[The functionality provided by Google Client Authentication has been deprecated since April 20, 2012. This API is no longer available and this page is being maintained purely for historical and research purposes.]
From their site: Developers of installed applications have the option of using a programmatic login method to access Google services protected by user login. An installed application is installed on a device, such as a desktop computer or a cell phone, as opposed to a web application. With programmatic login implemented, an application's user can log into their Google account from inside the application. The application then contacts Google with the login data and requests access to a specified Google service, such as Calendar. Once access is authorized, the user can create, read, update, or delete data as needed using the application interface. Programmatic login and authentication is a big step up from the "low-tech" approach, which is to simply include the user's login name and password in every request to Google. With programmatic login, Google supplies the application with a token that can referenced in all requests instead of login data.
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