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I want to create an encrypted paper backup, and to do so I'm thinking about encrypting only the root key and the chain code, so that when I have to recover it, I don't have to type a lot.

But I'm wondering if leaving the unique ID unencrypted can give any sort of information about the wallet to the person who finds it, like what kind of pattern to look for, or how much bitcoin there is in the wallet.

For example, it's been said that for extra security, you shouldn't have your savings in a address if its public key is known, because in the future the private key could be found by using quantum computing or whatever. I know the unique ID is a different thing, but still I want to know what it is, how it is generated, etc.

Another way to ask the question: What do I need the unique ID for in the paper backup, if all I need to recover it is the root key and the chain code? Can't I just remove the unique ID from the paper backup? Would that be theoretically more secure?

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According to the source code the wallet ID is an address byte and the last 5 bytes of the first address, encoded as base 58. The last 4 bytes of the address are part of a SHA-256 hash of the first part of the address. The address itself is the private key hashed once with SHA-256 and once with RIPEMD-160. So the only information contained in the Wallet ID is checksum information, which is also contained in your publicly available address. The address is available since it is the one you transferred your coins to.

I'm pretty certain that having the wallet ID visible isn't going to leak any information.

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