Address generator for Bitcoin wallet
A previous draft of BIP0032 did this, actually. (Sorry about linking to the bitcoin wiki - that change was made before we switched over to git for BIP tracking.)

According to the changelog, it was done for speed reasons.


  
  [30 Apr 2013] Switched from multiplication by IL to addition of IL (faster, easier implementation)
  


It's much faster when deriving a child private key from a parent private key. The new method requires only a normal addition (mod n) rather than an ECDSA point multiplication.

It's not faster when deriving a child public key from a parent public key. That still requires an ECDSA multiplication followed by an ECDSA addition. (In fact, it's about 2% slower.)

Using addition does not add any security issues. It's possible to get a parent private key from a child private key and an extended public key, but that would also be true if multiplication was used.