That was close..!

This Dilbert cartoon has given computer security professionals something to think about their whole careers, and I ran head first into it tonight.

I’ve been working on the Cipherpod Black provisioning program, which randomly generates an HMAC 512 hash. Since we can’t actually visually verify that a given key has been properly implemented (it’s transparent to the operator, we cannot even lay eyes on a CPod Black’s onboard key much less record it), I added a chi square analysis to the POST testing routine to ensure that the HMAC key is sufficient and hasn’t been otherwise tampered with in firmware.

I provisioned a pair of Cipherpod Blacks and what happens.. the red light starts blinking and the system halted..!  These cases are super tough, there’s no way to press an onboard reset button, I’m thinking something’s wrong with the Seeed 2040 and the device has been bricked, but I hit CNTL-C on the provisioning program and just try again… and this time it worked!

I had Claude compute the probability that a brand new randomly generated 512 bit key would be cryptographically poor, and its response was:

The probability of a randomly generated 512-bit HMAC key having poor chi-square statistics is astronomically small.

Here’s why:

Expected nibble distribution:

• 128 total nibbles (2 per byte)
• Expected frequency: 8 per nibble value (128/16)
• Chi-square critical value at p=0.05: ~25

Probability calculation:

For a truly random 512-bit key, the nibble frequencies follow a multinomial distribution. The probability of getting a chi-square value > 25 (poor randomness) is approximately:

• P(chi-square > 25) ≈ 2^-20 to 2^-25
• That’s roughly 1 in a million to 1 in 32 million

Why it’s so unlikely:

1. Law of Large Numbers – With 128 nibbles, random variation naturally averages out
2. Central Limit Theorem – The distribution of frequencies converges to expected values
3. High entropy source – If using a CSPRNG, bias is essentially impossible

Practical example: If you generated 1 million random 512-bit keys:

• ~999,999 would show “excellent” chi-square (< 25)
• Maybe 1 might show “acceptable” (25-30)
• Essentially 0 would show “poor” (> 30)

Real-world consideration: If your HMAC key actually failed chi-square, it would almost certainly indicate:

• Faulty random number generator
• Implementation bug
• Intentional backdoor/weakness
• Hardware failure

A genuinely random 512-bit key failing chi-square would be like flipping a fair coin 20+ times and getting all heads – theoretically possible but so unlikely that you’d suspect the coin first.

That’s why your POST check of the HMAC key is actually a great diagnostic – if it ever fails, something is seriously wrong with the system, not just bad luck.