So I have partial answer to my question how to store large files on blockchain. However, after googling for several hours I can't decide which are the best algorithms for encrypting the content of the file and producing the hash. I've checked many answers explaining the differences, but I would like to ask, as of today, end of 2017, what are the industry best encrypting and hashing algorithms?

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    Probably AES (encryption) and SHA2 (hashing) is a safe bet (modern processors has hardware support for AES). But better ask in forums like for up to date information. – Ismael Nov 26 '17 at 5:45

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