Conquering Generals: an NP-Hard Proof-of-Useful-Work Angelique Faye - - PowerPoint PPT Presentation

Conquering Generals: an NP-Hard Proof-of-Useful-Work

Angelique Faye Loe Information Security Group angelique.loe.2016@rhul.ac.uk Elizabeth A. Quaglia Information Security Group elizabeth.quaglia@rhul.ac.uk

Introduction

Information Security Group

• Proof-of-Work algorithms are used to establish consensus in

distributed untrusted Peer-to-Peer systems, such as cryptocurrencies

• The most widely deployed PoW is based on Hashcash, which

is used by Bitcoin

• The Hashcash scheme has 2 commonly identified issues:
• 1. The electrical energy consumption of the scheme has

attracted criticism

• 2. The ‘Hardness’ of the scheme does not belong to a known

computational complexity class

Goals

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• Address the energy consumption by devising a two-round

Hybrid Proof-of-Useful-Work

• Address the heuristic notion of ‘Hardness’ by offering a well

known NP-Hard problem for the Proof-of-Useful-Work

• We opt to construct an instance of the Travelling

Salesman Problem (TSP)

• Identify and address another waste issue, by highlighting the

capital expenditure into ASIC mining Hardware

Energy Usage and Hashrate Growth

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Bitcoin Energy Consumption Index

Related Work: PoW Variants

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Our Contribution

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• Differentiate our PoUW as

the first to consider a hybrid approach to include ASIC based miners

• Calculations show that CapEx
• n ASIC mining hardware is

circa 4.3 Billion USD, - not counting the data centre hardware!

Conquering Generals

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• Conquering Generals is a Hybrid two round

Proof-of-Useful-Work

• Overview of the Proof-of-Useful-Work:

1. Runs on a 10 min deterministic mining interval 2. The first round is the Hashcash round 3. The second round is the NP-Hard TSP round

Constituent Algorithms

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• Three Algorithms make up the PoUW

scheme:

• 1. Gen: generate challenge
• 2. Solve: solution to challenge
• 3. Verify: validate solution
• Gen & Verify run in polynomial time
• Hashcash round: Solve is heuristically

believed to run in O(2n) time

• TSP round: Solve algorithm is one (or

more) algorithms which may be selected or designed by the miner

Round 1: Hashcash

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• {1,…,m} miners will perform the PoW
• Gen1: Create a challenge based on Candidate Block
• Solve1: Perform a double iterated SHA256 hash on the

Block Header & concatenate a nonce

• Submit lowest hash/solution after 3 minutes to other

miners (this limits the energy usage of the ASIC miners)

• Verify1 algorithm: run on each of the {1,…,m-1} solutions
• Sort each sound solution and extract the min value
• The min value in Round 1 will be used in Round 2

Round 2: Construct a TSP instance

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• Gen2 will create a challenge as follows:

1. Recursively double SHA256 hash the min solution for Round 1, n times. (where n is the number of cities on the TSP instance, and also the difficulty parameter) 2. Extract the 128 LSB’s from each of the n hashes to act as x and y coordinates on a 2^64 x 2^64 Euclidean Plane 3. Calculate l

l

2 norms for each n(n-1)/2 edges on a

complete graph 4. Construct a graph distance matrix

• Submit lowest solution after 4 minutes to other

miners

• Sort received solutions and extract min2 value
• Verify2 will validate the permutation of n cities and

associated sum of min2

• If min2 a Valid solution, Increment Block Number,

Mint Currency (for winning miner), Commit Transactions and Loop to create next Block

• Solve2 will then run and find a solution consisting of

the permutation of cities providing the min tour distance (sum) via all cities, returning to the starting city

Toy Example

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The Name ‘Conquering Generals’

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• Conquering Generals comes from the merger of two problems
• 1. The Travelling Salesman Problem
• 2. The Byzantine Generals Problem
• A group of Generals have a conquering mission
• Initially, the Hashcash round represents the reconnaissance to determine which

cities to conquer

• Subsequently, the TSP round represents the optimal order in which they wish

to launch their mission ensuring an optimal path is taken

• Instead of the innocuous Salesman, we have a group of Conquering Generals

Conclusion

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• We have presented a concept for a Proof-of-Useful-Work which mitigates the

potential loss of 4.3 Billion USD on ASIC hardware

• It addresses electrical energy usage by limiting the Hashcash stage to 3 minutes
• It also addresses electrical energy usage by introducing a fiscally incentivised

platform to engage in algorithm research and design for the NP-Hard TSP. This dovetails into addressing the heuristic ‘Hardness’ issue associated with Hashcash.

• We finally recall that: ‘NP-Complete problems have the intriguing property that

if any NP-Complete problem can be solved in polynomial time, then EVERY problem in NP has a polynomial time solution, that is P = NP’