Obviously, changing group passwords when group membership changes is a good idea. What I am arguing about is periodic changes of personal passwords.
Changing passwords on a ($bruteforcetime/2) - e timescale is only really useful if you know when the brute force attack began. For instance, if we assume an off-line attack, and assume that the attacker can download your password file at will, or at least at relatively frequent intervals, then the attacker has a 50-e% chance of having your password at the time you change it. Then, it has to start over. After two runs through half of the password file, the equivalent time to one complete run, the attacker has a (100 - (50+e)^2)% (about 75%) chance of having your password. The expected time to get the password is something like the time to process (50+e^2)% of the password space. If the attack is on-line, then the attacker has a (50-e)% chance of having your password when you change it, and a ((50+e)% chance that the new password is in the remaining space)*((50+e)% of the search space) of finding the new password, which is once again about 75%. Assuming that the attacker can trojan your system as soon as they get a valid password, there is no difference between the two attacks.
Unfortunately, if you assume that the attack is at T((50-e)%, while it is really at T(20%), then the attacker has a 20% + (80%)*(80%) = 84% chance of finding your password in one brute-force round, at an expected time of T(57.5%). If the attacker is at T(80%), then the attacker once again has a 84% chance of finding it, with an expected time of T(50%).
So, the more accurately you know when the attack started, and how fast it is progressing, the more you can improve your chances. The only safe assumptions to make about when the attack started is that it started as soon as the password was set, or not at all. However, determining the speed of the attack is another issue. If you're using a long password, stored with a strong hash, then an offline attack could several years on a modern computer. Unfortunately, the old estimates about needing a machine costing $large_amount_of_money to speed up password cracking are no longer valid; many attackers could have access to bot-nets of thousands of modern machines, which allow relative unsophisticated attackers to crack your long passwords in a few days. Do you really want to change your passwords every three days to keep ahead? |
