| 13| 100000| 300|0.60473178| PASSED
sts_serial| 14| 100000| 300|0.24687487| PASSED
sts_serial| 14| 100000| 300|0.66722555| PASSED
sts_serial| 15| 100000| 300|0.85162176| PASSED
sts_serial| 15| 100000| 300|0.81632309| PASSED
sts_serial| 16| 100000| 300|0.72398028| PASSED
sts_serial| 16| 100000| 300|0.26061444| PASSED
# The file file_input_raw was rewound 61 times
rgb_bitdist| 1| 100000| 200|0.80303319| PASSED
# The file file_input_raw was rewound 62 times
rgb_bitdist| 2| 100000| 200|0.44511426| PASSED
# The file file_input_raw was rewound 62 times
rgb_bitdist| 3| 100000| 200|0.15306427| PASSED
# The file file_input_raw was rewound 63 times
rgb_bitdist| 4| 100000| 200|0.52424083| PASSED
# The file file_input_raw was rewound 64 times
rgb_bitdist| 5| 100000| 200|0.62602197| PASSED
# The file file_input_raw was rewound 64 times
rgb_bitdist| 6| 100000| 200|0.27582205| PASSED
# The file file_input_raw was rewound 65 times
rgb_bitdist| 7| 100000| 200|0.83928387| PASSED
# The file file_input_raw was rewound 67 times
rgb_bitdist| 8| 100000| 200|0.78920891| PASSED
# The file file_input_raw was rewound 68 times
rgb_bitdist| 9| 100000| 200|0.10426661| PASSED
# The file file_input_raw was rewound 69 times
rgb_bitdist| 10| 100000| 200|0.56345552| PASSED
# The file file_input_raw was rewound 71 times
rgb_bitdist| 11| 100000| 200|0.67837353| PASSED
# The file file_input_raw was rewound 73 times
rgb_bitdist| 12| 100000| 200|0.77285406| PASSED
# The file file_input_raw was rewound 73 times
rgb_minimum_distance| 2| 10000| 2000|0.99326519| PASSED
# The file file_input_raw was rewound 73 times
rgb_minimum_distance| 3| 10000| 2000|0.89490386| PASSED
# The file file_input_raw was rewound 74 times
rgb_minimum_distance| 4| 10000| 2000|0.63482997| PASSED
# The file file_input_raw was rewound 74 times
rgb_minimum_distance| 5| 10000| 2000|0.04956198| PASSED
# The file file_input_raw was rewound 74 times
rgb_permutations| 2| 100000| 200|0.59389551| PASSED
# The file file_input_raw was rewound 74 times
rgb_permutations| 3| 100000| 200|0.84473217| PASSED
# The file file_input_raw was rewound 75 times
rgb_permutations| 4| 100000| 200|0.67098621| PASSED
# The file file_input_raw was rewound 75 times
rgb_permutations| 5| 100000| 200|0.71477222| PASSED
# The file file_input_raw was rewound 76 times
rgb_lagged_sum| 0| 1000000| 200|0.20844392| PASSED
# The file file_input_raw was rewound 77 times
rgb_lagged_sum| 1| 1000000| 200|0.52704060| PASSED
# The file file_input_raw was rewound 79 times
rgb_lagged_sum| 2| 1000000| 200|0.68631913| PASSED
# The file file_input_raw was rewound 82 times
rgb_lagged_sum| 3| 1000000| 200|0.04971017| PASSED
# The file file_input_raw was rewound 86 times
rgb_lagged_sum| 4| 1000000| 200|0.11342937| PASSED
# The file file_input_raw was rewound 91 times
rgb_lagged_sum| 5| 1000000| 200|0.08126696| PASSED
# The file file_input_raw was rewound 96 times
rgb_lagged_sum| 6| 1000000| 200|0.20866831| PASSED
# The file file_input_raw was rewound 102 times
rgb_lagged_sum| 7| 1000000| 200|0.52239049| PASSED
# The file file_input_raw was rewound 109 times
rgb_lagged_sum| 8| 1000000| 200|0.68232225| PASSED
# The file file_input_raw was rewound 116 times
rgb_lagged_sum| 9| 1000000| 200|0.13755031| PASSED
# The file file_input_raw was rewound 124 times
rgb_lagged_sum| 10| 1000000| 200|0.82473876| PASSED
# The file file_input_raw was rewound 133 times
rgb_lagged_sum| 11| 1000000| 200|0.10861154| PASSED
# The file file_input_raw was rewound 143 times
rgb_lagged_sum| 12| 1000000| 200|0.10432254| PASSED
# The file file_input_raw was rewound 153 times
rgb_lagged_sum| 13| 1000000| 200|0.18082599| PASSED
