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  • Intro
    • Welcome
    • The Benefits of BSV Blockchain
    • What Can I Do?
    • Overview of GitHub repositories
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  • Protocol
    • Introduction
    • BSV Blockchain
      • Blocks
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      • Table of Contents
      • Background to the Rules
      • PART I - MASTER RULES
      • PART II - GENERAL RULES
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          • Creating a Simple Transaction
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          • Creating the R-puzzle Script Template
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      • Python
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  • BSV Academy
    • Getting Started
    • BSV Basics: Protocol and Design
      • Introduction
        • Bit-Coin
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      • Introduction
      • About BSV Blockchain
        • Introduction
        • Safe, Instant Transactions at a Predictably Low Cost
          • Reliably Low Fees
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          • Big Blocks Show Big Potential
        • A Plan for Regulatory Acceptance
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      • Technical Details
        • The Network
          • The Small World Network
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        • The Bitcoin SV Node Client
          • Teranode - The Future of BSV
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    • Hash Functions
      • What are Hash Functions?
        • The Differences Between Hashing and Encryption
        • The Three Important Properties of Hash Functions
        • The Hash Functions Found in BSV
      • Base58 and Base58Check
        • What is Base58 and Why Does Bitcoin use it?
        • What is Base58 and How Does BSV use it?
      • SHA256
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    • Merkle Trees
      • The Merkle Tree
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      • Merkles Trees in BSV
        • The Data Elements
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      • Merkle Trees and the Block Header
        • What is the Block Header
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        • Broadcasting the Block
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      • Standarised Merkle Proof
        • What is a Merkle Proof?
        • The BSV Unified Merkle Path (BUMP) Standard
        • Simple and Composite Proofs
      • Merkle Trees and Simplified Payment Verification
        • SPV
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    • Digital Signatures
      • What are Digital Signatures
        • Background
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      • ECDSA Prerequisites
        • Disclaimer
        • Modular Arithmetic
        • Groups, Rings and Finite Fields
        • Discrete Logarithm Problem
        • Elliptic Curve Cryptography (ECC)
        • Discrete Logarithm Problem with Elliptic Curves
      • ECDSA
        • Introduction
        • ECDSA
        • Further Discussion
      • BSV and Digital Signatures
        • Introduction
        • BSV Transaction
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        • Summary
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    • BSV Theory
      • Abstract
        • Peer-to-Peer Cash
        • Digital Signatures and Trusted Third Parties
        • Peer-to-Peer Network
        • Timechain and Proof-of-Work
        • CPU Power
        • Cooperation in the Network
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        • Messaging Between Nodes
      • Introduction
        • Commerce on the Internet
        • Non Reversible Transactions
        • Privacy in Commerce
        • The Paradigm of Fraud Acceptance
        • What is Needed...
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        • Security and Honesty
      • Transactions
        • Electronic Coins
        • Spending a Coin
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        • First Seen Rule
        • Broadcasting Transactions
        • Achieving Consensus
        • Proof of Acceptance
      • Timestamp Server
        • Timestamped Hashes
        • A Chain of Timestamped Hashes
      • Proof of Work
        • Hashcash
        • Scanning Random Space
        • Nonce
        • Immutable Work
        • Chain Effort
        • One CPU, One Vote
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        • Attacking the Longest Chain
        • Controlling the Block Discovery Rate
      • Network
        • Running the Network
        • The Longest Chain
        • Simultaneous Blocks
        • Breaking the Tie
        • Missed Messages
      • Incentive
        • The Coinbase Transaction
        • Coin Distribution
        • Mining Analogy
        • Transaction Fees
        • The End of Inflation
        • Encouraging Honesty
        • The Attacker's Dilemma
      • Reclaiming Disk Space
        • Spent Transactions
        • The Merkle Tree
        • Compacting Blocks
        • Block Headers
      • Simplified Payment Verification
        • Full Network Nodes
        • Merkle Branches
        • Transaction Acceptance
        • Verification During Attack Situations
        • Maintaining an Attack
        • Invalid Block Relay System
        • Businesses Running Nodes
      • Combining and Splitting Value
        • Dynamically Sized Coins
        • Inputs and Outputs
        • A Typical Example
        • Fan Out
      • Privacy
        • Traditional Models
        • Privacy in Bitcoin
        • Public Records
        • Stock Exchange Comparison
        • Key Re-Use
        • Privacy - Assessment 2
        • Linking Inputs
        • Linking the Owner
      • Calculations
        • Attacking the Chain
        • Things the Attacker Cannot Achieve
        • The Only Thing an Attacker Can Achieve
        • The Binomial Random Walk
        • The Gambler's Ruin
        • Exponential Odds
        • Waiting For Confirmation
        • Attack Via Proof of Work
        • Vanishing Probabilities
      • Conclusion
        • Conclusion Explained
    • Introduction to Bitcoin Script
      • Chapter 1: About Bitcoin Script
        • 01 - Introduction
        • 02 - FORTH: A Precursor to Bitcoin Script
        • 03 - From FORTH to Bitcoin Script
        • 04 - Bitcoin's Transaction Protocol
        • 05 - Transaction Breakdown
        • 06 - nLockTime
        • 07 - The Script Evaluator
      • Chapter 2: Basic Script Syntax
        • 01 - Introduction
        • 02 - Rules Around Data and Scripting Grammar
        • 03 - The Stacks
      • Chapter 3: The Opcodes
        • 01 - Introduction
        • 02 - Constant Value and PUSHDATA Opcodes
        • 03 - IF Loops
        • 04 - OP_NOP, OP_VERIFY and its Derivatives
        • 05 - OP_RETURN
        • 06 - Stack Operations
        • 07 - Data transformation
        • 08 - Stack Data Queries
        • 09 - Bitwise transformations and Arithmetic
        • 10 - Cryptographic Functions
        • 11 - Disabled and Removed Opcodes
      • Chapter 4: Simple Scripts
        • 01 - Introduction
        • 01 - Pay to Public Key (P2PK)
        • 02 - Pay to Hash Puzzle
        • 03 - Pay to Public Key Hash (P2PKH)
        • 04 - Pay to MultiSig (P2MS)
        • 05 - Pay to MultiSignature Hash (P2MSH)
        • 06 - R-Puzzles
      • Chapter 5: OP_PUSH_TX
        • 01 - Turing Machines
        • 02 - Elliptic Curve Signatures in Bitcoin
        • 03 - OP_PUSH_TX
        • 04 - Signing and Checking the Pre-Image
        • 05 - nVersion
        • 06 - hashPrevouts
        • 07 - hashSequence
        • 08 - Outpoint
        • 09 - scriptLen and scriptPubKey
        • 10 - value
        • 11 - nSequence
        • 12 - hashOutputs
        • 13 - nLocktime
        • 14 - SIGHASH flags
      • Chapter 6: Conclusion
        • Conclusion
    • BSV Infrastructure
      • The Instructions
        • The Whitepaper
        • Steps to Run the Network
        • Step 1
        • Step 2
        • Step 3
        • Step 4
        • Step 5
        • Step 6
      • Rules and their Enforcement
        • Introduction
        • Consensus Rules
        • Block Consensus Rules
        • Transaction Consensus Rules
        • Script Language Rules
        • Standard Local Policies
      • Transactions, Payment Channels and Mempools
      • Block Assembly
      • The Small World Network
        • The Decentralisation of Power
        • Incentive Driven Behaviour
        • Lightspeed Propagation of Transactions
        • Ensuring Rapid Receipt and Propagation of New Blocks
        • Hardware Developments to Meet User Demand
        • Novel Service Delivery Methods
        • MinerID
      • Conclusion
  • Research and Development
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    • Technical Standards
  • Support & Contribution
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  1. BSV Academy
  2. Merkle Trees
  3. Merkle Trees and the Block Header

