An answer to whether it is permissible to invest in the various forms of cryptocurrencies should be sought from a reputable Sunni mufti (or a panel of muftis).
However, the difficulty with that is explaining to them how cryptocurrencies work. Even if you do a great job of explaining, they may not understand fully due to the (sort of) intricate nature of it. In fact, not even many from the laity understand how blockchain and cryptocurrencies work. Maybe we should, together, draft an istifta in English and urdu which can be sent to various reputable dar al-iftas.
Kifl al-Faqih, muna wa al-durar and fatawa ridawiyyah Vol 17 of alahazrat would be a starting point.
Questions to provoke thinking:
Can cryptocurrencies fall under the category of ‘maal’ (property)? Cryptocurrencies are intangible, which is an important aspect when considering whether it can be ‘maal’ or not. There are four types of maal generally, of which one is ‘that which is always thaman’. So the main question to answer is whether cryptocurrencies are a form of maal, and if so, which type of maal is it.
I very much doubt it can fall under the category of ‘currency’ as it is not widely accepted as a form of payment nor used as such by the general population (these are general points mentioned about the nature of thaman e istilahi in fiqh books). However, that begs the question: what are all the requirements for something to become a currency according to the shari’at? The situation may change in the near future, whereby people accept and use cryptocurrencies as an actual form of payment, which also needs to be addressed for when the situation does happen.
If it is deemed to be currency, it would have to be thaman e istilahi/urfi (currency due to public usage and acceptance) of course and not thaman e khalqi (created as currency: eg gold and silver).
Then there is the important fact that crypto trading occurs mainly online. This is important due to the ‘one majlis’ (sitting) requirement for bay’. If it is deemed a currency, then there is also the requirement of gaining control over one (either the cash or the purchased cryptocurrency) within that sitting in which the transaction was agreed.
There are many many important points to consider...