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// Copyright 2019 The Tari Project // // Redistribution and use in source and binary forms, with or without modification, are permitted provided that the // following conditions are met: // // 1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following // disclaimer. // // 2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the // following disclaimer in the documentation and/or other materials provided with the distribution. // // 3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote // products derived from this software without specific prior written permission. // // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, // INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE // DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR // SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, // WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE // USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. //! The Merkle mountain range was invented by Peter Todd more about them can be read at: //! https://github.com/opentimestamps/opentimestamps-server/blob/master/doc/merkle-mountain-range.md //! https://github.com/mimblewimble/grin/blob/master/doc/mmr.md //! //! A Merkle mountain range(MMR) is a binary tree where each parent is the concatenated hash of its two //! children. The leaves at the bottom of the MMR is the hashes of the data. The MMR allows easy to add and proof //! of existence inside of the tree. MMR always tries to have the largest possible single binary tree, so in effect //! it is possible to have more than one binary tree. Every time you have to get the merkle root (the single merkle //! proof of the whole MMR) you have the bag the peaks of the individual trees, or mountain peaks. //! //! Lets take an example of how to construct one. Say you have the following MMR already made: //! ''' //! /\ //! / \ //! /\ /\ /\ //! /\/\/\/\ /\/\ /\ //! ''' //! From this we can see we have 3 trees or mountains. We have constructed the largest possible tree's we can. //! If we want to calculate the merkle route we will bag each of the mountains in the following way //! ''' //! /\ //! /\ \ //! / \ \ //! /\ \ \ //! / \ \ \ //! /\ /\ /\ \ //! /\/\/\/\/\/\/\ //! ''' //! Lets continue the example, by adding a single object. Our MMR now looks as follows //! ''' //! /\ //! / \ //! /\ /\ /\ //! /\/\/\/\ /\/\ /\ / //! ''' //! We now have 4 mountains. Lets bag and calculate the merkle root again //! ''' //! /\ //! /\ \ //! /\ \ \ //! / \ \ \ //! /\ \ \ \ //! / \ \ \ \ //! /\ /\ /\ \ \ //! /\/\/\/\/\/\/\ \ //! ''' //! Lets continue thw example, by adding a single object. Our MMR now looks as follows //! ''' //! /\ //! / \ //! / \ //! / \ //! /\ /\ //! / \ / \ //! /\ /\ /\ /\ //! /\/\/\/\/\/\/\/\ //! ''' //! Now we only have a single binary tree, we dont have to bag the mountains to calculate the merkle root. This //! process continues as you add more objects to the MMR. //! ''' //! /\ //! / \ //! / \ //! / \ //! / \ //! / \ //! / \ //! /\ \ //! /\ \ /\ //! / \ \ / \ //! /\ \ \ /\ \ //! / \ \ \ / \ \ //! /\ /\ /\ \ /\ /\ /\ //! /\/\/\/\/\/\/\ /\/\/\/\/\/\ //! ''' //! Due to the unique way the MMR is constructed we can easily represent the MMR as a list of the nodes, as when //! adding nodes you only append. Lets take the following MMR and number the nodes in the order we create them. //! ''' //! 7 //! / \ //! / \ //! 3 6 //! / \ / \ //! 1 2 4 5 //! ''' //! Looking above at the example of when you create the nodes, you will see the nodes will have been created in the //! order as they are named. This means we can easily represent them as a list: //! Height: 0 | 0 | 1 | 0 | 0 | 1 | 2 //! Node: 1 | 2 | 3 | 4 | 5 | 6 | 7 //! //! Because of the list nature of the MMR we can easily navigate around the MMR using the following formulas: //! Jump to sibling : 2^(H+1) -1 //! find peak : 2^(H+1) -2 where < total elements //! left down : 2^H //! right down: -1 //! Note that the formulas are for direct indexes in the array, meaning the nodes count from 0 and not 1 as in //! the examples above. H - Height //! I - Index //! //! Pruning the MMR means flagging a node as pruned and only removing it if its sibling has been removed. //! We do this as we require the sibling to prove the hash of the node. Taking the above example, let's prune leaf 1. //! ''' //! /\ //! / \ //! / \ //! / \ //! / \ //! / \ //! / \ //! /\ \ //! /\ \ /\ //! / \ \ / \ //! /\ \ \ /\ \ //! / \ \ \ / \ \ //! /\ /\ /\ \ /\ /\ /\ //! /\/\/\/\/\/\/\ /\/\/\/\/\/\ //! ''' //! Node 1 has now only been marked as pruned but we cannot remove it as of yet because we still require it to //! prove node 2. When we prune node 2, the MMR looks as follows //! ''' //! /\ //! / \ //! / \ //! / \ //! / \ //! / \ //! / \ //! /\ \ //! /\ \ /\ //! / \ \ / \ //! /\ \ \ /\ \ //! / \ \ \ / \ \ //! /\ /\ /\ \ /\ /\ /\ //! /\/\/\/\/\/\ /\/\/\/\/\/\ //! ''' //! Although we have not removed node 1 and node 2 from the MMR, we cannot yet remove node 3 as we require node 3 //! for the proof of node 6. Let's prune 4 and 5. //! ''' //! /\ //! / \ //! / \ //! / \ //! / \ //! / \ //! / \ //! /\ \ //! /\ \ /\ //! / \ \ / \ //! /\ \ \ /\ \ //! / \ \ \ / \ \ //! /\ /\ \ /\ /\ /\ //! /\/\/\/\/\ /\/\/\/\/\/\ //! ''' //! Now we removed 3 from the MMR pub mod error; pub mod merklemountainrange; pub mod merklenode; pub mod mmr { pub use crate::merklemountainrange::*; }