So, now I have to figure out what's wrong with my Oracle JDK NSS setup.
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As for OpenJDK + NSS, it looks like that NSS implementation simply does not provide a SecureRandom provider.
Therefore, there should be a different way how to generate secret key. I verified that branch mentioned in https://github.com/danbev/aerogear-simplepush-server/tree/0.8.0-secret-key-issue is working fine with OpenJDK7 + NSS.
So, now I have to figure out what's wrong with my Oracle JDK NSS setup.