In this question I introduce a new mode of operation for an n-bit block cipher Enc with secret key k.
Let x1, x2, . . . be the blocks of n bits to be encrypted. The process starts by choosing a random n-bit value IV .
Then compute c1 = Enck(IV ⊕ x1) and, for i = 2, 3, . . . , to compute
ci = Enck(xi−1 ⊕ xi).
I call this mode of operation CRAP-mode.
(a) Explain how to decrypt a ciphertext (IV, c1, c2, . . . , ct) in CRAP-mode.
(b) Can encryption be parallelised? Can decryption be parallelised?
(c) Let δ ∈ {0, 1}n. Show that if (IV, c1, c2) is an encryption of (x1, x2) in CRAP-mode, then (IV ⊕δ, c1, c2)
is an encryption of (x1 ⊕ δ, x2 ⊕ δ).