Security Question

[Eadeqa]

Hi,

Just a question

I know that the master seed is created randomly with 128-bit entropy. All the private and change keys are derived from the master seed; so all your keys are related to each other in some mathematical way.

Now, if someone sends bitcoins to internal private key, would it be possible someday (theoretically) that some hacker who looks at the transaction between two of your internal keys on blockchain would be able to figure out the private keys because of that mathematical relation between the two keys?

Has this been looked at deeper? So lets say the transaction happened between 2 keys that were connected by publicly known mathematical function (as is the case with Electrum keys).  Could this create a security hole?