In iOS 8, Apple has added Shared Web Credentials which lets you share login information between your iOS app and Safari. Adding support for Shared Web Credentials consists of 2 parts:

1. Serving up a site association file on your website.
2. Reading/writing to the keychain in your iOS app.

Note that sharing of login is 2-way, so when your user logs in manually with username/password or changes password in your app, it's also helpful to save it into the keychain so your website can use it (when accessed with Safari).

Detailed instruction is available at Apple.

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