SANS inform that there is a significant increase in port 443 scans. They said if you see attacks against https servers, please let them know. If you see something like that, I think you can send your web server logs/IDS logs/Firewall logs to them to confirm whether there is an attack or not.
Last year, I got the same problems at my client site. One of my team reported to my Security Consultant that she detected series of Attack Response alerts from our Snort IDS. This alert involves 443 port (https). So we analyzed that alert and checked the source IP because the 443 service comes from that source IP. After analyzing that alert, we confirmed that there is no SSL/https related services available on the source IP. It looks like a normal website. There is no https service available on that IP. If there is https service, it should be encrypted. We want to analyze details and make decision about that alert, but we didn't have more resources. Maybe attacker was compromised earlier and installed backdoor/trojan/malware at that IP and used it to communicate through 443 port? Or maybe misconfiguration?? See this link:
From my experience, this question is not easy to answer if you only have Snort alerts. It will make this question too difficult to answer. Looking at the alerts, there is nothing else we can do. You cannot give right answer to this question.
That's why I like to use Sguil. Sguil is an open source suite for performing NSM (Network Security Monitoring). NSM equips security staff to deal with the inevitable consequences of too few resources and too many responsibilities. NSM collects the data needed to generate better assessment, detection, and response processes, resulting in decreased impact from unauthorized activities.