LUKS volumes have the ability to allow multiple independently usable passwords, as explained here: [https://code.google.com/p/cryptsetup/wiki/FrequentlyAskedQuestions]
The intuition behind basic encryption with a single key is pretty straightforward.
ciphertext = BIG_FUNCTION(plaintext, key) plaintext = BIG_FUNCTION^(-1)(ciphertext, key)
Can anyone explain how a LUKS volume can permit independently usable passwords? I'm just looking for the intuition - not necessarily a detailed explanation of how LUKS in particular handles this.