It is trivial to compromise the browser context of the page. In the case of a browser bug another tab can interact badly with the current tab. In the case of a MITM attack on (sadly quite possible given the potential adversary) the attacker can modify the JS in flight to the browser. In the case of an externally loaded resource embedded on the page that resource may modify the execution of your crypto. There are also CSFR, XSS and other JS vulnerabilities to account for.
Javascript is a hopelessly bad place to do crypto. Consider doing an signed browser extension that does this on the desktop and native apps on the phone. I would also suggest a native app on the desktop as well. People seem to really like them for twitter.