I need to distribute a shared 256 bit key to 100's or 1000's of nodes (I have the public key of each node).
There's no networking involved - this will all be done by loading a single file on to each node. That file is generated by a "master".
In some cases, the nodes use 2048-bit RSA keys, and others it is a p521 Elliptic Curve key.
The idea is to create a line for each node in the distributed file encrypting the shared key.
If the node uses EC, then the node's public EC and the master's private EC keys are used to generate a symmetric key which is used to encrypt the shared key . The encrypted shared key and signature generated by the master are stored on a line in the file. The node would then loop through each line in the file, use the master's public EC key and its own private EC key to generate the same symmetric key, decrypt the data, then check the signature. If correct, then that is the shared key.
If the node uses RSA, then the shared key would be encrypted with the node's public RSA key, and a signature generated by the master and both stored on a line in the file. The node would then loop through each line in the file, use its private RSA key to decrypt the data, then check the signature. If correct, then that is the shared key.
My worry is that does knowing that a single piece of data being encrypted with 1000 different keys give an attacker a significant advantage for deriving a private key?