PUPoW A F RAMEWORK FOR DESIGNING BLOCKCHAINS WITH PRACTICALLY -USEFUL -PROOF -OF-WORK VanityCoin

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PUPoW:AFRAMEWORK FOR DESIGNING BLOCKCHAINS WITH

PRACTICALLY-USEFUL-PROOF-OF-WORK

& VanityCoin

Yash Chaurasia

International Institute of Information Technology

yash.chaurasia@research.iiit.ac.in

Visvesh Subramanian

International Institute of Information Technology

visvesh.subramanian@research.iiit.ac.in

Sujit Gujar

International Institute of Information Technology

sujit.gujar@iiit.ac.in

ABSTRACT

Bitcoin is the ﬁrst of its kind, a truly decentralized and anonymous cryptocurrency. To realize it, it

has developed a blockchain technology using the concept of ‘Proof of Work’ (PoW). The miners,

nodes responsible for writing transaction database, solve a cryptographic puzzle to claim the right

to write to the database. Though bitcoin and many other relevant cryptocurrencies such as ether use

revolutionary ideas, the main criticism involves the computing resource and energy consumption to

solve the puzzles that have otherwise no use. There are attempts to use the PoW to do something

useful, commonly referred to as Proof-of-Useful-Work (PoUW). In this paper, we attempt to (i)

make PoUW more usable – describe how a central problem setter can crowdsource their work as

PoUW and (ii) in the true spirit of blockchains, decentralize the role of problem setter, whom we

call puzzlers. We propose a formal framework to do so, namely PUPoW.PUPoW has an inbuilt

provision of payments from puzzler to the miner who solves its puzzle. Additionally, miners have

the option to not rely on continuous feed of the puzzles and instead use original PoW puzzles.

We also propose a way to use PUPoW for solving TOR vanity URL generation and bitcoin vanity

address generation problems. We call this PUPoW blockchain solving vanity address generation

problems as VanityCoin. Both the problems require generating public keys from private keys such

that resultant addresses are of interest. Such key pairs are found only by a brute force search.

However, there are privacy concerns that miners would know the private keys of the puzzlers. We

resolve this by splitting the private keys, and the miners would know only one part of it. In summary,

we are proposing how PoW can be made practically useful, and we believe such an approach is

needed for PoW blockchains to survive.1

1 Introduction

Bitcoin: A Peer-to-Peer Electronic Cash System [19], published in 2008, introduced us to blockchain and Nakamoto

consensus. A blockchain is a decentralized and distributed chain of blocks such that each block stores the hash

of the previous block, thereby prohibiting any changes in the committed blocks once newer blocks are published.

Bitcoin solved many problems in the online currency systems by using Proof-of-Work (PoW) as the mechanism to

achieve consensus. Miners, who maintain the blockchain, try to publish blocks to earn mining rewards by solving

a computationally intensive cryptographic puzzle. With PoW, bitcoin proved that eventual distributed consensus is

possible under mild technical assumptions.

1The preliminary version was presented at IEEE Blockchain 2021

arXiv:2210.06738v1 [cs.CR] 13 Oct 2022

PUPoW: A Framework for Designing Blockchains with Practically-Useful-Proof-of-Work

& VanityCoin

One of the key factors in PoW is that the probability of a miner mining a block is equal to the fraction of the entire

network’s computational power held by them. Consequently, miners keep investing in these resources as long as it

is proﬁtable to do so. Apart from establishing consensus in Bitcoin’s network, the solutions to these puzzles have

no use. These two factors combined mean that a lot of electricity (120 TWh per year [12]) and hardware resources

(91 ×1018 Hashes per second [1]) are spent just to mine Bitcoin, with no other useful work done. The total electricity

used in mining bitcoin exceeds the electricity consumption of many countries [12], which has been a major criticism

of Bitcoin. This criticism also had been one of the major reasons for the crypto-crash in May 2021 [13, 20], reducing

the public trust in all cryptocurrencies in general, even those not relying on PoW for consensus. If the total hardware

resources invested in Bitcoin mining also produce useful work, any supercomputer built in the foreseeable future won’t

parallel the network’s capability. The implications will be profound depending on how useful the problem being solved

is.

