IP Security Architecture

Let h be a secure cryptographic hash function. For this problem, a password consists of a maximum of 14-characters and there are 32 possible choices for each character. If a password is less than 14 characters, it’s padded with nulls until it is exactly 14 characters. Let P be the resulting 14 character password. Consider the following two password hashing schemes.

(i) The password P is split into two parts, with X equal to the first 7 characters and Y equal to the last 7 characters. The password is stored as (h(X), h(Y)). No salt is used.

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(ii) The password is stored as h(P). Again, no salt is used.

Note that the method in scheme (i) is used in Windows to store the so-called LANMAN password.

a. Assuming a brute force attack, how much easier is it to crack the password if scheme (i) is used as compared with scheme (ii)?

b. If scheme (i) is used, why might a 10-character password be less secure than a 7-character password?14

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