Great article! Love the focus on implementing. Fingers crossed he will explain PQ signatures like SPHINCS+ as a follow up.
There is a good talk given out by a NIST guy that starts from the simplest one time hash signature construction and builds up to XMSS/SPHINCS: <https://www.youtube.com/watch?v=jiU0ICoiPI0>
TLDR;
SPHINCS+ is a hypertree of Merkle trees where leafs of Merkle trees are used to sign Merkle roots of other Merkle trees. Leafs of the hypertree (final layer of Merkle trees) are used to sign messages.
Paths through the hypertree need only be constructed on demand through the use of a PRF - computing paths through the hypertree requires computing entire Merkle trees. The private key is just a secret key to a PRF.
A hypertree can be as big as you want it. Merkle roots are parts of the public key and public signatures and can only be determined through computation, if the Merkle tree is too big you will not compute the root in reasonable time.
> Paths through the hypertree need only be constructed on demand through the use of a PRF - computing paths through the hypertree requires computing entire Merkle trees. The private key is just a secret key to a PRF.
Wow, thank you so much. Such a perfect match between exactly what I didn't know described in terms I do. "Cool. Now I could write a high performant SPHINCS+ c++ impl, if i ever wanted to or thought it was cool" :D
Edit: I love it when stuff like that happens, it's the reason I still bother to read the comments on this website.
I/we've all got our own unique decades of experience and collection of earned wisdom, and sometimes substantial technological progress happens when the right people get the right "holes in understanding" filled at the right time.