Currently, researchers are investigating if this computational intensive process of achieving consensus can be made

useful. Primecoin [14] requires miners to produce a Cunningham chain or bi-twin chain of some length decided by the

computation power of the network as proof-of-work. Though these chains of primes generated as PoW in Primecoin

are available to everyone for use, its practical applications are limited. PermaCoin [18] replaces proof of work with

proof of retrievability. The idea proposed here ensures that participating nodes store a very large data-set (like a library

of books) in a distributed manner. Proofs of Work From Worst-Case Assumptions [17] gives proof-of-work based on

problems like Orthogonal Vector, 3SUM, All-Pairs Shortest Path, and other problems which reduce to them. A Proof

of Useful Work for Artiﬁcial Intelligence on the Blockchain [16] describes a protocol that lets clients to submit Machine

Learning tasks to the miners and pay all the actors involved in the process (miners, supervisors, and evaluators) if the

model is satisfactory. Miners get to mine with some nonce after every iteration. The problem solved here is not easily

veriﬁable and regular nodes only check if the hash is less than the network target T.Proof of Learning (PoLe) [15]

is a consensus algorithm having data nodes and consensus nodes to do ML on blockchain. Data nodes push training

requests and consensus nodes choose the request with highest reward/time value to train. The model with the highest

test accuracy wins and the corresponding block is published. Gridcoin [11] is a proof-of-stake blockchain that awards

gridcoins to individuals contributing to BOINC white-listed crowdsourcing projects. In Coin.AI [10], miners must

design a neural network instead of solving the hash puzzle. The previous hash, the nonce, and the list of transactions

determine a neural network architecture. A miner trains this model on a publicly agreed-upon data-set. Any model

which crosses a threshold is valid. These works are often referred to as Proof-of-Useful-Work (PoUW), the work that

is used for two purposes: (i) to solve some useful problems, and (ii) to prove that some problem is solved to use as

PoW to maintain a distributed ledger.

The PoUW-based blockchains are limited at this point as (i) they propose a very speciﬁc problems which leads to

solving limited types of useful problems. (ii) Some proposals involve centralized administrator and data sharing (e.g.,

Coin.AI or Permacoin) with the miners. (iii) A currency built on top of such blockchain should continue to be useful

forever. At this point, it is not clear that in the absence of any problem to be solved how these blockchains will

continue. There is a need for a formal approach to build a PoUW protocol that leverages PoW concepts and the work

done for achieving consensus on the blockchain has some usefulness in the real world.

Contributions: In this work, we list important characteristics of the problem that one can use to build a PoUW

blockchain, namely, Easy Veriﬁability, Adjustable Difﬁculty, Proportional Advantage, and Non-reusable. These es-

sentially capture the fact that the problem should be hard to solve but a solution should be easy to verify, we should

be able to adjust the difﬁculty easily, the chance of solving should be proportional to the computing power, and the

solution to one problem in a previous block cannot be reused in another block. With these, we propose a framework

in Section 3 to build a PoUW based blockchain with a center, whom we call problem setter, that sets up the problem

to be solved. However, in the true spirit of decentralization, it is better to have a decentralized system where anybody

can participate as a problem setter. In decentralized PoUW, we refer to them as puzzler, provided the problem they

set meets the desired conditions. Towards this, we propose a framework, PUPoW, a decentralized PoUW blockchain

framework. Key interesting features of our framework are (i) anybody can be a puzzler, (ii) in the absence of problems

to solve, it can revert to a normal PoW blockchain, (iii) provision of puzzlers rewarding miners (thereby reducing the

importance of transaction fees). We illustrate how to use PUPoW with an interesting problem, speciﬁcally, generating

vanity .onion URL. One can use a similar technique for generating vanity addresses in bitcoin and other applications

using DSA-like scheme to generate addresses. We refer to a PUPoW blockchain generating vanity addresses for

proof-of-work as VanityCoin.

