In the RSA public key cipher, encryption is done as C $=$ Me mod n$,$ where n $=$ pq for suitably chosen large primes p$,$ q$,$ and gcd$($e$,$ $($n$))=1.$ In a chaining attack on the RSA, given a ciphertext block C $=$ Me mod n$,$ an attacker computes

Ce mod n$,$ Ce$2$ mod n$,$ Ce$3$ mod n$,...,$Ce mod n$,$

untilCe modn$=$C$.$Thatis,istheleastpositiveintegerthatsatisfiesCe modn$=$C$.$

$($a$)$ Explainwhytheattackercanalwaysfind in $\{1,2,...,$n$1\}$suchthatCe modn$=$ C$?$

$($b$)$ Can the attcker recover the message M from the observed sequence above in case thatCe modn$=$Cisvalid?