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So, unless you use a common phrase (spelled correctly) - Long passwords are still a great idea because it would take forever to generate a 55 character random p

So, unless you use a common phrase (spelled correctly) - Long passwords are still a great idea because it would take forever to generate a 55 character random password. Is that correct?

KMag 13y ago
Short answer: if you're talking about 55 perfectly randomly chosen mixed-case alphanumeric characters, yes. Otherwise, you're going to have to be more precise about your definition of "random password" if you're going to perform any analysis. >>> from math import log >>> log( 62 * * 55 ) / log( 2 ) 327.4807970712782 55 character uniformly cryptographically chosen alphanum passwords contain over 327 bits of entropy. If an attacker were using an irreversible but thermodynamically ideal computer floating in space passively cooled to the temperature of cosmic background radiation... the amount of waste heat from her computer would be enough to boil away Earth's oceans. I'm too lazy to look up Bruce Schneier's calculation for counting to 2 * * 256, but counting to 2 * * 327 may very well require more energy than our Sun will output between now and when it goes cold. Now, all of the basic qbit operations are reversible, so the above theoretical lower bound on waste heat doesn't apply to a quantum computer. However, if the hash algorithm doesn't have any weaknesses and has at least 326 bits of state in an optimal implementation, it will still take an attacker 2 * * 163 hash operations on a quantum computer, so at least 2 * * 163 times the clock cycle of the quantum computer. Or... even given some rather weak assumptions about SHA-1, if your bank and FunnyCatPitcures.com both use salted SHA-1, and the stolen password hash is 160 bits, but the password itself is 327 bits, an ideal attacker is going to find your password along with about 2 * * 167 false correct answers. As long as your bank uses a different salt for your account than FunnyCatPictures.com did, then having your password hash from FunnyCatPictures.com doesn't help an attacker. Basically, as long as your password has at least twice as many bits of entropy as the stolen salted hash, the number of false positives (hash collisions) from cracking the hash is more than the expected number of random guesses needed to get a false positive (hash collision) at your bank, so the attacker is better off just throwing random guesses at the bank.

So, unless you use a common phrase (spelled correctly) - Long passwords are still a great idea because it would take forever to generate a 55 character random password. Is that correct?

KMag 13y ago

Short answer: if you're talking about 55 perfectly randomly chosen mixed-case alphanumeric characters, yes. Otherwise, you're going to have to be more precise about your definition of "random password" if you're going to perform any analysis. >>> from math import log >>> log( 62 * * 55 ) / log( 2 ) 327.4807970712782 55 character uniformly cryptographically chosen alphanum passwords contain over 327 bits of entropy. If an attacker were using an irreversible but thermodynamically ideal computer floating in space passively cooled to the temperature of cosmic background radiation... the amount of waste heat from her computer would be enough to boil away Earth's oceans. I'm too lazy to look up Bruce Schneier's calculation for counting to 2 * * 256, but counting to 2 * * 327 may very well require more energy than our Sun will output between now and when it goes cold. Now, all of the basic qbit operations are reversible, so the above theoretical lower bound on waste heat doesn't apply to a quantum computer. However, if the hash algorithm doesn't have any weaknesses and has at least 326 bits of state in an optimal implementation, it will still take an attacker 2 * * 163 hash operations on a quantum computer, so at least 2 * * 163 times the clock cycle of the quantum computer. Or... even given some rather weak assumptions about SHA-1, if your bank and FunnyCatPitcures.com both use salted SHA-1, and the stolen password hash is 160 bits, but the password itself is 327 bits, an ideal attacker is going to find your password along with about 2 * * 167 false correct answers. As long as your bank uses a different salt for your account than FunnyCatPictures.com did, then having your password hash from FunnyCatPictures.com doesn't help an attacker. Basically, as long as your password has at least twice as many bits of entropy as the stolen salted hash, the number of false positives (hash collisions) from cracking the hash is more than the expected number of random guesses needed to get a false positive (hash collision) at your bank, so the attacker is better off just throwing random guesses at the bank.