I am sill checking how it works to find out if I can generate the priv key for an "i" without having to calc all the priv keys in the sequence.
Let me know if u figure out how they do this, plz. If u can create a new public key without knowledge of the corresponding private key... it's something awesome. Or insecure, coz 2 consecutive public keys would reveal ur private key.
asked that question last year and an electrum dev answered me here
https://bitcointalksearch.org/topic/question-the-security-of-disclosing-mpk-and-gap-limit-security-332500.
granted that weakens the security of the keys but not significantly that they become insecure. I agree with you it is futile to search for a way to reproduce the priv of an arbitrary "i" instantly, that would mean the generating hashing function is basically broken, And that means such thing doesn't exist in electrum.
Now for nxt that would be awesome it means we can make the passphrase generate numerious account numbers and the client can track them all BUT, there is the "gap limit issue".
Basically you cannot know when the addresses will replicate but it is VERY unlikely, so how would you know which addresses are in use? What electrum does is you have to tell it that you use for example up to 100 addresses so when you regenerate the wallet from seed it generates the first 100, But what if you used the 101? The client will have no idea unless you tell it to look beyond 100 keys.
So I got you interested?
. Lets make this happen.
Basically my exchange is delayed mainly because of this, right now NXT is hot on the server which I do not like, Bitcoin is 100% cold and withdrawals are automated with an external requests fetcher. This feature would be so awesome to make this easy for alot of things
.