I spent a bunch of time getting the mingw-cross-compiled Qt compiled with -openssl-linked for the payment protocol work (it uses QtNetwork to fetch PaymentRequest/PaymentACK messages via https).
The magic configure incantation was:
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Nothing special needed to be done for the openssl build:
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The payment protocol code add a couple more depedencies to Bitcoin-Qt:
+ QtNetwork with OpenSSL support
+ Google's protocol buffer library and compiler.