Digital Signature Example using Public key crypto and Hash. A message with the

text "Let's be friends" has been received, along with the digital signature $(23,6,17,6).$

The message was sent by a user, whose public decryption function is $P=C^7$mod$35.$ The

signature was produced using the following known conventions:

The digest $d$ of the message is produced by dividing the text into blocks of $4$ characters.

The decimal values corresponding to the $4$ ASCII characters are added together modulo

The digital signature is produced by encrypting each digit of the digest with the sender$\text{'}$s

private function $C=P^e$mod$35,$ where $e$ is kept secret.

Determine whether the received message is genuine and could not be repudiated by the sender$.$

Hint: The decimal ASCII codes corresponding to the text "Let's be friends" are:

$76,101,116,39,115,32,98,101,32,102,114,105,101,110,100,115.$

Charlie has arranged a blind date for Alice and Bob, who are both cryptographers, and they

do not know each other before. Bob wants to make sure that the person he is dating is actually

Alice, not somebody else. Before going to the dating, he got a copy of Alice's public key from

Charlie. Please describe how Bob can ask Alice to prove that she is Alice $($please do not try

this in the real life, or you will probably never see your date again$).$