Existing standards and tools exist to support your requirement today. As Scott noted, this requires either using the built-in browser in iOS in your application, or allowing the browser of the iOS browser to process part of SAML / Browser SSO (each of them has its pros and cons). You can check out this free White Paper titled, “Standards-Based IdM Architecture for Mobile Applications ,” which talks about how Ping customers (my employer) are addressing this today if you want a few more ideas.
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