$($a$)$ Show that $2753$ is the inverse of $17$ modulo $3120.$

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$(2$ marks$)$

$($b$)$ Using the fast modular exponentiation algorithm, show that $(3185{)}^{2753}$mod

$(3233)$ is $1816$mod$(3233).$

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$(2$ marks$)$

$($c$)$ We received the encrypted message $3185.$ Show that the decrypted mes$-$

sage is $SQ,$ if it was encrypted using the RSA cipher with key $(3233,17)?$

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$(3$ marks$)$