"Martin Geisler" <[EMAIL PROTECTED]> wrote: > When you have 64 different possibilities, all of equal likelyhood, > then you can code them using 6 bit. This is what the entropy tells > you. > > The fact that A in the 7-bit ASCII standard is 01000001 is just a > coincedence --- they could just as well have put your chosen 64 > characters into the lower 6 bits, and then have the other 64 available > characters use the high bit. > > In general it doesn't change anything if you encode your message (a > passphrase in your example) in a different encoding: the amount of > information stays the same if you still just select your characters > From the same subset. > > > So making a passphrase of ASCII characters, and then encoding it using > UTF-16 doesn't make it more secure. Sure, with UTF-16 gives you the > potential to encode something like 2^16-1 characters, but to calculate > the entropy you can disregard all characters which you will never > choose. > > The formula for entropy explains this: > > H(X) = - sum_{i=1}^n p(i) * log_2(p(i)) > > Here the p(i)'s are the probability that your message will be "i". > With a bigger space of possible messages (a bigger n) then the sum > contains more terms, but if you still select your message from the > same small set, then most of the terms will be zero. So if a message > of value "j" is, say, a Chinese passphrase, then p(j) = 0 would mean > that know that you'll never such a passphrase. And thus the term > disappears from the sum (well, actually you get a problem with taking > the logarighm of zerolet's not go into that). > > > See http://en.wikipedia.org/wiki/Information_entropy for more on how > to calculate the entropy, but I hope this helped a bit.
Thanks for your anwser, but I'm afraid you mostly told me what I already know. What I don't understand is how this relates to breaking passphrases. For example, say I use the passphrase foobar. It has 6 characters, each represented by 8 bits, so it will be represented by 46 bits. These 46 bits are then the key used to symmetrically encrypt/decrypt my secret key, right? (Another question; is salt added to it, and/or is it hashed?) Now if the attacker knows that I have only used the 23 characters a-z in the passphrase, then she/he can represent all of them using 5 bits. But I don't understand how this helps the attacker, since foobar represented this way would obviously produce a completely different key (of only 30 bits). I thought that all this was about time and the amount of data you have to deal with. That, for example, when someone is brute forcing a passphrase it would be 25% faster if all the characters used were represented with only 6 bits instead of 8. I understand why this would be faster, but not who it could possibly work. Oskar _______________________________________________ Gnupg-users mailing list Gnupg-users@gnupg.org http://lists.gnupg.org/mailman/listinfo/gnupg-users