blog/content/2022/02/nearly-complete-rng-guide.html

---
title: Nearly Complete Guide to RNG on a microcontroller
description: >
  How to initialize and run an RNG on an STM32L151CC microcontroller.
created: !!timestamp '2022-02-12'
time: 11:50 AM
tags:
  - security
  - rng
  - microcontroller
---

Security depends upon cryptography and which in turn depends upon a
Random Number Generator (RNG).  An RNG is used for key generation (both
symmetric and asymmetric) and key negotiation (session establishment).
The later is an absolute requirement to ensure that communications can
be secured.  The former (key generation) can be used at first boot for
personalization, but isn't necessary as it could be done when personalizing
the device at programming or first deployment.

There are two types of RNGs, the first is a True Random Number Generator
(TRNG).  This is one that takes some non-deterministic process, often
physical, and measures it.  Often, these are slow and are not uniform,
requiring a post processing step before the are useful.

The second type is a Pseudo Random Number Generator (PRNG)<label
for="sn-drbg" class="margin-toggle sidenote-number"></label><input
type="checkbox" id="sn-drbg" class="margin-toggle"/><span
class="sidenote">[NIST](https://www.nist.gov/) also refers to a
PRNG as a Deterministic Random Bit Generator (DRBG).</span>.  PRNGs
take a seed, and can generate large, effectively unlimited amounts of
random data, when seeded properly.  The issue is than if someone is able
to obtain the seed, they will be able to predict the subsequent values,
allowing breaking security.

The standard practice is to gather data from a TRNG, and use it to seed
a PRNG.  It used to be common that the PRNG should more additional random
data mixed in, but I agree w/ djb (D. J. Bernstein) that once seeded, no
additional seeding is needed<label for="sn-entropy" class="margin-toggle
sidenote-number"></label><input type="checkbox" id="sn-entropy"
class="margin-toggle"/><span class="sidenote">See his blog post
[Entropy Attacks!](https://blog.cr.yp.to/20140205-entropy.html)</span>
as modern PRNGs are secure and can generate random data such that their
state will not leak.<label for="sn-prng-secure" class="margin-toggle
sidenote-number"></label><input type="checkbox" id="sn-prng-secure"
class="margin-toggle"/><span class="sidenote">That is, taking it's output,
that neither past nor future output can be predicted.</span>

There are lots of libraries and papers that talk about how to solve the
problem for RNGs on a microcontroller that may not have an integrated
[T]RNG block, but I have not been able to find a complete guide for
integrating their work into a project where even a relative beginner
could get it functional.

This article was written as I developed the
[lora-irrigation](https://www.funkthat.com/gitea/jmg/lora-irrigation)
project.  This project will be used as an example, and the code reference
is mostly licensed under the 2-clause BSD license, and so is freely
usable for your own projects.


Sources of Randomness
---------------------

As mentioned, most microcontrollers do not have a dedicated hardware
block like modern AMD64 (aka x86-64) processors do w/ the RDRAND
instruction.  Though they do not, there are other sources that are
available.

The first, and easiest one is the Analog Digital Converter (ADC).  Even
if the ADC pin is tied to ground, the process of digital conversion is
not 100% deterministic as there are errors in the converter or noise
introduced on the pin.<label for="sn-adcnoise"
class="margin-toggle sidenote-number"></label><input type="checkbox"
id="sn-adcnoise" class="margin-toggle"/><span class="sidenote">The article
[ADC Input Noise: The Good, The Bad, and The Ugly. Is No Noise Good
Noise?](https://www.analog.com/en/analog-dialogue/articles/adc-input-noise.html)
talks about this.</span>

The data sheet for the microcontroller will help determine the expected
randomness from the part.  In the case of the
[STM32L151CC](https://www.st.com/content/st_com/en/products/microcontrollers-microprocessors/stm32-32-bit-arm-cortex-mcus/stm32-ultra-low-power-mcus/stm32l1-series/stm32l151-152/stm32l151cc.html)
that I'm using, Table 57 of the data sheet lists the Effective number
of bits (ENOB) as typically 10 bits, which is a couple bits short of
the 12 bit resolution of the ADC.  This means that the 2 least
significant bits are likely to have some noise in them.  I did a run,
and collected 114200 samples from the ADC.  The [Shannon
entropy](https://en.wikipedia.org/wiki/R%C3%A9nyi_entropy#Shannon_entropy)
calculated using the empirical probabilities was 2.48.<label
for="sn-shannonenropy" class="margin-toggle sidenote-number"></label>
<input type="checkbox" id="sn-shannonenropy" class="margin-toggle"/>
<span class="sidenote">Now this is not strictly Shannon entropy, as the
values were calculated from the experiment, and Shannon entropy should
be calculated from the a priori probabilities.</span>  Discarding the
0's (which makes up over half the results) improves the entropy
calculation to 3.29.  The
[min-entropy](https://en.wikipedia.org/wiki/R%C3%A9nyi_entropy#Min-entropy)<label for="sn-min-entropy-fwdref" class="margin-toggle sidenote-number"></label>,
<input type="checkbox" id="sn-min-entropy-fwdref" class="margin-toggle"/>
<span class="sidenote">Forward reference:
<a href="#min-entropy-awk">min-entropy awk script</a></span>
a better indicator of entropy, calculation is 1.2 bits, and if all the
0's are dropped, it improves to 2.943.  This does help, but in the end,
subtracting the data sheet's ENOB from the ADC resolution does result
in an approximate estimate of entropy.

