user8933: My understanding is that the 12-word seed is used to recover wallets' private keys. However, if each private key is 256-bits long, and the dictionary for the seed only contains 2048 words, then that's not nearly enough to cover them all: 2048^12 = 2^132 << 2^256.
Where is my misunderstanding?

user3511: 
2048^12 = 2^132 << 2^256

It doesn't need to be able to describe every private key. You always start with the mnemonic, never calculating a mnemonic from a private key.

8933: <p>My understanding is that the 12-word seed is used to recover wallets' private keys. However, if each private key is 256-bits long, and the dictionary for the seed only contains 2048 words, then that's not nearly enough to cover them all: 2048^12 = 2^132 &lt;&lt; 2^256.</p>

<p>Where is my misunderstanding?</p>
 3511: <blockquote>
  <p>2048^12 = 2^132 &lt;&lt; 2^256</p>
</blockquote>

<p>It doesn't need to be able to describe every private key. You always start with the mnemonic, never calculating a mnemonic from a private key.</p>
