Assume that an attacker knows that a user’s password is either p1 = abcd or p2 = bedg. say the user encrypts his password using the vigen´ere cipher, and the attacker sees the resulting ciphertext c. show how the attacker can determine the user’s password, or explain why this is not possible, when the period t used by cipher is 1, 2, 3, or 4 respectively.

I will Show how the attacker can determine the user’s password

Explanation:

If we assume an attacker knows that a user’s password is either abcd or bedg. Say the user encrypts his password using the shift cipher, and the attacker sees the resulting ciphertext. Show how the attacker can determine the user’s password, or explain why this is not possible.  

The alphabet{A, B, . . . , Z}is identified  with the set Σ = {0, 1, . . . 25} and all additions are implicitly taken mod26.  

Then, the possible passwords are p0 = abcd = (0, 1, 2, 3) and p1 = bedg = (1, 4, 3, 6).  

All possible encryptions of p0 are C0 = {(k, k + 1, k + 2, k + 3) | k ∈ Σ} and the ones of p1 are C1 = {(k + 1, k + 4, k + 3, k + 6) | k ∈ Σ}.  

These two sets are disjoint and so in order to obtain the password  it is necessary to check in which set the ciphertext lies.