This repository contains an implementation of an algorithm called FTS-TREE which can be used to sample block leaders from a set of stakeholders stored in a Merkle tree. The algorithm builds upon an idea called follow-the-satoshi introduced in [1].
The idea is simple: The edges the Merkle tree are labelled with the amount of coins in the left and right subtree respectively. Given a psuedo-random number generator, one can randomly select a stakeholder from the tree, weighted by the amount of coins they own, by traversing the tree down to a leaf node, containing one of the stakeholders. Each stakeholder controls a number of coins and a private key used to sign blocks.
The image above shows a Merkle tree with eight stakeholders (yellow nodes), controlling a total of 95 coins. The nodes highlighted in green are the nodes visited after an execution of FTS-TREE where stakeholder A4 was chosen as the next block leader.
The siblings to the nodes traversed by FTS-TREE constitutes a Merkle proof which can be used to prove that the stakeholder was chosen correctly. This Merkle proof can then be put into the block header of the block and other blockchain nodes can use the Merkle root hash of the tree to verify the block.
This makes it possible to prune away old transactions and still be able to verify old blocks, enabling a lightweight blockchain scheme based on proof of stake.
It is fairly easy to prove that FTS-TREE is fair. More precisely; given a Merkle tree with N stakeholders, containing a total of x1 + x2... + xN coins, FTS-TREE selects the k:th stakeholder 1 ≤ k ≤ N controlling xk coins with probability xk / (x1 + x2... + xN).
Example output from FTS-TREE
Creating Merkle tree with 15 nodes.
Hash 1: 04CA42FBD140569E6B647B13DDAC3D85B9626FD0B2D98AE6717EBA5B96EB0CCE
Hash 2: 0FF2AA9DF6C8845E89A8952A4EC5C74E64FFA39E2813C3D22EB9D31DDE1DE39A
Hash 3: 7333612E8DD6A02C9B0595E27B537851FCB27B44FF25FFBC024BF554C3E9B939
Hash 4: AE0668DDE2F58A9E913480D0B5D3F4F15C4A4945068DD524D9D4B9BFB6480F3E
Hash 5: 2F4DE43A312F30EA4303F1088E6F4D6EBEB4FFFECF669286423AD2C4D2A3AC18
Hash 6: 3EF21DAF7CB37B8E68929872C4132E9021812CC3DE60A5C4345541728CECCE50
Hash 7: 44E8B580F897CCAA525E7CA6E05D07350F53681FB4D6B4223032C0D6FBFE9537
Hash 8: 3AF7519C8A2EDE05A8F5E63041824B453EF989ED616FD80F99A7043DA4303E24
Hash 9: 67BEBFBB2B7A3312E1C330A5E904FE6B24868D30CB1E78DA16C13C25FE0F7E64
Hash 10: 33C51A085F5A65ADB2A6096D8140CBF8E9AFA635D384C2C393A66C262112835B
Hash 11: 36195B3A1FE4BFAD55817C40C2041B0EF98005BAE6C79F7DE21BF190801A2A56
Hash 12: 4F171E075FB62B62EBDA820D3FFCA8287922FEE53710D8FEACD42DEAD202C29B
Hash 13: D0D8072D186E08048C23B3E92C80F1AB50DD61F8A7E2E8910B64E757A604B604
Hash 14: 35F9843C6BF03C26052F4589CF2F11F4A709A02CBC4035E2941E34A2E5B5BA16
Hash 15: BC1D39F92E64DB7005809B17E2A79FC181BC929968FEAE7B6393420768AFB419
Doing follow-the-satoshi in the stake tree
Left subtree 51 coins / right subtree 15 coins. Picking coin number 63
Choosing right subtree...
Left subtree 12 coins / right subtree 3 coins. Picking coin number 4
Choosing left subtree...
Left subtree 8 coins / right subtree 4 coins. Picking coin number 1
Choosing left subtree...
merkleProof {
...(0FF2AA9DF6C8845E89A8952A4EC5C74E64FFA39E2813C3D22EB9D31DDE1DE39A, 51, 15)
...(44E8B580F897CCAA525E7CA6E05D07350F53681FB4D6B4223032C0D6FBFE9537, 12, 3)
...(D0D8072D186E08048C23B3E92C80F1AB50DD61F8A7E2E8910B64E757A604B604, 8, 4)
}
stakeholder {
...Stakeholder 4
}
Verifying the result
Building audit path... 1 0 0 OK
Next hash: 3EF21DAF7CB37B8E68929872C4132E9021812CC3DE60A5C4345541728CECCE50
Next hash: 7333612E8DD6A02C9B0595E27B537851FCB27B44FF25FFBC024BF554C3E9B939
Next hash: 04CA42FBD140569E6B647B13DDAC3D85B9626FD0B2D98AE6717EBA5B96EB0CCE
Root hash matches!
[1] Bentov, Iddo, et al. "Proof of Activity: Extending Bitcoin's Proof of Work via Proof of Stake [Extended Abstract] y." ACM SIGMETRICS Performance Evaluation Review 42.3 (2014): 34-37.