How many 4-digit numeric PINs are there? How many 6-digit PINs? Suppose a ban pr

Question

How many 4-digit numeric PINs are there? How many 6-digit PINs?

Suppose a ban prohibits “obvious” PINs like 0000(00) and 1234(56). What would you define as obvious, and how many PINs would that disallow?

Now assume people choose PINs not for their numeric significance, but because they are all or the first four or six letters of a word, as on a telephone keypad: A,B,C = 2, D,E,F = 3, etc. Using the cryptanalysis lessons from Chapter 2 of the textbook, estimate how many 4-digit PINs and 6-digit PINs that could be chosen would not be chosen, because, for example, they are not a word, or part of a word.

The goal of this exercise is not to obtain a definitive answer but to present a reasonable analysis. In what network settings is a PIN still justified as an authenticator, in spite of the small numbers you obtain in this exercise?

How would you enforce use of a 6-digit PIN rather than a 4-digit PIN?

Explanation / Answer

total number of 4 digit numeric pin will be 104

and total number of 6 digit numeric pin will be 106

if the ban prohibits the use of pin like 000000, 123456, there will a significant number of pins that will be rejected.

because they are having a simple pattern which anyone can decode.

pins like 111111, 222222,...... 999999, 012345, 101010 will be rejected.

Since it is not clearly mentioned what kind of patterns the ban is prohibiting it is difficult to calculate them.

It would be better to enforce 6- digit PIN since it has more combinations than 4 digit PIN and more possibilities.

So it would be hard to crack 6 - digit PIN, but at same time it will be diffcult for the user to remember the PIN if it is of 6 digit. But for better security 6 - digit PIN is better option

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