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# rorand
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# rorand
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Ring oscillator-based TRNG for the RP2040
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## What is it
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`rorand` provides a true random number generator (TRNG) using only hardware
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that's available inside the
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[RP2040](https://www.raspberrypi.com/documentation/microcontrollers/rp2040.html)
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chip. It can be used either in its 'raw' form, or with an extra
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whitening/compression step based on [Ascon](https://ascon.iaik.tugraz.at/)-Xofa.
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## Comparison
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| Name | Throughput | Entropy assurance | Extra components | Whitening | URL |
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|:--------------------- |:------------------------ |:------------------------------ |:---------------- |:---------- |:------------- |
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| rorand (this work) | 40 kbit/s | passes Dieharder (see below) | none | Ascon-Xofa | you are here! |
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| Adafruit Trinkey TRNG | (40 kbit/s comms. limit) | Common Criteria EAL6+ | Infineon Trust M | ? | https://learn.adafruit.com/trinkey-qt2040-true-random-number-generator/overview |
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| caprand | ? | ? | one 10nF capacitor | ChaCha20 | https://github.com/mkj/caprand |
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| rp2040-entropy | 300 kbit/s? | fails a few dieharder tests | none (ADC noise) | none | https://github.com/hashky/rp2040-entropy |
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| rprand | ~10 kbit/s | ? | none (ROSC+DMA) | CRC32 | https://github.com/alastairpatrick/rprand |
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| pico-sdk | ? (probably >1Mbit/s) | ? (seed only, RNG is Xorshiro) | none (ROSC seed) | Xorshiro128 | https://github.com/raspberrypi/pico-sdk/blob/master/src/rp2_common/pico_rand/rand.c |
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| Cornell ECE4760 | ? | convergence to normal distribution | none (ROSC seed) | newlib/RAND48 | https://people.ece.cornell.edu/land/courses/ece4760/RP2040/C_SDK_random/index_random.html |
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## Requirements
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* Pico C SDK
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* System must not run from ROSC, and the system clock must be at least 48 MHz
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(80 MHz or higher preferred, 125 MHz or higher ideal).
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* SysTick not used by something else
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## How it works
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The RP2040 includes a [ring
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oscillator](https://en.wikipedia.org/wiki/Ring_oscillator) (unimaginatively
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called ROSC). Such an oscillator is nothing more than a chain of inverters
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wired up in a loop. If the number of inverters is odd, the circuit will
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oscillate.
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Ring oscillators (just like many other oscillators) exhibit a phenomenon called
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*jitter*: the length of the clock period varies ever so slightly from one
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period to the next. This stems from various forms of noise (thermal noise, shot
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noise, etc.) in the semiconductor, which are ultimately caused by the inherent
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randomness of quantum physics.
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The RP2040 ROSC has a register called
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"[RANDOMBIT](https://datasheets.raspberrypi.com/rp2040/rp2040-datasheet.pdf#reg-rosc-RANDOMBIT)",
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which is basically a way of sampling the current state of the oscillator. On
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first sight, this *sounds* like it would be random. However, much of the
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perceived 'randomness' would actually stem from
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[aliasing](https://en.wikipedia.org/wiki/Aliasing), because the code reading
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this register would be undersampling.
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Instead, let's use the jitter phenomenon slightly differently: the phase
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(jitter) noise from multiple oscillator cycles accumulates. Thus, the actual
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real-world time it takes to complete `N` clock cycles has a larger variance
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than the jitter of just one clock cycle. This is visualized in the image below:
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By using the [COUNT](https://datasheets.raspberrypi.com/rp2040/rp2040-datasheet.pdf#reg-rosc-COUNT)
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register of the RP2040 ROSC, we can time how long it takes for it to reach zero
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(compared to eg. the ARM SysTick timer running from the CPU clock). We can use
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the least-significant bit of this timing difference (counted in CPU cycles) as
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the randomness output!
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(As a sidenote: 'real professional' ring oscillator-based TRNGs typically use a
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"transient effect ring oscillator" (TERO) design, which is a bit more robust.
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Though, it also needs multiple oscillators and counters, and we don't have that
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available here. So, the basic RO TRNG it is.)
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Well, almost. We still need to do a crucial final step: [entropy
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extraction](https://en.wikipedia.org/wiki/Randomness_extractor). There are two
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types of entropy extractors used most often: the parity filter (which XORs the
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last N output bits together), and the Von Neumann filter (described in the link).
