Will they be looking more into quantum proofing the Monero protocol or Cuckoo Cycle testing etc?

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Monero Research Lab Publications MRL-0001 to MRL-0005 have been published.

MRL-0006 - Difficulty Adjustment Algorithms in Cryptocurrency Protocols have been started. According to fluffypony

The difficulty research that Surae was working on is quite extensive, but incomplete.

EDIT: as of November 17th, it appears MRL-0006 will be renamed MRL-0007.

Someone would have to pick it up and run with it, as Surae is basically burnt out on difficulty and has moved on to other challenges:)

A version of MRL-0008 - Ring Multisignature exists but is not published yet.


Additionally to what Clement J. said, there are a lot of potential future reserach tasks on the Monero Design & Development goals, including Research goals on the bottom half of that page.

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