My Note on Solutions.: replace Google Search provider url with HTTPS,SSL

you may have already noticed that Google supports SSL for the search page, SSL is a great protocol which enables the point-to-point transport security, with SSL, Nobody can filter or monitor you searching activity,I think it’s a Pain for the IT security Guy:). SSl does require more server side capacity to handle the SSL handshake and encryption which is CPU expensive. Google offer those features to end users at Google's cost, what a great company.

Simply replace any url begins with http://www.google.com with https://www.google.com. i.e https://www.google.com/finance.

Here I will show to to replace the default Google search provider url with https. Different Browser differs.

For Internet Explorer.
IE keeps those search provider data in registry.
here is the key, HKEY_CURRENT_USER\Software\Microsoft\Internet Explorer\SearchScopes
just go the the google provider, replace the url as https://www.google.com/search?q={searchTerms}&sourceid=ie7&rls=com.microsoft:{language}:{referrer:source}&ie={inputEncoding?}&oe={outputEncoding?}
you have to change the default search provider to others in order to apply the change. otherwise IE will override all you settings

Firefox
Firefox store the configuration in a xml file. which is located in C:\Program Files\Mozilla Firefox\searchplugins

rename the google.xml as gogole.xml.bck
create a new xml file named googlehttps.xml
copy the content from google.xml and replace http with https for the search url
like this

<SearchPlugin xmlns="http://www.mozilla.org/2006/browser/search/">
<ShortName>Google</ShortName>
<Description>Google Search</Description>
<InputEncoding>UTF-8</InputEncoding>
<Image width="16" height="16">data:image/png;base64,AAABAAEAEBAAAAEAGABoAwAAFgAAACgAAAAQAAAAIAAAAAEAGAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADs9Pt8xetPtu9FsfFNtu%2BTzvb2%2B%2Fne4dFJeBw0egA%2FfAJAfAA8ewBBegAAAAD%2B%2FPtft98Mp%2BwWsfAVsvEbs%2FQeqvF8xO7%2F%2F%2F63yqkxdgM7gwE%2FggM%2BfQA%2BegBDeQDe7PIbotgQufcMufEPtfIPsvAbs%2FQvq%2Bfz%2Bf%2F%2B%2B%2FZKhR05hgBBhQI8hgBAgAI9ewD0%2B%2Fg3pswAtO8Cxf4Kw%2FsJvvYAqupKsNv%2B%2Fv7%2F%2FP5VkSU0iQA7jQA9hgBDgQU%2BfQH%2F%2Ff%2FQ6fM4sM4KsN8AteMCruIqqdbZ7PH8%2Fv%2Fg6Nc%2Fhg05kAA8jAM9iQI%2BhQA%2BgQDQu6b97uv%2F%2F%2F7V8Pqw3eiWz97q8%2Ff%2F%2F%2F%2F7%2FPptpkkqjQE4kwA7kAA5iwI8iAA8hQCOSSKdXjiyflbAkG7u2s%2F%2B%2F%2F39%2F%2F7r8utrqEYtjQE8lgA7kwA7kwA9jwA9igA9hACiWSekVRyeSgiYSBHx6N%2F%2B%2Fv7k7OFRmiYtlAA5lwI7lwI4lAA7kgI9jwE9iwI4iQCoVhWcTxCmb0K%2BooT8%2Fv%2F7%2F%2F%2FJ2r8fdwI1mwA3mQA3mgA8lAE8lAE4jwA9iwE%2BhwGfXifWvqz%2B%2Ff%2F58u%2Fev6Dt4tr%2B%2F%2F2ZuIUsggA7mgM6mAM3lgA5lgA6kQE%2FkwBChwHt4dv%2F%2F%2F728ei1bCi7VAC5XQ7kz7n%2F%2F%2F6bsZkgcB03lQA9lgM7kwA2iQktZToPK4r9%2F%2F%2F9%2F%2F%2FSqYK5UwDKZAS9WALIkFn%2B%2F%2F3%2F%2BP8oKccGGcIRJrERILYFEMwAAuEAAdX%2F%2Ff7%2F%2FP%2B%2BfDvGXQLIZgLEWgLOjlf7%2F%2F%2F%2F%2F%2F9QU90EAPQAAf8DAP0AAfMAAOUDAtr%2F%2F%2F%2F7%2B%2Fu2bCTIYwDPZgDBWQDSr4P%2F%2Fv%2F%2F%2FP5GRuABAPkAA%2FwBAfkDAPAAAesAAN%2F%2F%2B%2Fz%2F%2F%2F64g1C5VwDMYwK8Yg7y5tz8%2Fv%2FV1PYKDOcAAP0DAf4AAf0AAfYEAOwAAuAAAAD%2F%2FPvi28ymXyChTATRrIb8%2F%2F3v8fk6P8MAAdUCAvoAAP0CAP0AAfYAAO4AAACAAQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACAAQAA</Image>
<Url type="application/x-suggestions+json" method="GET" template="https://suggestqueries.google.com/complete/search?output=firefox&client=firefox&hl={moz:locale}&q={searchTerms}"/>
<Url type="text/html" method="GET" template="https://www.google.com/search">
<Param name="q" value="{searchTerms}"/>
<Param name="ie" value="utf-8"/>
<Param name="oe" value="utf-8"/>
<Param name="aq" value="t"/>

<Param name="rls" value="{moz:distributionID}:{moz:locale}:{moz:official}"/>
<MozParam name="client" condition="defaultEngine" trueValue="firefox-a" falseValue="firefox"/>
</Url>
<SearchForm>https://www.google.com/firefox</SearchForm>
</SearchPlugin>