Click to install Google SSL Search Provider
supports ie7 later, maybe. and heere is OpenSearch XML of this.
<?xml version="1.0" encoding="UTF-8"?>
<OpenSearchDescription xmlns="http://a9.com/-/spec/opensearch/1.1/" xmlns:ie="http://schemas.microsoft.com/Search/2008/">
<ShortName>Google SSL</ShortName>
<Description>Google SSL Web Search</Description>
<Url type="text/html" xmlns:referrer="http://a9.com/-/opensearch/extensions/referrer/1.0/"
template="https://encrypted.google.com/search?q={searchTerms}&sourceid=ie8&ie={inputEncoding}&oe={outputEncoding}" />
<Url type="application/x-suggestions+xml"
template="https://encrypted.google.com/complete/search?q={searchTerms}&client=ie8&output=toolbar&mw={ie:maxWidth}&sh={ie:sectionHeight}&rh={ie:rowHeight}&inputencoding={inputEncoding}&outputencoding={outputEncoding}" />
<Image height="16" width="16" type="image/icon">http://www.google.com/favicon.ico</Image>
</OpenSearchDescription>