I think you're looking in the wrong direction. There are two
aspects to consider: the security of your laptop, and the
security of your connections. For the security of your
connections, what matters is that you are using SSL (or TLS —
treat it as a synonym of SSL) with a correct certificate. An
HTTPS connection means HTTP (the usual web protocol) over SSL.
SSL provides end-to-end confidentiality and integrity
protection, so it doesn't matter whether you are browsing from a
“secure” network or from a public wifi hotspot. What does
“correct certificate” mean? A certificate is a website's
“identity card”, providing a cryptographic means for your
browser to verify that the website is who it claims to be. If
the certificate verification didn't happen, you would have no
way to know whether the SSL connection was going to the
legitimate website or to a man-in-the-middle. In a good first
approximation, you need to check three things to know that you
have a secure connection to the desired website: - The URL must
beg