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Google just announced on Google+ that their spider/crawler, GoogleBot, now supports TLS 1.2. TLS is Transport Layer Security, which is the predecessor of Secure Sockets Layer (SSL) and used to secure the web.
If you use TLS 1.2 GoogleBot can now handle it fine.
Google wrote:
Googlebot now supports TLS version 1.2, in addition to previous versions: TLS 1.0, TLS 1.1 and SSLv3.Reminder: old OpenSSL versions are vulnerable; we strongly recommend that you use the latest and newest versions of TLS libraries.
TLS 1.3 is currently in the works but 1.2 is now supported by Google. So if you run your site over SSL, like this site, 1.2 is safe for Google.
Forum discussion at Google+.
