$19)$ In the RSA encryption algorithm, Bob's public key is

Kp$=(107,187).$ Calculate his private key.

$($a$)(5,187)($b$)(3,187)($c$)(2,187)($d$)(107,187)$

$19\mathrm{.}1($a$)$

$($b$)$

$($C$)$

$($d$)$

For the character H$=66$ the cypher text is given by:

$($a$)30$

$($b$)107($c$)187$

$($d$)19$

$19\mathrm{.}2$

$($a$)$

$($b$)$

$($c$)$

$($d$)$

Alice uses the same RSA algorithm with the private key Ks and the

public key Kr given by $(7,187)$ and $(23,187)$ respectively.

Alice wants to sign a message before sending it to Bob. The key

Alice must use is given by:

$($a$)(107,187)($b$)(5,187)($c$)(21,187)($d$)(7,187)$