Overall Entropy = 132 or log2(possibilities).Length =12 characters (or 12 words, some or all of which may repeat).Range = 2048 unique character values (or 2048 unique words).Entropy per character * Length = overall password entropy.Range^Length= Possible combinations (can also be rounded as 2^overall password entropy) Log2(Possible combinations)= overall password entropy Any character in the password has been chosen from a single common library or " range" of unique characters and chosen randomly using a cryptographically secure process.Number of characters, some of - or all of which - may beĭuplicate/identical and/or repeat consecutively). The password has a specific " length" (consisting of its. Let's first assume two following two points: Here is a simple explanation regarding password entropy, and depending on what needs to be measured. There is a difference though between the user choosing a word, versus randomly chosen letters that "happen" to equal a word when read from left to right etc. If the English word is a mnemonic and represents some underlying index value or other code value such as ASCII or UTF-8, then I don't think there is a difference so long as it was chosen randomly, as its entropy will depend entirely on the range of words or letters that it was chosen from. The entropy "H" of a discrete random variable "X" is defined as: by flipping a coin for each bit) it is a simple logarithmic scale: " $n$ bits of entropy" means "entropy is $S = 2^n$" (and the attack cost is then $2^$), see below for examples and Claude Shannon's formula. Entropy is often expressed in bits: an entropy of $n$ bits is what you get out of a sequence of $n$ bits which have been selected uniformly and independently of each other (e.g. For instance, if you have a list of 2000 words and choose one among them (uniformly), then the entropy is $S = 2000$. with dice or a computer with a good PRNG - as opposed to a human being making a "random" chance in his head). The attacker has a copy of the source code of the program what the attacker does not have is a copy of the random bits that the PRNG actually produced.Įntropy is easy to compute if the random parts of the selection process are uniform (e.g. dev/urandom on a Linux system, or CryptGenRandom() on Windows). The model is the following: we suppose that the password is generated with a program on a computer the program is purely deterministic and uses a cryptographically strong PRNG as source of alea (e.g. We assume that the "best attacker" knows all about what passwords are more probable to be chosen than others, and will do his guessing attack by beginning with the most probable passwords. We define the entropy as the value $S$ such the best guessing attack will require, on average, $S/2$ guesses. Entropy is a measure of what the password could have been so it does not really relate to the password itself, but to the selection process.
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