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The Von Neumann filter is able to remove all [statistical
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bias](https://en.wikipedia.org/wiki/Bias_(statistics)), but has more
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requirements on the probability distribution of the inputs (they must be
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"Independent and identically distributed", or IID for short). Meanwhile, the
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parity filter has fewer requirements (only independence of inputs), but it
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cannot remove all bias in practice (though it converges to this for larger and
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larger N).
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For a ring oscillator, one would expect the random bits (generated as described
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above) to be IID, so we can use the Von Neumann extractor. (This assumption
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seems to hold in practice.) Oh, and we can still XOR this bit with the
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RANDOMBIT register, because it's there.
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This is essentially how the "raw" output is generated. `rorand` also provides a
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"cooked" output, which feeds the output of the "raw" TRNG into Ascon-Xofa. This
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creature is a cryptographic PRNG based on what cryptographers call a "[sponge
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construction](https://en.wikipedia.org/wiki/Sponge_function)". Sponge
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constructions have all sorts of cool properties (which I won't talk about here
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because it'd detract from the article, sadly), but one of them is that you can
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build an *extensible-output function* (XOF) from them. XOFs are like hash
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functions, but the output length can be made arbitrarily long. This makes it
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rather easy to make a cryptographically-secure *reseedable* PRNG.
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Ascon is the finalist for the "lightweight portfolio" of the [CAESAR
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competition](https://competitions.cr.yp.to/caesar-submissions.html). It's a
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rather new (but promising, and built from solid foundations) cryptographic
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cipher, specifically designed for slow embedded devices, such as the RP2040. It
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should thus be faster than other options like ChaCha20/BLAKE2 or ARC4Random
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(which is now considered insecure). AEGIS and Deoxys-II, the other two CAESAR
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finalists for other purposes, are based on the AES round transformation, and
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would thus be quite a bit slower.
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## How good is it
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### Entropy
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The randomness obtained from this TRNG seems to pass the
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[Dieharder](https://webhome.phy.duke.edu/~rgb/General/dieharder.php) test
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suite. The output is given below.
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Note that a few entries are marked as `WEAK`, but those seem to appear and
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disappear when I try and retry different runs. This seems to happen due to the
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used sample size: one megabyte of random data takes a few minutes to generate,
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so much larger samples are quite a bit of a hassle to obtain. Running output
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from `/dev/random` with the same sizes also has the `WEAK` warnings pop up and
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disappear at random, so it should be fine.
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**WARNING**: However, these `WEAK` warnings seem to pop up more often with
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decreasing RP2040 system clock speed (and, slightly, voltage as well). While no
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`FAILED` errors have popped up, depending on your needs, only use `rorand` with
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a high enough system clock frequency (≥80 MHz preferred, ≥125 MHz ideal).
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Dieharder isn't the most stringent test suite, though.
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[TestU01](http://simul.iro.umontreal.ca/testu01/tu01.html)'s BigCrush suite is
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much more comprehensive, but requires ***much*** more data (many gigabytes).
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Thanks to the limited throughput of a hardware TRNG, using this test isn't very
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feasible. Real evaluations such as FIPS 140-2, or Common Criteria EAL4 or
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higher, is completely out of my means.
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In conclusion, don't trust someone's life --- neither your own nor someone
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else's --- with this. But otherwise, you should be fine. If you need the
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assurance (or if you're paranoid), please use a FIPS- or Common
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Criteria-certified hardware module, though.
