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child. The left-half 256 bits of the hash and the index number are added to the parent private key to produce the child private key. In the diagram below, we see this illustrated with the index set to 0 to produce the 0’th (first by index) child of the parent. Figure 4-11. Extending a parent private key to create a child private key Changing the index allows us to extend the parent and create the other children in the sequence, e.g. Child 0, Child 1, Child 2 etc. Each parent key can have 2 billion children keys. Repeating the process one level down the tree, each child can in turn become a parent and create its own children, in an infinite number of generations. Using derived child keys Child private keys are indistinguishable from non-deterministic (random) keys. Be‐ cause the derivation function is a one way function, the child key cannot be used to find the parent key. The child key can also not be used to find any siblings. If you have the nth child, you cannot find its siblings, such as the n-1 child or the n+1 child, or any other children that are part of the sequence. Only the parent key and chain code can derive all the children. Without the child chain code, the child key cannot be used to derive any grandchildren either. You need both the child private key and the child chain code to start a new branch and derive grandchildren. So what can the child private key be used for on its own? It can be used to make a public key and a bitcoin address. Then, it can be used to sign transactions to spend anything paid to that address. Wallets | 91PDF Image | Mastering Bitcoin
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