![]() ![]() And if an attacker sees a sequence of random numbers produced by the algorithm, they can use the sequence to compute the internal state of the algorithm, and recover the seed.įor security purposes, random numbers need an additional property, and that is to be unguessable. If an attacker guesses the seed value, they would know all the passwords that were generated. This is very useful for re-running simulations with the same statistically random data, but it is not good for security. If the seed value is repeated, the stream of numbers generated will be repeated. These algorithms are initialized with a value called the seed, and each time they are called they return a different number, producing a stream of values. They are more properly known as Pseudo-Random Number Generators (PRNGs). They are just math formulas that are created with the intent of producing numbers that are statistically evenly distributed, but there is no attempt to make them unguessable. Mathematical random number generators aren't actually random. However, you said that you are "randomly" generating a password but you did not specify how the random value would be generated. Yes, the entropy of a password generated with a truly secure random source for P would be E = log2(P^L) If you want to take a look at a real entropy estimator, then take a look at zxcvbn/src/ffee. ![]() If done right, the entropy estimate should line up roughly with the number of guesses it would take an attacker using standard wordlists and algorithms. Real entropy estimators are heuristic, I think giving your password a base score for length, and then taking off points for dictionary words, keyboard patterns, etc, giving extra points for caps and symbols. ![]() For example, my guessing algorithm above would never try qazwsxedc even though it's an obvious keyboard pattern. This entropy measure is clearly just an estimate because it depends heavily on which guessing algorithm / guess order I assumed. Then for a given password you can compute E = log2(num_guesses_until_correct) = log2(pos_in_guess_list) Repeat for triplets of words, with and without spaces.Repeat for pairs of words, with and without spaces.Try all English words in alphabetical order, with and without caps, with at the end, with 1337 s*bs, etc.Try top 1 million most common password from breach data.Unfortunately humans are ludicrously non-uniformly random in choosing passwords someone's password is far more likely to be password123 than ensr33nuo95 even though they are both 11 lowers and numbers.Īnother way to think about password entropy is to assume some guessing strategy, and then ask how many guesses until you guess correctly. That would be a good formula, if passwords were randomly and uniformly chosen across the character set. ![]()
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