Merkle mountain range

Merkle mountain range in C.

You can check unit tests to learn the usage.

Construct

# An 11 leaves MMR

          14
       /       \
     6          13
   /   \       /   \
  2     5     9     12     17
 / \   /  \  / \   /  \   /  \
0   1 3   4 7   8 10  11 15  16 18

In MMR, we use the insertion order to reference leaves and nodes. we inserting a new leaf to MMR by the following:

insert leaf or node to next position.
if the current position has a left sibling, we merge the left and right nodes to produce a new parent node, then go back to step 1 to insert the node.

For example, we insert a leaf to the example MMR:

insert leaf to next position: 19.
now check the left sibling 18 and calculate parent node: merge(mmr[18], mmr[19]).
insert parent node to position 20.
the node 20 also has a left sibling 17, calculate parent node: merge(mmr[17], mmr[20]).
insert new node to next position 21.
the node 20 have no left sibling, complete the insertion.

Example MMR after insertion of a new leaf:

          14
       /       \
     6          13            21
   /   \       /   \         /   \
  2     5     9     12     17     20
 / \   /  \  / \   /  \   /  \   /  \
0   1 3   4 7   8 10  11 15  16 18  19

Merkle root

An MMR is constructed by one or more sub merkle trees (or mountains). Each sub merkle tree's root is a peak in MMR, we calculate the MMR root by bagging these peaks from right to left.

For example, we have a MMR with 3 peaks: 14, 17, 18, we bagging thses peaks from right to left to get the root: merge(merge(mmr[18], mmr[17]), mmr[14]).

Merkle proof

The merkle proof is an array of hashes constructed by the follows parts:

A merkle proof from the leaf's sibling to the peak that contains the leaf.
A hash that bagging all right-hand side peaks, skip this part if no right-hand peaks.
Hashes of all left-hand peaks, the from right to left, skip this part if no left-hand peaks.

We can reconstruct the merkle root from the proofs. Pre calculate the peaks positions from the size of MMR may help us do the bagging.

References

LICENSE

MIT

AUTHOR

Jiang Jinyang jjyruby@gmail.com

jjyr / mmr-c