# The file file_input_raw was rewound 164 times
rgb_lagged_sum| 14| 1000000| 200|0.13220862| PASSED
# The file file_input_raw was rewound 176 times
rgb_lagged_sum| 15| 1000000| 200|0.08158678| PASSED
# The file file_input_raw was rewound 189 times
rgb_lagged_sum| 16| 1000000| 200|0.02760994| PASSED
# The file file_input_raw was rewound 202 times
rgb_lagged_sum| 17| 1000000| 200|0.14079614| PASSED
# The file file_input_raw was rewound 217 times
rgb_lagged_sum| 18| 1000000| 200|0.23268911| PASSED
# The file file_input_raw was rewound 231 times
rgb_lagged_sum| 19| 1000000| 200|0.50758360| PASSED
# The file file_input_raw was rewound 247 times
rgb_lagged_sum| 20| 1000000| 200|0.66798605| PASSED
# The file file_input_raw was rewound 263 times
rgb_lagged_sum| 21| 1000000| 200|0.13844382| PASSED
# The file file_input_raw was rewound 281 times
rgb_lagged_sum| 22| 1000000| 200|0.44084188| PASSED
# The file file_input_raw was rewound 299 times
rgb_lagged_sum| 23| 1000000| 200|0.90104158| PASSED
# The file file_input_raw was rewound 317 times
rgb_lagged_sum| 24| 1000000| 200|0.80347842| PASSED
# The file file_input_raw was rewound 337 times
rgb_lagged_sum| 25| 1000000| 200|0.07703809| PASSED
# The file file_input_raw was rewound 357 times
rgb_lagged_sum| 26| 1000000| 200|0.69854447| PASSED
# The file file_input_raw was rewound 377 times
rgb_lagged_sum| 27| 1000000| 200|0.26315861| PASSED
# The file file_input_raw was rewound 399 times
rgb_lagged_sum| 28| 1000000| 200|0.58852190| PASSED
# The file file_input_raw was rewound 421 times
rgb_lagged_sum| 29| 1000000| 200|0.42224280| PASSED
# The file file_input_raw was rewound 445 times
rgb_lagged_sum| 30| 1000000| 200|0.18274721| PASSED
# The file file_input_raw was rewound 468 times
rgb_lagged_sum| 31| 1000000| 200|0.18647377| PASSED
# The file file_input_raw was rewound 493 times
rgb_lagged_sum| 32| 1000000| 200|0.83130153| PASSED
# The file file_input_raw was rewound 493 times
rgb_kstest_test| 0| 10000| 2000|0.05507241| PASSED
# The file file_input_raw was rewound 494 times
dab_bytedistrib| 0| 51200000| 2|0.22222222| PASSED
# The file file_input_raw was rewound 494 times
dab_dct| 256| 50000| 2|0.98359769| PASSED
Preparing to run test 207. ntuple = 0
# The file file_input_raw was rewound 495 times
dab_filltree| 32| 15000000| 2|0.75609132| PASSED
dab_filltree| 32| 15000000| 2|1.00000000| FAILED
Preparing to run test 208. ntuple = 0
# The file file_input_raw was rewound 495 times
dab_filltree2| 0| 5000000| 2|1.00000000| FAILED
dab_filltree2| 1| 5000000| 2|1.00000000| FAILED
Preparing to run test 209. ntuple = 0
# The file file_input_raw was rewound 496 times
dab_monobit2| 12| 65000000| 2|1.00000000| FAILED
```
## Remove
```bash
sudo rmmod pico_rng
```
# About the random number generator
Raspberry Pi Pico has a Ring Oscillator (ROSC) that produces a random bit, despite that it is not intended for secure applications. In general, ROSC produce weak/correlated random bits. Thus, we increase the randomness by adding more entropy sources:
- A random word produced by ROSC.
- A current timestamp.
- A read from an open GPIO pin.
The produced random word is then passed through a whitener. In particular, the Fowler–Noll–Vo hash function is used as a whitener.
Finally, the word is packed into a byte array and returned to the host.
The performance of this RNG can be analyzed with [pico_rng_analyze.py](firmware/pico_rng_analyze.py) script and typical tools, such as `ent`, `rngtest` or `dierharder`. See results above.
### License
This project is licensed under the BSD 3-Clause "New" or "Revised" License - see the [LICENSE.md](LICENSE.md) file for details