I use dm-crypt for encrypting my partitions - both on local machine and on backup drive as well. From time to time it makes sense to change password, and... the question is how to do it.
First of all figure out in which slot luks stores password for your drive:
cryptsetup luksDump /dev/xxx
You will get something like this:
Key Slot 0: DISABLED Key Slot 1: ENABLED Iterations: 477611 Salt: 66 5d f0 cf 4b 7b d2 d7 62 6a 2f 0e d2 23 11 33 fe 35 2e 14 32 46 e0 8f cb f9 f0 16 2c 5b 03 72 Key material offset: 264 AF stripes: 4000 Key Slot 2: DISABLED Key Slot 3: DISABLED Key Slot 4: DISABLED Key Slot 5: DISABLED Key Slot 6: DISABLED Key Slot 7: DISABLED
In this case it is slot 1.
cryptsetup luksChangeKey /dev/xxx -S <slot>
And you will be prompted for the current key and for the new one.
It can be done while disk is mounted.