Decryption $($Dec$)$: Given the ciphertext $c,$ it computes the

message $m=c^d$modN.

Explain why this textbook version of RSA is not IND$-$CPA secure$.$

$($Hint: Don't be confused by the complex mathematics; recall a

fundamental principle about IND$-$CPA security that you've

learned.$)(10$ pts$)$

Q$4$: One$-$way security in a public key encryption scheme means

that, given a challenge ciphertext corresponding to a random

message, no efficient adversary can successfully recover the entire

plaintext. Explain, using a standard reduction $($proof by

contradiction$),$ why any public key encryption scheme that is

secure under the IND$-$CPA model must also be one$-$way secure$.(10$

pts$)$