$.$ Using the VIGEN$$RE CIPHER, provide a step by step solution on how to decrypt the

encrypted message in the example as seen belowcontinues until all of the plaintext sequence is encrypted. A general equation of the

encryption process is

$C_i=(p_i+k_{\text{i}\text{m}\text{o}\text{d}\text{m}})mod26$

Compare this with Equation $(3\mathrm{.}1)$ for the Caesar cipher. In essence, each plain$-$

text character is encrypted with a different Caesar cipher, depending on the corre$-$

sponding key character. Similarly, decryption is a generalization of Equation $(3\mathrm{.}2)$:

$p_i=(C_i-k_{\text{i}\text{m}\text{o}\text{d}\text{m}})mod26$

To encrypt a message, a key is needed that is as long as the message. Usually,

the key is a repeating keyword. For example, if the keyword is deceptive, the message

$"$we are discovered save yourself" is encrypted as

key:

deceptivedeceptivedeceptive

plaintext:

wearediscoveredsaveyourself

ciphertext:

ZICVTWQNGRZGVTWAVZHCQYGLMGJ

Expressed numerically, we have the following result.