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Dieharder output (raw output, RP2040 running at 250 MHz, core voltage 1.15 V):
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```
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#=============================================================================#
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test_name |ntup| tsamples |psamples| p-value |Assessment
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#=============================================================================#
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diehard_birthdays| 0| 100| 100|0.22538373| PASSED
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diehard_operm5| 0| 1000000| 100|0.63794545| PASSED
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diehard_rank_32x32| 0| 40000| 100|0.73090642| PASSED
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diehard_rank_6x8| 0| 100000| 100|0.99254745| PASSED
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diehard_bitstream| 0| 2097152| 100|0.58114397| PASSED
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diehard_opso| 0| 2097152| 100|0.18319256| PASSED
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diehard_oqso| 0| 2097152| 100|0.93914840| PASSED
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diehard_dna| 0| 2097152| 100|0.74871515| PASSED
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diehard_count_1s_str| 0| 256000| 100|0.20413208| PASSED
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diehard_count_1s_byt| 0| 256000| 100|0.56507750| PASSED
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diehard_parking_lot| 0| 12000| 100|0.43004782| PASSED
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diehard_2dsphere| 2| 8000| 100|0.68150341| PASSED
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diehard_3dsphere| 3| 4000| 100|0.50961304| PASSED
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diehard_squeeze| 0| 100000| 100|0.73895828| PASSED
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diehard_sums| 0| 100| 100|0.89067279| PASSED
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diehard_runs| 0| 100000| 100|0.88549264| PASSED
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diehard_runs| 0| 100000| 100|0.17826705| PASSED
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diehard_craps| 0| 200000| 100|0.74363795| PASSED
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diehard_craps| 0| 200000| 100|0.92809716| PASSED
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marsaglia_tsang_gcd| 0| 10000000| 100|0.21033260| PASSED
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marsaglia_tsang_gcd| 0| 10000000| 100|0.90826850| PASSED
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sts_monobit| 1| 100000| 100|0.66704052| PASSED
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sts_runs| 2| 100000| 100|0.82376608| PASSED
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sts_serial| 1| 100000| 100|0.40789077| PASSED
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sts_serial| 2| 100000| 100|0.11533197| PASSED
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sts_serial| 3| 100000| 100|0.57906405| PASSED
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sts_serial| 3| 100000| 100|0.88247272| PASSED
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sts_serial| 4| 100000| 100|0.35109410| PASSED
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sts_serial| 4| 100000| 100|0.06001064| PASSED
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sts_serial| 5| 100000| 100|0.24597035| PASSED
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sts_serial| 5| 100000| 100|0.42776664| PASSED
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sts_serial| 6| 100000| 100|0.34671248| PASSED
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sts_serial| 6| 100000| 100|0.63443378| PASSED
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sts_serial| 7| 100000| 100|0.34901523| PASSED
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sts_serial| 7| 100000| 100|0.87482945| PASSED
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sts_serial| 8| 100000| 100|0.83333396| PASSED
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sts_serial| 8| 100000| 100|0.98096154| PASSED
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sts_serial| 9| 100000| 100|0.18613150| PASSED
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sts_serial| 9| 100000| 100|0.98222632| PASSED
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sts_serial| 10| 100000| 100|0.06064720| PASSED
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sts_serial| 10| 100000| 100|0.53659409| PASSED
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sts_serial| 11| 100000| 100|0.48783888| PASSED
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sts_serial| 11| 100000| 100|0.44013196| PASSED
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sts_serial| 12| 100000| 100|0.89056741| PASSED
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sts_serial| 12| 100000| 100|0.55084354| PASSED
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sts_serial| 13| 100000| 100|0.55991536| PASSED
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sts_serial| 13| 100000| 100|0.79919790| PASSED
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sts_serial| 14| 100000| 100|0.99559967| WEAK
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sts_serial| 14| 100000| 100|0.60230091| PASSED
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sts_serial| 15| 100000| 100|0.91600221| PASSED
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sts_serial| 15| 100000| 100|0.29385991| PASSED
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sts_serial| 16| 100000| 100|0.80170010| PASSED
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sts_serial| 16| 100000| 100|0.89169608| PASSED
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rgb_bitdist| 1| 100000| 100|0.25864662| PASSED
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rgb_bitdist| 2| 100000| 100|0.41244241| PASSED
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rgb_bitdist| 3| 100000| 100|0.80837541| PASSED
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rgb_bitdist| 4| 100000| 100|0.93133416| PASSED
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rgb_bitdist| 5| 100000| 100|0.70903269| PASSED
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rgb_bitdist| 6| 100000| 100|0.29717638| PASSED
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rgb_bitdist| 7| 100000| 100|0.71361547| PASSED
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rgb_bitdist| 8| 100000| 100|0.03450956| PASSED
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rgb_bitdist| 9| 100000| 100|0.14545557| PASSED
