Can participation in online academic competitions destroy patent rights? I have developed an algorithm/software that does a specific task. I want to let the algorithm compete in an academic competition, where the code is run on a password protected server on a secret test set by another researcher. I will describe my research vaguely in the few lines that each researcher must submit about their work to be able to compete.

Will any of this destroy my chances of acquiring a patent for the algorithm afterwards?
It very well could. Talk to a patent attorney. If you can get the contest runner to sign a non-disclosure agreement, then you might be able to protect your patent rights. 

That being said, algorithms are not patentable in most jurisdictions, and software is quickly losing its patentability in the US.