I find that truly random diceware passphrase, more often than not, either contain a word that is easily misspelled or has an order that is illogical. I think there are three ways to make a diceware passphrase more memorable:
- Throw out passphrases until you get one you can remember
- Throw out individual words that are difficult for you to remember
- Rearrange words so that it is easier to remember
Of course, the issue is that all three options reduce the bits of entropy. Number 2 can be avoided by editing the diceware list manually but that is too much work for most people. I still believe that the resulting passphrase will better then many other options and useful for most purposes. However, I am interested what the resulting bits of entropy for each method of these methods.
The entropy of a truly random 4 word passphrase is log2(7776*7776*7776*7776) = 51.7 bits. The worst case for option 3 is that there is only one logically way to rearrange the words. In this case, I believe that the bits of entropy is log2( (7776*7776*7776*7776) / (4*3*2*1) ) = 47.1. I am not sure what formula to use for 1 & 2. For example, if I throw out a word three times what are the bits of entropy. I think 1 is much more ambiguous. On paper, it should not reduce entropy but clearly it does.