Speed drops after connecting to a secure site

Somebody asked the following on a Yahoo forum yestereday. Does anybody
here have an explanation for him?

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Hope someone has insight into a problem I have encountered on
several different WiFi cards and WiFi routers (both paired i.e two
linksys products, and unpaired D-Link Router and built-in Intel
Wifi). I'll establish a g connection with good to excellent signal
strength and connection speed of 30-50+mbps. I'll surf non-secure
web sites for any length of time with no speed degradation. I'll
sign into any secure site MSN Finance, Yahoo Mail, Comcast Mail,
etc. and the signal strength will remain constant, but the
connection speed will drop to 1 mbps. Going to a non-secure web
site does not improve the speed. The only way to re-establish the
speed is to break the WiFi link (repair, etc.). The speed then
resumes performing at the high level vs 1mbps.

I can repeat this at will at home or on the road.
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--
Dave