Is a SSL'ed JSON API that uses cookies for authentication and nonces generally secure?

If I build an SSL'ed API that authenticates with a session ID held within a cookie, adds a nonce as a query parameter, and always responds with a JSON 'Object' response (as opposed to a JSONP-style response with a callback), is it secure in general, and in particular against XSRF?

The intent with such an API to only have it available to pages on my own domain, and to be free to expose private data (such as username and emails) through this API (but not be consumable by other domains)--and retain a reasonable amount of simplicity for developers on the team.

Let me at least share what I understand about this approach, and why I think it's secure. Please enlight me if wrong!:

• A <script> tag dropped on a 3rd-party domain to our site would send my cookies, but would not be able to parse the JSON object response (and the response would always deliberately be a JSON object at the top level). Also, I need to make sure that API calls that affect state on the server are all protected by non-GET method access, because <script> tags must use GET and so can not cause havok by attempt to call state-changing calls (in other words, the API would be adherent to REST in so far as HTTP methods go). Also, I deliberately do not support JSONP because it would be a security hole.


• Man-in-the-middle used to hijack cookies (the session) is not a concern because I'm using SSL with valid certificates.


• Replay attacks are a temporally limited concern because of the use of a nonce will limit how long one could send in a replay of an HTTPS request, because the server will make sure that the API call is only valid for a small amount of time in a typical nonce-validating way.


• XMLHttpRequest can not make cross-domain calls, so it can't request anything from my site.


• CORS (Cross ORigin Resource Sharing) is not of concern because I don't have a crossdomain.xml file or any other advertisement of cross-domain support associated with HTML 5.


• An iframe in a 3rd-party site doesn't matter because even though it can load my page graphically, the host site can't access any data within that iframe, and because I've made no attempt to support cross-domain iframe communication (so they can attempt to set # on the iframe URL like folks do to enable communication between cross-domain iframes, but my page won't be responsive to it).

EDIT:
A nonce would also protect against even GET requests (i.e., <script> tags) as russau says. In thinking on that specifically, I like the idea of asking for a nonce in a 'POST' API call that is not itself nonce protected; it should be the case that only XmlHTTPRequest's on the same domain can then generate a nonce to begin with. This seems to be a simple way of making the generation of nonce's developer-friendly. (i.e., nothing server-side for the website/javascript developers--just ask for your nonce from the same API you are using to develop against, and make requests with that nonce until you get a 'bad nonce' response--then ask for a new one, and repeat.

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