Is this secure?

Paul Rubin at nospam.invalid
Wed Feb 24 03:39:53 CET 2010

Steven D'Aprano <steven at> 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:

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. 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('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))


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