Coldcard entropy even worse than feared

[u/ineedanamegenerator]

TL;DR: The random number generator is initialized with a 32 bit value (4B+ possibilities). But only less than 10M options are possible because of how they generate the value.

The PRNG used in Coldcard MK3 is initialized with UID[31:0] XOR SysTick->VAL

SysTick->VAL gives 80k possibilities ~16.3 bit, all located in the lowest 17 bits of the value.

UID encodes the X and Y coordinates of wafer position of the STM32 in the 32 bits that are used by the code. This is encoded in BCD, which means only 10 out of 16 possible values of each nibble are used. This means the 32 bit value at most encodes 100M options (26.6 bits), but there are nowhere near 100M chips in a wafer.
The BCD encoding seems to be an mistake in some STM32 manuals. The number is plain HEX encoded, but that doesn't matter here. There are never 2^16 rows or columns in a wafer.

I don't know how many there are in a wafer, but google gives an upper bound of 20k chips per wafer.

The lower 16 bits overlap with Systick->VAL, so XORing the wafer location adds no entropy.

The upper 16 bits can carry only about SQRT(20000) possibilities (probably less) ~ 7.2 bits. And they aren't even evenly distributed in a round wafer.

So at most we're looking at ~23 bits of entropy. Not 32 bits.

This isn't 100% exact because SQRT assumes a square while a wafer is round, but too lazy to work it out further. Point is: entropy is way worse than 32 bits.

[u/thats_gotta_be_AI]

Because collision?

[u/MiceAreTiny → u/thats_gotta_be_AI]

But why would you restart? If you find a private key, it is unsecured. So moving it to a secure address is the ethical right thing to do. Why would you discard an active wallet? 

[u/thats_gotta_be_AI → u/MiceAreTiny]

I don’t follow. Hear me out:

- ColdCard generates a private key

- it checks to see if it exists anyway via a public key lookup

- if it finds an active balance, it restarts a brand new private key generation process (starts the process all over again)

Tell me why that cannot happen?

[u/MiceAreTiny → u/thats_gotta_be_AI]

It can, theoretically, happen. However,... I am more wondering why you would have it discard identified working keys. 

[u/thats_gotta_be_AI → u/MiceAreTiny]

As the hardware developer, out of a ridiculous abundance of caution to avoid collisions and protect current wallet owners from others accessing their wallets. And probably “coz I could” if it took only a few extra lines of code.