$[25]4.$ Consider the following ECC curve $E$ :

$Y^2=x^3+231x+473,p=17389,q=1321,G=(11259,11278)inE(F_p).$

A$.$ Assume the signing key of Alice is $sk=542.$ What is her corresponding public key $pk?$

What is her signature on the hash of a message $H(m)=644$ with the ephemeral key

$k=847?$

B$.$ Assume the public key of Bob is $pk=(14594,308).$ What is his private key $sk?($you

can use any method to find it$,$ but describe it in details$).$ Use his private key $sk$ that you

found to forge his signature on the hash of a message $H(m)=516$ using the ephemeral

key $k=365.$