PUPoW: A Framework for Designing Blockchains with Practically-Useful-Proof-of-Work

& VanityCoin

2 Notations & Deﬁnitions

2.1 Bitcoin’s Proof-of-Work Puzzle

An online decentralized currency needs a mechanism to achieve consensus considering that the system will have

some malicious participants. Satoshi Nakamoto brought a revolution in online currency systems by introducing

Proof-of-Work protocol which achieves consensus in the network and is also safe against attackers having less than

50% of the network’s computing power. Miners get to accept and publish valid transactions on their blocks but to

publish their block they need to solve a partial hash pre-image puzzle, i.e., the hash of their block header should be

less than some target.

H(nonce||prevhash||merkleroot||timestamp||version||target)< t

The target tis adjusted after every 2016 blocks so that the average block publishing rate remains ∼1 block per 10

minutes. To try out different hashes, the miners change the nonce ﬁeld. The block header also has a ﬁeld for the hash

of the previous block’s header, also known as hash pointer. We discuss components of Bitcoin-like blockchains next.

2.2 Blockchain Components

•Blocks: These contain the transactions in a Merkle tree and the block header.

•Block header: This contains the hash of the previous block, Merkle root of the transactions, timestamp, nonce,

version and target.

•Transactions: Each transaction contains inputs and outputs. Inputs typically have signatures and public keys.

Outputs have scripts depending on the usage.

• Merkle Tree: All the transactions are contained outside the block header of the block and arranged in a Merkle

tree. The Merkle root is committed in the block header.

• Transaction mempool: Valid transactions generated by the users are relayed to other users/miners. Transac-

tion mempool is where valid transactions wait to be conﬁrmed.

2.3 Hash function H

A hash function Htakes an input iand outputs hash hwith nbits. For our purpose, the input will be the block header

of the block. We write this as H(block header), where

block header = (nonce||prevhash||merkleroot||timestamp||version||target)

in the case of Bitcoin. It is possible to build a hash function outputting hash of any required length n.

2.4 Actors in our framework

Miners: Actors who solve the problem to be able to publish their block are called miners. They receive ﬁxed mining

rewards for publishing a block and a variable problem and transaction fee based on the problem/transactions chosen.

Users: Full nodes and Light nodes which only focus on transactions happening on the blockchain are called users.

Problem setter: In the centralized scenario, the authority responsible for setting the problem for the miners to solve

is called the problem setter.

Puzzlers: In the decentralized scenario, the actors who propose their problems to be solved are called puzzlers.

2.5 Practically Useful Work

A lot of effort has been put to identify useful algorithmically generated problems, but limited success has been

achieved. We thus deﬁne a practically useful problem to be one that is proposed by an individual/organisation, a

problem for which the individual/organisation might be willing to pay to get solved. For example, the primecoin

protocol won’t be considered as a practically useful PoW under this deﬁnition, but if a puzzler requests to get a

Cunningham chain, this will be considered a practically useful problem. Practically-Useful-Proof-of-Work (PUPoW)

framework shows how such practically useful problems can be used in place of Bitcoin’s puzzle as Proof-of-Work.

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PUPoW:AFRAMEWORKFORDESIGNINGBLOCKCHAINSWITHPRACTICALLY-USEFUL-PROOF-OF-WORK&VanityCoinYashChaurasiaInternationalInstituteofInformationTechnologyyash.chaurasia@research.iiit.ac.inVisveshSubramanianInternationalInstituteofInformationTechnologyvisvesh.subramanian@research.iiit.ac.inSujitGujarInternatio...

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PUPoW A F RAMEWORK FOR DESIGNING BLOCKCHAINS WITH PRACTICALLY -USEFUL -PROOF -OF-WORK VanityCoin

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