Just for information: the security errors you are seeing are coming from SSL/TLS encryption as used by “https://” web pages.
For a secured connection, you need an encryption protocol, and a certificate to make sure the web site you are connecting to is genuine. Encryption protocols are often updated.
Today, we mostly use the TLS 1.2 standard for encryption (and TLS 1.3 is upcoming but not yet widely supported). However the system library for secure connections in Android 4.2 does not support versions beyond TLS 1.0. As of 30 June this year, it is not allowed to use TLS 1.0 any more on web sites which process credit card information (https://blog.pcisecuritystandards.org/are-you-ready-for-30-june-2018-sayin-goodbye-to-ssl-early-tls), and in general usage of TLS 1.0 is now discouraged. This is mainly a precaution as there are no ‘big’ vulnerabilities found yet that would require such a move.
Android 4.4 does support TLS 1.2 - so upgrading your FP1 to one of the beta 4.4 versions which can be found on this forum also fixes this part.
Certificates can become an issue in future. A certificate of a web site will be trusted, when it is signed by a certificate authority (CA) known by your phone (or browser, for browsers which implement their own certificate store). The so-called root certificates of these authorities, which are installed on your device, are typically valid for a limited time, and sometimes one may be revoked by the browser & OS vendors when a CA has been found to misbehave. Examples of the latter are Diginotar (2011) and WoSign/Startcom (2017).