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Verifying Dice Roll Math

Background#

Video: COLDCARD Dice Rolls seed entropy

You have the option of creating the seed value for your Coldcard by rolling a six-sided dice (D6). Choose "Dice Rolls" from the "Import Wallet" screen.

You just keep pressing 1–6 as you roll.

This allows you to remove any risk of the Coldcard's random number generator (RNG) being compromised, and you are creating the private key directly. In that way it's not really an 'key import', but a 'create key'.

Number of Rolls#

Please note that each roll of a D6 dice provides only 2.585 bits of additional entropy (randomness). Therefore, for 128-bit security, which we consider the absolute minimum, you need 50 rolls, and for 256-bits of security, 99 rolls. The Coldcard does not limit the number of rolls, but will warn you if you apply too few rolls.

Duplicating Our Math#

But what if we lied and still used some tricky way to pick a non-random but random-looking value for the seed?

Video: Dice Rolls on Tails

You may have noticed the first screen always looks like this:

zero rolls

The seed value is calculated as SHA256 over the rolls, when expressed as an ASCII string. Therefore, you will always see e3b0c... 27ae4... b855 as a starting value, since that's SHA256 over an empty string. You can calculate other values using Python as follows:

>>> from hashlib import sha256
>>> sha256(b'').hexdigest()
'e3b0c44298fc1c149afbf4c8996fb92427ae41e4649b934ca495991b7852b855'
>>> sha256(b'123456').hexdigest()
'8d969eef6ecad3c29a3a629280e686cf0c3f5d5a86aff3ca12020c923adc6c92'

Values can also be calculated from the command line (shell) of most computers using one of the following commands:

$ echo -n 123456 | sha256sum
8d969eef6ecad3c29a3a629280e686cf0c3f5d5a86aff3ca12020c923adc6c92

$ echo -n 123456 | openssl sha256
(stdin) = 8d969eef6ecad3c29a3a629280e686cf0c3f5d5a86aff3ca12020c923adc6c92

The ideal environment to perform this checking is a computer running Tails - The Amnesic Incognito Live System, preferable without any network connection and no hard drives. Do not use your actual dice rolls on a normal desktop system as that will completely comprise the security of your Coldcard!

You may be worried that this hex number shown on the Coldcard is not honestly converted into the seed words. To check that we are applying BIP-39 correctly, you can use this simple python3 program: rolls.py or rolls12.py for 12 word seeds.

$ echo 123456 | python3 rolls.py
8d969eef6ecad3c29a3a629280e686cf0c3f5d5a86aff3ca12020c923adc6c92

WARNING: Input is only 15 bits of entropy

   1: mirror
   2: reject
   3: rookie
   4: talk
   5: pudding
   6: throw
   7: happy
   8: era
   9: myth
  10: already
  11: payment
  12: own
  13: sentence
  14: push
  15: head
  16: sting
  17: video
  18: explain
  19: letter
  20: bomb
  21: casual
  22: hotel
  23: rather
  24: garment


$ echo 123456 | python3 rolls12.py
8d969eef6ecad3c29a3a629280e686cf

WARNING: Input is only 15 bits of entropy

   1: mirror
   2: reject
   3: rookie
   4: talk
   5: pudding
   6: throw
   7: happy
   8: era
   9: myth
  10: already
  11: payment
  12: owner

As you can see, it shows the hash (which you can cross verify as above with other command-line tools) and then shows the corresponding BIP-39 mnemonic words.

Again, a Tails system is ideal for this verification process.

  1. Get a copy of rolls.py (or rolls12.py for 12 word seeds) onto the Tails system.

  2. Run your dice rolls through rolls.py (or rolls12.py):

    • In Tails, open "Applications > System Tools > Terminal".

    • Type this sequence of commands:

$ cd "Tor Browser"
$ ls

  • You should see the rolls.py (or rolls12.py) program you downloaded already. If you used some other means to get it into your Tails system, go to the directory where it's located.

  • Further Internet access or write access to any media is not required or desired past this point.

  • Type this:

$ echo 123456 | python3 rolls.py
# or
$ echo 123456 | python3 rolls12.py

  • It should print the hash and seed words shown above (8d96...6c92 and mirror .. garment).

  • Repeat but using the dice rolls you provided to Coldcard. Both should arrive at the same set of seed words.