Assume an attacker is using a processor capable of executing 100 million instructions per second and has designed an algorithm to test passwords that requires 10 instructions. Assume that the attacker has correctly guessed an ID and plans to carry out a brute force attack against all possible passwords to try to get into the account for that ID. How long would you tell the account user to make her/his password, using a combination of alphanumeric string, to ensure that it is reasonably safe for 3 months? Back up your answer with calculations of the time to crack a password of the recommended length.

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First of all it is needed to state the assumptions made.
Since there is nothing mentioned about how the passwords must look like or how unique to be, it is fair to assume each password is any combination between lowercase, uppercase and numbers. This means each password can be any of 26+26+10=62 characters. Let the length of the password be x. This means that...

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