In this problem we explore the relationship between password length and cryptographic security.

Suppose a password consists of 77 ASCII characters. You can review the ASCII characters here.. Exactly 27=12827=128 of these codes are for printable characters; we will assume every character in the password is printable.

What is the size of the keyspace that consists of passwords of this form? What is the equivalent key length in bits? Assuming that you could check one password every 108108 seconds, what is the worst case running time for cracking this password by brute force search (in days)? Now assume that the user used only 3131 characters from the keyboard. What is the key length in bits in this case? How many days, in the worst case, would it take to break this weaker password? You can't round to the nearest day here -- be as exact as possible. Supposing you used only 3131 characters, how long is the shortest password that achieves 252252 bits of security?