Beaufort cipher:-

Let k = (k₁, k₂, ... , k_n) be a keyword of length n, and let p = ( p₁, p₂, ... , p_n) be a plaintext message of length n. The Beaufort encryption of the message is the cipher text c = (c₁, c₂, ... , c_n) = (k₁-p₁, k₂-p₂, ... , k_n-p_n), where ki-pi denotes a backward shift of k_i by the shift corresponding to the letter pi. For example, if k = (H, I) and p = (B, Y), then c = (G,K).

(a) Encode the message HELLO with the keyword JUMPS.

(b) Show that encryption and decryption of a Beaufort cipher are identical processes. That is, to decipher it is only necessary to encrypt the cipher text with the same keyword.