A 3 GHz processor can execute on the order of 100 Million Instructions per secon

Question

A 3 GHz processor can execute on the order of 100 Million Instructions per second = 108 IPS = 100 Instructions per microsecond (1 microsecond = 10-6 second).

Assume that an attacker can write a routine to check passwords that uses 10 instructions to check each password.

Using that routine, an attacker could check 100/10 = 10 passwords per microsecond.

How many minutes would it take to check all passwords of length 6 characters or less consisting of lowercase Latin alphabetic characters + numbers from 0 to 9 at 10 passwords checked per microsecond?

Explanation / Answer

Solutions:

Number of lower letter = 26
Number numbers [0-9] = 10

Total number of characters = 26 + 10 = 36
Total password combinations possible = permutation of number of characters = 36*36*36*36*36*36 = 2176782336

Hacker check 10 password per microsecond i.e 1 password in (10^(-6))/10 sec = 10^(-7) sec

Hence for 2176782336 password, time = 2176782336 * 10^(-7) sec
                                   = 217.6782336 sec
                                   = 217.6782336/60 min
                                   = 3.62797056 min
                                   = 3.6 min (approx)

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