It's impossible. The keystore contains a certificate that is used to digitally sign your apk. Each certificate is completely unique and cannot be restored or restored from old apks.
Google relies on this because it is extremely secure and allows them to truly reduce the likelihood that someone could hack your developer account details and download a malicious apk as an update to an existing application.
Even if Google allowed you to download an apk signed with a different key as an update, Android devices will not allow the user to update the application, since the installed apk will have a different signature than the installed one. This is the same problem that you will encounter if you install the application from Google Play and then try to install the debug version from Eclipse.
Now you have to re-download the application under a different package name using a different key. In the future, please remember to back up the keystore in several places (but do it safely. Do not put it in a public version control system. The keystore should be kept confidential at any time).
Digital signatures are based on public key cryptography. You cannot restore a private key with a public key - this is the whole cryptography item with a public key. Such algorithms are based on one-way functions: things that are easy to do but hard to undo.