Steven D'Aprano <ste...@remove.this.cybersource.com.au> writes: > Paul, if you were anyone else, I'd be sneering uncontrollably about now, > but you're not clueless about cryptography, so what have I missed? Why is > reducing the number of distinct letters by more than 50% anything but a > disaster? This makes the task of brute-forcing the password exponentially > easier.
Reducing the number of distinct letters by 50% decreases the entropy per character by 1 bit. That stuff about mixing letters and digits and funny symbols just makes the password a worse nuisance to remember and type, for a small gain in entropy that you can compute and make up for. The main thing you have to make sure is that the min-entropy is sufficient for your purposes, and it's generally more convenient to do that by making the password a little bit longer than by imposing contortions on the person typing it. Ross Anderson's "Security Engineering" chapter about passwords is worth reading too: http://www.cl.cam.ac.uk/~rja14/Papers/SE-03.pdf When I mentioned entropy loss to the OP though, I mostly meant loss from getting rid of the letter z. The (binary) Shannon entropy of the uniform probability distribution on 26 letters is 4.7004397 bits; on 25 letters, it's 4.6438561 bits. The difference isn't enough to give an attacker that much advantage. I like the diceware approach to passphrase generation and I've been using it for years. www.diceware.com explains it in detail and the docs there are quite well-thought-out and informative. Keep in mind that the entropy needed for an online password (attacker has to make a server query for every guess, and hopefully gets locked out after n wrong tries) and an offline one (attacker has something like a hash of the password and can run a completely offline search) are different. Here is a program that I use sometimes: from math import log dictfile = '/usr/share/dict/words' def genrandom(nbytes): with open('/dev/urandom') as f: return int(f.read(nbytes).encode('hex'), 16) def main(): wordlist = list(x.strip() for x in open(dictfile) if len(x) < 7) nwords = len(wordlist) print "%d words, entropy=%.3f bits/word"% ( nwords, log(nwords, 2)) print '-'.join(wordlist[genrandom(10)%nwords] for i in xrange(6)) main() -- http://mail.python.org/mailman/listinfo/python-list