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rgb_bitdist| 10| 100000| 100|0.90299368| PASSED
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rgb_bitdist| 11| 100000| 100|0.53321027| PASSED
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rgb_bitdist| 12| 100000| 100|0.65243210| PASSED
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rgb_minimum_distance| 2| 10000| 1000|0.29295560| PASSED
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rgb_minimum_distance| 3| 10000| 1000|0.28825100| PASSED
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rgb_minimum_distance| 4| 10000| 1000|0.84249889| PASSED
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rgb_minimum_distance| 5| 10000| 1000|0.53807064| PASSED
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rgb_permutations| 2| 100000| 100|0.72182964| PASSED
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rgb_permutations| 3| 100000| 100|0.98132372| PASSED
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rgb_permutations| 4| 100000| 100|0.32426721| PASSED
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rgb_permutations| 5| 100000| 100|0.94033412| PASSED
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rgb_lagged_sum| 0| 1000000| 100|0.78964883| PASSED
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rgb_lagged_sum| 1| 1000000| 100|0.82881744| PASSED
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rgb_lagged_sum| 2| 1000000| 100|0.90805811| PASSED
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rgb_lagged_sum| 3| 1000000| 100|0.21428921| PASSED
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rgb_lagged_sum| 4| 1000000| 100|0.67964064| PASSED
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rgb_lagged_sum| 5| 1000000| 100|0.64463634| PASSED
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rgb_lagged_sum| 6| 1000000| 100|0.94268050| PASSED
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rgb_lagged_sum| 7| 1000000| 100|0.33288741| PASSED
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rgb_lagged_sum| 8| 1000000| 100|0.79565468| PASSED
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rgb_lagged_sum| 9| 1000000| 100|0.26291492| PASSED
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rgb_lagged_sum| 10| 1000000| 100|0.23887951| PASSED
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rgb_lagged_sum| 11| 1000000| 100|0.75511918| PASSED
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rgb_lagged_sum| 12| 1000000| 100|0.44806331| PASSED
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rgb_lagged_sum| 13| 1000000| 100|0.57950849| PASSED
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rgb_lagged_sum| 14| 1000000| 100|0.37109436| PASSED
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rgb_lagged_sum| 15| 1000000| 100|0.89758378| PASSED
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rgb_lagged_sum| 16| 1000000| 100|0.06000037| PASSED
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rgb_lagged_sum| 17| 1000000| 100|0.87051454| PASSED
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rgb_lagged_sum| 18| 1000000| 100|0.47509380| PASSED
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rgb_lagged_sum| 19| 1000000| 100|0.34523765| PASSED
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rgb_lagged_sum| 20| 1000000| 100|0.98418490| PASSED
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rgb_lagged_sum| 21| 1000000| 100|0.17652983| PASSED
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rgb_lagged_sum| 22| 1000000| 100|0.17374595| PASSED
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rgb_lagged_sum| 23| 1000000| 100|0.63170066| PASSED
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rgb_lagged_sum| 24| 1000000| 100|0.28953394| PASSED
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rgb_lagged_sum| 25| 1000000| 100|0.64849257| PASSED
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rgb_lagged_sum| 26| 1000000| 100|0.78468683| PASSED
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rgb_lagged_sum| 27| 1000000| 100|0.36484261| PASSED
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rgb_lagged_sum| 28| 1000000| 100|0.66712700| PASSED
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rgb_lagged_sum| 29| 1000000| 100|0.48604229| PASSED
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rgb_lagged_sum| 30| 1000000| 100|0.17591412| PASSED
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rgb_lagged_sum| 31| 1000000| 100|0.32433586| PASSED
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rgb_lagged_sum| 32| 1000000| 100|0.12971163| PASSED
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rgb_kstest_test| 0| 10000| 1000|0.47803450| PASSED
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dab_bytedistrib| 0| 51200000| 1|0.29203091| PASSED
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dab_dct| 256| 50000| 1|0.06993184| PASSED
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Preparing to run test 207. ntuple = 0
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dab_filltree| 32| 15000000| 1|0.38387488| PASSED
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dab_filltree| 32| 15000000| 1|0.55295440| PASSED
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Preparing to run test 208. ntuple = 0
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dab_filltree2| 0| 5000000| 1|0.24922510| PASSED
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dab_filltree2| 1| 5000000| 1|0.98227801| PASSED
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Preparing to run test 209. ntuple = 0
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dab_monobit2| 12| 65000000| 1|0.71153312| PASSED
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```
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At 48 MHz and a core voltage of 0.95 V, there would be three or four `WARN`ings.
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### Throughput
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The TRNG is rather CPU-intensive (due to its IRQ-blocking busyloop) and not
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very fast. The "cooked" (whitened) throughput is about 10 times higher than the
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"raw" throughput.
|
||||||
|
|
||||||
|
| System clock | Raw TRNG throughput |
|
||||||
|
|:------------ |:------------------- |
|
||||||
|
| 48 MHz | 10 kbit/s |
|
||||||
|
| 125 MHz | 40 kbit/s |
|
||||||
|
| 250 MHz | 50 kbit/s |
|
||||||
|
|
||||||
|
## What is missing?
|
||||||
|
|
||||||
|
* **Online health tests**: I don't know how to do this. I don't know what a
|
||||||
|
"chi-squared" is. Health tests are rather important for TRNGs (to make sure
|
||||||
|
nothing weird is happening), so this is not a small downside.
|
||||||
|
* **DMA+PIO-based implementation**: to relieve the CPU from some of its load.
