Given a cryptosystem CS and an adversary A that can recover the key from CS$\text{'}$s ciphertext with non$-$negligible probability. Prove that CS does not provide CPA insurance.

$$ A cryptosystem CS is given which encrypts all messages using the

CBC mode. But instead of selecting a new IV each time, the CS increments the previous one

IV by $1.$ That is$,$ for the i$-$th message: IVi $$ IVi$1+1.$ Show how an adversary can

to win the CPA game for CS with non$-$negligible probability.

$$ Show that the OFB encryption function does not provide CCA security.