I'd like to know if using the ECDH shared secret of a static EC Private Key with it's own corresponding static EC Public Key causes a problem / weakness.
(edit) not asking if it's ok to re-use the keys multiple times. Static EC Keys are known to be ok in this usage case.
In this environment, several agents are producing and consuming data, and the streams are being protected with static ECDH keys.
The ECDH Shared secret is hashed before it is used as a key in the asymmetric stream cipher. The shared secret will be the same each iteration / connection.
The stream is eventually stored to disk (encrypted)
Typical usage (not considered a problem): $$ Alice( public ) : \ Q_A = d_A G $$ $$ Bob( private ) : \ d_B $$ $$ ECDH Secret (Alice Bob) = d_B Q_A = d_B d_A G $$
Normal so far...
In some instances, the Producer and Consumer are the same agent, and this ECDH secret devolves into:
$$ ECDH Secret (Alice Alice) = d_A Q_A = d_A d_A G = (d_A)^2G $$
Is this a problem?