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I am currently reading the "Green Book" (http://csrc.nist.gov/publications/secpubs//rainbow/std002.txt) of the "Rainbow Series" and have a question on chapter "C.4 Password Space".


From this chapter:

S = password space

A = number of alphabet symbols

M = password lenght

S = AM

To illustrate: If passwords consisting of 4 digits using an alphabet of 10 digits (e.g., 0-9) are to be generated:

S = 104

That is, 10,000 unique 4 digit passwords could be generated. Likewise, to generaterandom 6-character passwords from an alphabet of 26 characters (e.g., AZ) :

S = 266

That is 3.089 * 108 uniques 6-character passwords could be generated.


My question:

I thought that the 10 000 is the solution of 10^4 (because there is an alphabet of 10 and we have a password consisting of 4 characters). Anyway as we see in the next example there we have 26 characters and a 6-character password -> how do we get "3.089 * 108"?

I would be very glad, if someone out there has an answer for that question. Thx in advance ;)


The Answer to my own question:

Unfortunataly the official source posted in my question is not formatted very well. The corrections are:

S = AM -> should be formatted like this S = A^M

Therefore further formatting changes:

S = 104 -> 10^4

S = 266 -> 26^6

3.089 * 10^8

The answer

"3.089 * 10^8" is correct in scientific notation but it doesn't represent the exact result which is 26^6 = 308.915.776.

Thx @ Tom Leek who answered my question too.

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1 Answer 1

up vote 1 down vote accepted

It is a mere typographic problem. The document is in ASCII text but was obviously converted from another format, probably automatically, and was poorly reviewed afterwards. All the "exponents" suffered. Let's put it right:

Password length and alphabet size are factors in computing the maximum password space requirements. Equation [2] expresses the relationship between S, A, and M where:

S = password space
A = number of alphabet symbols
M = password length

S = AM    [2]

To illustrate: If passwords consisting of 4 digits using an alphabet of 10 digits (e.g., 0-9) are to be generated:

S = 104

That is, 10,000 unique 4-digit passwords could be generated. Likewise, to generate random 6-character passwords from an alphabet of 26 characters (e.g., A-Z):

S = 266

That is 3.089 * 108 unique 6-character passwords could be generated.

Indeed, 26 raised to the power 6 is equal to 308915776.

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