I browse isn't the only Amiga browser you know.. Have you tried Voyager? It does support SSL.. If you are buying tickets off of a java app, I have no solution for you.. I just think that Voyager supports flash, and has really the best Amiga specific solution right now..
It works with AmigaOS 3.9. I am not sure about 4.0 or if they have plans. But this really is THE BEST if you want to use classic Amiga software this rocks. The company is great too..
Voyager Web BrowserIt supports:
* HTTP/1.1 connection keepalive, content negotiation and resume support
* FTP connects keepalive and resume support
* SSLv2, SSLv3 and TLSv1 encryption support, with up to 168 bit keys
* 'Javascript' (ECMA-Script) scripting support
* Low Level Plugin API supporting embedded objects
* Fully user-controllable GUI with custom control panel placement, configurable navigation and fastlink buttons.
* Macromedia Shockwave Flash compatible Player
* Versatile Bookmarking system utilizing ContactManager
* Internal web page editing with HTML tag highliting
* Internal GIF, JPG, PNG, XBM decoding
* Image buffers in Fast RAM