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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:
https://en.wikipedia.org/wiki/Integrated_Encryption_Scheme
It seems that at least one developer is doubtful about the security of such schemes:
https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2014-August/006581.html
Security aside, what practical reason would anyone have to encrypt a message with a Bitcoin key?
This doesn't work because frequently the keys that signed the transaction are not controlled by the actual payee. See also: https://en.bitcoin.it/wiki/From_address
– G. Maxwell – 2019-01-23T19:21:40.927Yes, it assumed that the person who maintains access to their key. Should they lose access to their private key they will be unable to decrypt the message. Should someone else gain access to their private key the message's contents is no longer confidential.
It also assumes that the type of transaction revealed a public key such as Pay-to-PubkeyHash. – Owen Delahoy – 2019-01-24T07:59:48.187
1I think you did not read the link in my response as it has nothing to do with losing access. – G. Maxwell – 2019-01-24T08:14:41.420
From that page, I addressed unreliability assumptions 3.2, 3.3 and 3.4. Which unreliability assumption were you specifically referring to? – Owen Delahoy – 2019-01-24T12:40:37.437