Evaluating Master Password Security: How Many Bits Are Enough for Economic Safety?

I would not trust ChatGPT on this. I do generally trust the Passwordbits site, but its cost estimates are based in part on data from a 1Password blog that is not fully transparent in its methodology; in addition, the method used to extrapolate from PBKDF2-SHA256 hashing to Argon2id, while not unreasonable, is tied to the hardware used by the blog author (which has not been reported).

The calculations are not that difficult, but the results are dependent on assumptions made. Aaron Toponce has reviewed the cracking speeds available on different types of hardware. Personally, I like the benchmark used by Steve Thomas (sc00bz), which evaluates hash rates achievable by a GPU that costs approximately $1000 USD (high end but not top end) — OWASP recommendations for KDF are based on Steve’s data for throttling cracking speeds to 10,000 hashes/second when one such GPU is used. Thus, one can estimate that an exhaustive search of all possible 4-word passphrases (EFF wordlist) will take almost 12,000 GPU-years. Thus, with a million-dollar investment to acquire 1000 GPUs, the average cracking time would take almost 6 years; bringing the cracking time down to something reasonable (1 month) would require hardware acquisition costs on the order of 140 million dollars.

However, to fully estimate cracking costs, one also needs to take into account the cost of electricity required to run the GPUs nonstop 24/7 for months or years. To estimate the utility costs, one needs to make additional assumptions about the specific hardware used. The fastest available GPU today (Nvidia GeForce RTX 4090) gets 15,000 hashes per second for Bitwarden’s default KDF (600,000 iterations of PBKDF2-SHA256), but draws 450 W of power in so doing. Thus, it can basically crunch 120 million hashes per kW-hour (no matter how many GPUs are used). Therefore, the average amount of electric energy required to crack a random 4-word passphrase is more than 15 million kWh. In the United States, electricity costs are billed at an average rate of $0.14 USD/kWh; therefore, the operating costs for cracking a 4-word passphrase would on average be 2 million dollars.

The total cost is a combination of amortized capital equipment costs and the operating costs (e.g., electrical power), so further assumptions would be required to get a final number. Nonetheless, it is clear that cracking a 4-word passphrase (randomly generated from a list of 7776 words) will require a multimillion dollar investment.

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