|
||||||
|
Currently, it's 100% a spinloop on the CPU, with interrupts disabled.
|
||||||
|
* **Multicore mutex**: currently, both CPU cores could run this code, which
|
||||||
|
would then modify the ROSC `COUNT` register in parallell. This is bad and
|
||||||
|
will lead to bad results. Don't do this. (Or alternatively, add mutex guards,
|
||||||
|
or bug me to do so.)
|
||||||
|
* **More useful `rand()` functions**: currently, the code just gives you bits,
|
||||||
|
and turning these bits into a random integer in a range, or a random float,
|
||||||
|
..., is left as an exercise for the reader.
|
||||||
|
* **Protections against physical attacks**: if an adversary is in the physical
|
||||||
|
proximity of the device, it's game over. They could attach an SWD debugger to
|
||||||
|
the RP2040 (it has no protection against this), use a power side channel or
|
||||||
|
EM emanations to look at the ROSC doing its oscillate-y thing, or tamper with
|
||||||
|
the environment (e.g. freeze spray or harmonic EM emissions) to slow down the
|
||||||
|
ROSC or make it lock onto a different frequency. I don't plan to add any
|
||||||
|
defenses against such attacks. (Please get a properly certified hardware
|
||||||
|
module if such attacks are part of your threat model, I'm begging you, don't
|
||||||
|
use this.)
|
||||||
|
|
||||||
|
## Usage
|
||||||
|
|
||||||
|
Here's a quick example:
|
||||||
|
|
||||||
|
```c
|
||||||
|
#include <stdint.h>
|
||||||
|
#include <limits.h>
|
||||||
|
|
||||||
|
#include "rorand.h" /* raw rng */
|
||||||
|
#include "rourand.h" /* 'cooked'/whitened rng */
|
||||||
|
|
||||||
|
|
||||||
|
static void health_alarm(const char* msg) {
|
||||||
|
// TRNG health alarm raised!
|
||||||
|
iprintf("TRNG health alarm! %s\n", msg);
|
||||||
|
}
|
||||||
|
|
||||||
|
int main() {
|
||||||
|
/** raw randomness **/
|
||||||
|
enum rourand_error r = rorand_init(health_alarm);
|
||||||
|
if (r != rr_ok) {
|
||||||
|
panic("rorand failed to initialize!");
|
||||||
|
}
|
||||||
|
|
||||||
|
// get 128 bits of raw randomness
|
||||||
|
uint8_t data[16];
|
||||||
|
rorand_get(data, sizeof(data)*CHAR_BIT); // specified in bits
|
||||||
|
|
||||||
|
/** 'cooked'/whitened randomness **/
|
||||||
|
int rate = 0; // rate at which the CSPRNG will reseed with true random data. 0 is default.
|
||||||
|
// you (the user) must call rorand_init first before calling rourand_init!
|
||||||
|
struct rourand_state* ur = rourand_init(rorand_get, rate);
|
||||||
|
if (!ur) {
|
||||||
|
panic("rourand failed to initialize!");
|
||||||
|
}
|
||||||
|
|
||||||
|
rourand_get(ur, data, sizeof(data)); // specified in bytes
|
||||||
|
rourand_free(ur);
|
||||||
|
}
|
||||||
|
```
|
||||||
|
|
||||||
|
## License
|
||||||
|
|
||||||
|
License is TBD.
|
||||||
|
|
||||||
|
The [Ascon reference implementation](https://github.com/ascon/ascon-c) is
|
||||||
|
licensed under CC0 1.0.
|
||||||
|
|
||||||
|
The [Raspberry Pico C SDK](https://github.com/raspberrypi/pico-sdk) is licensed
|
||||||
|
under the BSD-3-Clause license.
|
||||||
|
|
||||||
|
|
|
||||||
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|
After Width: | Height: | Size: 9.7 KiB |
|
|
@ -27,6 +27,8 @@ static uint8_t data[32];
|
||||||
|
|
||||||
|
|
||||||
int main() {
|
int main() {
|
||||||
|
vreg_set_voltage(VREG_VOLTAGE_1_15);
|
||||||
|
set_sys_clock_khz(250*1000, true);
|
||||||
// high freq, high voltage
|
// high freq, high voltage
|
||||||
//vreg_set_voltage(VREG_VOLTAGE_1_25);
|
//vreg_set_voltage(VREG_VOLTAGE_1_25);
|
||||||
//set_sys_clock_khz(250*1000, true);
|
//set_sys_clock_khz(250*1000, true);
|
||||||
|
|
|
||||||
Loading…
Reference in New Issue