Final answer:
To exhaustively test all possible passwords on a UNIX system, it will take approximately 8.23 x 10^12 seconds.
Step-by-step explanation:
In this question, we are asked to calculate how long it will take to test all possible passwords on a UNIX system. We are given that passwords are limited to the use of 95 printable ASCII characters and are 10 characters in length. Additionally, we are told that the password cracker has an encryption rate of 6.4 million encryptions per second.
To calculate the time it will take, we can use the formula:
Time = Total Number of Passwords / Encryption Rate
Since we know that the length of the passwords is fixed at 10 characters and that only printable ASCII characters are used, there are:
Total Number of Passwords = (number of printable ASCII characters) ^ (number of characters in the password)
In this case, the number of printable ASCII characters is 95 and the number of characters in the password is 10, so:
Total Number of Passwords = 95 ^ 10
Using a calculator, we can calculate this value to be approximately 5.27 x 10^19.
Now, we can substitute this value and the encryption rate into our formula to calculate the time it will take:
Time = (5.27 x 10^19) / (6.4 million)
Calculating this, we find that it will take approximately 8.23 x 10^12 seconds to exhaustively test all possible passwords on a UNIX system.