This is actually not a malware or adware issue. This problem is, unfortunately, normal with Mac OS X 10.9.
Recently, 10.9 systems began to have problems verifying certificates for certain sites. The bluekai.com sites, as well as the Oracle site (who owns bluekai.com), are among the affected sites.
I am not clear at this point what the cause of the problem is, but I have been able to confirm this behavior on a freshly-installed, clean 10.9 system.
Unfortunately, there are only two options available to you. One is to upgrade or downgrade your system. Mac OS X 10.10 and higher do not suffer from this problem, and strangely, for whatever reason, Mac OS X 10.8 is also not affected.
The other option is to stop using Safari and switch to Chrome or Firefox.
Note that Avast would only solve this problem because Avast, in essence, performs a man-in-the-middle attack on your system by installing their own root certificate as a means to decrypt and route all encrypted SSL (https) traffic through their software. This essentially short-circuits the ability of the browser to warn you of certificate issues, covering up the issue without fixing it. This also presents a serious security vulnerability, since A) Avast is intercepting all your encrypted network traffic, and B) Avast is preventing you from seeing normal warnings that would show up if, for example, a site's certificate had been revoked due to bad behavior.
Any other anti-virus software that solves this problem would be engaging in the same bad behavior.