bump, please answer, this is important!
Good question. Have you Googled on this topic? BIP32, k values, etc. ?
My understanding is that only one Private - Public key pair is created with BIP32. From these, decendents are created. Therefore, the "k" value occurs only once.
I didnt know there was a BIP in it. So i have to look it up, but i`d prefer if somebody with electrum code knowledge would answer it.
There is a K value created every time a transaction occurs from a wallet. Thats how a transaction chain is formed, and it links your previous spendings from thad address to the new one.
And of course if the RNG is compromized, the K value will leak info about the private key.
So its imperative to have a random, yet deterministic signature for every transaction, to not rely on flawed hardware RNG
Here was a question asked 1 year ago, and back then the wallets havent got it:
http://bitcoin.stackexchange.com/questions/36127/problems-with-deterministic-ecdsa-based-on-rfc6979-in-bitcoin