If you need to generate a new exim.cert and exim.key files, run:
/usr/bin/openssl req -x509 -newkey rsa:1024 -keyout /etc/exim.key -out /etc/exim.cert -days 9999 -nodes
and answer all questions with information you want the certificate to have. Once done, continue by typing:
chown mail:mail /etc/exim.key chmod 600 /etc/exim.key chmod 644 /etc/exim.cert /etc/init.d/exim restart
Related error message in the /var/log/exim/mainlog:
(SSL_CTX_use_PrivateKey_file file=/etc/exim.key): error:0200100D:system library:fopen:Permission denied