It is possibly that a correlation analysis between samples could
further reduce the entropy gathers via the ADC, but with sufficient
collection, this should be able to be avoided.

The second is using uninitialized SRAM.  It turns out that this has
been studied in [Software Only, Extremely Compact, Keccak-based Secure
PRNG on ARM Cortex-M](https://dl.acm.org/doi/10.1145/2593069.2593218)
and [Secure PRNG Seeding on Commercial Off-the-Shelf
Microcontrollers](https://www.intrinsic-id.com/wp-content/uploads/2017/05/prng_seeding.pdf).
Depending upon how the SRAM is designed in the chip, it can create a
situation where each bit of SRAM will be indeterminate at boot up.
Both of these papers studied a similar microcontroller, an
STM32F100R8 to the one I am using, a STM32L151CC.

I ran my own experiments where I powered on an STM3L151CC and dumped
the SRAM 8 times and analyzed the results.  I limited my analysis to
26863 bytes the 32 KiBytes of ram (remaining was data/bss or stack, so
would not change, or was zeros). I then calculated the min-entropy for
each bit across power cycles and the resulting sum was 11188, or
approximately .416 bits per byte.  This is 5.2% and in line with what
the later paper observed for a similar device.

Part of using a source of randomness is making sure that it is usable.
In the case of the ADC, each reading can be evaluated against previous
reads to ensure that the data being obtained is possibly random.  In
the case of SRAM, this is more tricky, as the state of SRAM is static,
and short of a reset, will not change.  This means that to use SRAM,
proper analysis of the device, or family of devices, need to be evaluated
for suitability.  There are cases where a device's SRAM does not provide
adequate entropy, as discussed in the papers, and so this method should
not be used in those cases, or not solely relied upon.

The following is an `awk` script for calculating the min-entropy of the
provided data.  Each sample must be the first item on a line, and each
sample must be a hexadecimal value w/o any leading `0x` or other leading
identifier:
<pre id="min-entropy-awk" class="language-awk fullwidth"><code># Copyright 2021 John-Mark Gurney
# This script is licensed under the 2-clause BSD license

function max(a, b)
{
        if (a > b)
                return a;
        else
                return b;
}

{
        v = ("0x" $1) + 0; a[NR] = v;
        maxv = max(maxv, v);
}

END {
        tcnt = length(a);
        me = 0;
        for (bit = 0; 2^bit <= maxv; bit += 1) {
                cnt0 = 0;
                cnt1 = 0;
                for (i in a) {
                        tbit = int((a[i] / 2 ^ bit) % 2);
                        if (tbit)
                                cnt1 += 1;
                        else
                                cnt0 += 1;
                }
                v = -log(max(cnt0, cnt1) / tcnt) / log(2);
                print "bit " bit ":\t" v;
                me += v;
        }
        printf "total:\t%0.3f\n", me;
}
</code></pre>

It is also possible that there are other parts of the board/design
that could be a source of randomness.  The project that started this
journey is using [LoRa](https://en.wikipedia.org/wiki/LoRa) for
communication.  It turns out that the sample code for the radio chip
([LoRaMac&#x2011;node](https://github.com/Lora-net/LoRaMac-node)) implements
a [random interface](https://github.com/Lora-net/LoRaMac-node/blob/7f12997754ad8e38a84daa85f62e7e6c0e5dbe59/src/radio/radio.h#L154-L163).
The function just waits one milisecond, reads the RSSI value, takes
the low bit and repeats this 32 times to return a 32-bit word.  There
are issues with this as I cannot find any description of the expected
randomness in the data sheet, nor in the code.  It also does not do
any conditioning, so just because it returns 32-bits, does not guarantee
32-bits of usable entropy.  I have briefly looked at the output, and
there does appear to be higher lengths of runs than expected.  Another
issue is that it's collection takes a while, as the fastest is 1 bit
per ms.  So, assuming the need to collect 8 bits for 1 bit of entropy
(pure speculation), that means at minimum 2 seconds to collect the
2048 bits necessary for 256 bits of entropy.


Uniquifying
-----------

One of the other ways to help ensure that a microcontroller is to
integrate per device values into the PRNG.  This does not guarantee
uniqueness between boots, but it does make it harder to attack if an
attacker is able to control the other sources of randomness.

