A Wired Equivalent Privacy (WEP) key is a security code that one must enter in o

Question

A Wired Equivalent Privacy (WEP) key is a security code that one must enter in order to access a secure WiFi network. The charac- ters in the key are used from the numbers 0 to 9 and letters from A to F, which gives 16 possibilities for each character of the key. Note that repeats are allowed, that is, the same letter or number can be used more than once in a key. A WEP key for a WiFi network with 64-bit security is 10 characters long.

a. How many different 64-bit WEP keys can be made by using the given numbers and letters?

b. A specific 64-bit network has a WEP key in which the 2nd, 5th, 8th, and 9th characters are numbers and the other 6 char- acters are letters. How many different WEP keys are possible for this network?

Explanation / Answer

a. solution:

number of digits is, n = 16 (10 numbers and 6 letters)

key length is 10 characters long, i.e., r = 10

And the repetitions are allowed. A key can also start with the number 0.

Thus, the number of different keys that can be made using the given numbers and digits where each one can be repeated more than once is, nr = 1610 keys.

b. solution:

2nd, 5th, 8th and 9th are numbers and so, r = 4. These 4 numbers are to be taken from 0 to 9 and so, n = 10.

Repetition is allowed. Thus the number of arrangements of these 4 places(2nd, 5th, 8th and 9th) = nr = 104

Now, the remaining 6 places (r = 6) can be filled by using 6 letters (A to F) (n = 6) in nr = 66ways since repetition is allowed.

Thus, the number of different keys that can be made are 104 + 66 = 10,000 + 46,656 = 56,656 keys.

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