Can the Monero block chain be used to transmit anonymous messages or for data storage?,

For example a military secret, confidential state data, company private records, employee payroll, private communication between two users, or a group, private data stored in block chain in a decentralized and a private way in the block chain (instead of current private communication model like Off The Record/ pidgin/Tor which has several drawbacks like accidental loss of data and news of Tor being cracked by NSA).

If so, what needs to be done, how can such technology be created on the Monero block chain?

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You can put potentially any data into tx_extra and it will be stored on the blockchain with your transaction, only accessible with your keys.

This however, will bloat your transaction size and your transaction will be more expensive as you have to pay per kb. For now, beside the elastic blocksize limit (median of last 100 blocks * 2) there is no maximum how much data tx_extra can contain, so if you can afford, you can store almost anything you want.

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The basics are already here: encrypted payment IDs are private information encrypted by the sender, which only the recipient can decrypt. If the sender and the recipient are the same party, you can store data that only yourself is able to recover.

A similar system could be used to enable "chat like" behavior. Transactions would have to be marked as non-mineable, and would propagate through daemons, never be mined, and drop off the pool after some time.

Large scale data is more problematic, especially for long term storage. Large scale data hits the block size limit (you can embed arbitrary data in a transaction's metadata, but a transaction still has to fit within a block, and the current block size limit). The typical way to "add/notarize data to the blockchain" is to merely embed the data's hash (and possibly other metadata, such as a URL) in the blockchain, but this means the data itself is at risk of loss, though you do keep the unforgeability under the hash's security assumptions.

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    Yes keep chat and stuff out of the blockchain, Monero works perfectly well as a simple and fungible digital currency, an "appscoin" it is not. – user20 Oct 19 '16 at 15:00

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