add initial spec of the merkletree (#10)

* add initial spec of the merkletree

* update gh workflow to work with the new book path

* rephrase non-inclusion section

book/src/merkletree.md

@@ -1 +1,48 @@
 # MerkleTree
+
+In the POD system, MerkleTrees are used to store the key-values of the POD.
+
+- Each leaf contains a touple of `key` and `value`
+- Leaf position is determined by the `key` content binary representation (little-endian)
+
+![](img/merkletree0.png)
+
+So for example, suppose we have the following data in a POD:
+```js
+{
+	id: "11000...",
+	kvs : {
+		idNumber: "424242",
+		dateOfBirth: 1169909384,
+		userPk: 9876543210, // target user of this POD
+		_signerPk: 1234567890, // signer of the POD
+	}
+}
+```
+
+The merkletree will contain the key values from the `kvs` field.
+
+Suppose that the binary representation of the key `userPk` is `1011...`. This uniquely defines the leaf position that contains the public key of the authenticated user.
+
+![](img/merkletree1.png)
+
+
+## Proofs of inclusion and non-inclusion
+Merkle proofs contain the siblings along the path from the leaf to the root, where the leaf position is determined by the key binary representation. 
+
+Since leaf positions are deterministic based on the key, the same approach is used for non-inclusion proofs, where it can be proven that a key is not in the tree, and furthermore, that a value is not in the tree (although the key exists):
+- Proving that the key does not exist in the tree is achieved by generating the merkle-proof for the specific key, and showing that the (virtual) leaf is empty - this is, showing that going down the path of the non-existing key, there is a leaf with a different key, meaning that the non-existing key has not been inserted in the tree.
+- Proving that a value is not in the tree (although the key exists) is achieved by generating the merkle-proof for the specific key, and showing that the leaf exists but it has a different value than the one being proved.
+
+
+
+## Encoding
+> TODO: how key-values, nodes, merkle-proofs, ... are encoded.
+
+## Temporary first version
+The first iteration of the implementation uses a hash of the key-values concatenated, with the idea of replacing it by the MerkleTree approach described above.
+
+
+## Resources
+- [https://docs.iden3.io/publications/pdfs/Merkle-Tree.pdf](https://docs.iden3.io/publications/pdfs/Merkle-Tree.pdf)
+- [https://eprint.iacr.org/2018/955](https://eprint.iacr.org/2018/955)