Bitcoin and Cryptocurrency Technologies

The cryptographic magic that makes this useful is that for every ​i​, the ​i​’th address and ​i​’th secret key
“match up” — that is, the ​i​’th secret key controls, and can be used to spend, bitcoins from the ​i​’th
address just as if the pair were generated the old fashioned way. So it’s as if we have a sequence of
regular key pairs.
The other important cryptographic property here is security: the address generation info doesn't leak
any information about the private keys. That means that it's safe to give the address generation info
to anybody, and so that anybody can be enabled to generate the 'i'th key.
Now, not all digital signature schemes that exist can be modified to support hierarchical key
generation. Some can and some can't, but the good news is that the digital signature scheme used by
Bitcoin, ECDSA, does support hierarchical key generation, allowing this trick. That is, the cold side
generates arbitrarily many keys and the hot side generates the corresponding addresses.
Figure 4.2: Schema of a hierarchical wallet​. The cold side creates and saves private key generation
info and address generation info. It does a one-time transfer of the latter to the hot side. The hot side
generates a new address sequentially every time it wants to send coins to the cold side. When the
cold side reconnects, it generates addresses sequentially and checks the block chain for transfers to
those addresses until it reaches an address that hasn’t received any coins. It can also generate private
keys sequentially if it wants to send some coins back to the hot side or spend them some other way.
Here’s how it works. Recall that normally an ECDSA private key is a random number ​x​and the
corresponding public key is ​g​ x​ . For hierarchical key generation, we’ll need two other random values ​k
and ​y​.
105