It's pretty clear how signing a message with a Bitcoin key can be useful in proving ownership of funds.

However, it's far from clear how encrypting a message with a Bitcoin key can do anything useful. This feature is available from Tools/Encrypt/decrypt message, and appears to use ECIES or some variant of it:


It seems that at least one developer is doubtful about the security of such schemes:


Security aside, what practical reason would anyone have to encrypt a message with a Bitcoin key?

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