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 $10.$

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