Is the 12 word Bitcoin recovery phrase safe enough?

If you have a Bitcoin wallet, you'll get a 12 word recovery phrase corresponding to your private key. If you visit the english word list on GitHub, you'll see that there are 2048 words available.

That means:

totalcomb=204812=5.44451791039total_{comb} = 2048 ^ {12} = 5.4445179 \cdot 10^{39}

What if someone tried to hack it by brute force; is a 12 recovery phrase secure enough? 🤔

The supercomputer Fugaku can perform 5371015537 \cdot 10^{15} operations per second (flops). In the worst case scenario:

thack=totalcombflops=5.444517910395371015=1.01387671022secondst_{hack} = \frac{total_{comb}}{flops} = \frac{5.4445179 \cdot 10^{39}}{537 \cdot 10^{15}} = 1.0138767 \cdot 10^{22} seconds

Transforming seconds into years:

1.01387671022seconds3.21498191014years1.0138767 \cdot 10^{22} seconds \approx 3.2149819 \cdot 10^{14} years

Hi, I'm Erik, an engineer from Barcelona. If you like the post or have any comments, say hi.