In the case of the STM32L151 chip I am using, there is a unique
device id register.  The device register is programmed at the
factory.  Because it is unknown if this unique id is recorded by the
manufacturer, and possibly traced through the supply chain, and no
guarantees are made to both the uniqueness or privacy, it has limited
use to provide any serious additional randomization.

Another method, is to write entropy at provisioning time.  This can be
done in either flash memory or EEPROM, which may have a more granular
write access.


Using SRAM
----------

The tricky part of using SRAM is figuring out how to access the
uninitialized memory.  Despite having full access to the environment,
modifying the startup code, which is often written in assembly, to do
the harvesting makes an implementation less portable.  Using standard
C, or another high level language, makes this easier, *but* we need to
know where the end of the data and bss segments are.  This is where
looking at the linker script will come in.

A linker script is used to allocate and map the program's data to the
correct locations.  This includes allocating memory so that all the
code and data fits in flash, but also allocating ram for variables, and
stack.  Often there will be a symbol provided that marks where the data
and bss sections in ram end, and the heap should begin.  For example,
in [`STM32L151CCUX_FLASH.ld` at lines 185 &
186](https://www.funkthat.com/gitea/jmg/lora-irrigation/src/commit/91a6fb590b68af1bcd34f776d4a58c89ac581c7d/stm32/l151ccux/STM32L151CCUX_FLASH.ld#L185-L186)
it defines the symbols `end` and `_end`, the later of which is often
used by `sbrk` (or `_sbrk` in my project's case in
libnosys<label for="sn-sbrk-sample" class="margin-toggle sidenote-number"></label><input type="checkbox" id="sn-sbrk-sample" class="margin-toggle"/>
<span class="sidenote">A sample `_sbrk` is in [utils_syscalls.c](https://www.funkthat.com/gitea/jmg/lora-irrigation/src/commit/91a6fb590b68af1bcd34f776d4a58c89ac581c7d/loramac/src/boards/mcu/saml21/hal/utils/src/utils_syscalls.c#L67-L83),
though this particular implementation is not used by my project.</span>)
to allocate memory for the heap.  Using sbrk is the easiest method to
access uninitalized SRAM, but modifying or adding a symbol can be used
if your microcontroller's framework does not support sbrk.


Putting it together
-------------------

It is accepted that integrating as many difference sournces of entropy
(TRNGs) is best.  This ensures that as long as any single soruce is
good, or each one is not great, but combined they provide enough
entropy (preferably at least 128 bits), that the seeded PRNG will be
secure and unpredictable.

As some sources are only available at first boot, e.g. SRAM, it is
best to save a fork of the PRNG to stable storage.  In my
implementation, I decided to use EEPROM for this.  I added an
additional EEPROM section in the linker script, and then added a symbol
[rng_save](https://www.funkthat.com/gitea/jmg/lora-irrigation/src/branch/main/strobe_rng_init.c#L39)
that is put in this section.  This should be 256-bits (32-bytes) as
the savings of smaller does not make sense, and any proper PRNG when
seeded with 256-bits will provide enough randomness.  Writing to EEPROM
does require a little more work to have the code save to this region,
rather than RAM, but the STM32 HAL layer has functions that make this
easy.

It would be great if the PRNG seed could be stored in read-once,
write-once memory to ensure that it can be read, mixed in with any
additional entropy, and then written out, but I do not know of any
microcontroller that supports this feature.

Part of this is is to ensure that the the state between the saved
seed, and the PRNG state used for this boot is disjoint, and that if
either seed is compromised, neither can be backtracked to obtain the
other.  In the case of [strobe](https://strobe.sourceforge.io/papers/strobe-latest.pdf),
the function [strobe_randomize](https://www.funkthat.com/gitea/jmg/lora-irrigation/src/branch/main/strobe/strobe.c#L319-L331)
does a RATCHET operation at the end, which ensure the state cannot be rolled
back to figure out what was generated, and as the generated bytes does
not contain the entire state of the PRNG, it cannot be used to
reconstruct the future seed.

Another advantage of using EEPROM is the ability to provide an initial
set of entropy bytes at firmware flashing time.  I did attempt to add
this, but OpenOCD, which I use for programming the Node151 device,
does not support programming EEPROM, so in my case, this was not
possible<label for="sn-eeprom-flash" class="margin-toggle sidenote-number"></label><input type="checkbox" id="sn-eeprom-flash" class="margin-toggle"/><span class="sidenote">Despite not using it, the infrastructure to generate perso entropy is still present in the [Makefile](https://www.funkthat.com/gitea/jmg/lora-irrigation/src/branch/main/Makefile#L152-L157).</span>.
I could have added an additional source data file to the flash, but
figured that the other sources of entropy were adequate enough for my
project.


{#
Conclusion
----------

Modern microcontrollers do have a number of sources of entropy that can
be used.  With a little bit of work, a PRNG seed can be saved between
resets, allowing for more secure operation, and even preloading of
entropy. #}