The Hash Puzzle

PreviousWhat is the Block HeaderNextProof-of-Work in Action

Last updated 3 months ago

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The final 4 bytes of the block header is the ‘number used once’ (nonce) which is used in proof of work. When proof of work is done, the nonce value is changed, and the block header is put through the HASH256 function. A valid block header hashes to a value which is lower than the target value specified in the nBits field in the header. If the output is above the difficulty target, the nonce is incremented and the hashing process is repeated.

If a valid block header is discovered the miner can submit their block to the network for validation by their peers. Successful validation and acceptance of the block commits the batch of transactions whose Merkle root is in the block header to the public ledger. The nature of this outcome leads to valid block headers hashing to a value with numerous leading zeroes.

The difficulty target as specified by nBits is calculated by taking the elapsed time in seconds between a specific number of blocks that have been produced and seeing how far above or below that number is in seconds relative to an ideal elapsed time in seconds that averages one block being created every ten minutes. The difference between the elapsed time is divided by the ideal time to yield the value for the coefficient in the bitcoin difficulty adjustment algorithm.

This algorithm places the difficulty target value somewhere between the maximum and minimum values that can be generated as an output from the SHA256 function. An elapsed time that reveals the hash puzzle was taking longer than 10 minutes to find a solution for means that the difficulty target will increase, thus increasing the number space for available solutions below that target. Conversely, an elapsed time that indicated blocks were being produced quicker than a ten-minute average means the target will be lowered, thus decreasing the number space for a valid solution or making the challenge more difficult. The lowest possible outcome of the SHA256 hash function is 0, and the largest 1.17∗10771.17 * 10^{77}1.17∗1077 (or 64 F’s in hex). The difficulty target is a value somewhere within this range, for example 3.5∗10553.5 * 10^{55}3.5∗1055. This has the effect of creating a probability for a valid solution as 1:102010^{20}1020 or 0.00000000000000000001%.

The network tunes itself such that the cumulative computing power being applied to the hash function generates a valid block approximately every 10 minutes. Just as a new coin toss following 100 heads still has a 50:50 chance of landing on heads, any string being put through a hash function will always have the same probability of its output being less than a target value.

As the BSV system scales and transactions move into the tens of thousands per second, this means that tens of thousands of times per second, a new Merkle root is calculated by each node. The Merkle root is incorporated into a mining candidate which is relayed to the hashing machines periodically. These then perform the process hashing and testing iterations of the header until they generate an outcome that satisfies the difficulty target.

This colossal task is known as Proof of Work in the bitcoin system, and it is by engaging in this intensive process in order to produce blocks that qualifies systems connected to the network as nodes within BSV small world network. The collective hash power designated to this Proof of Work process is measured in a unit of hashes per second. A hash rate of 1 Exahash means 1 000 000 000 000 000 hashes are executed by the network per second, across a variety of block header candidates. The system will continue to adjust the difficulty target to maintain average 10-minute block discovery rate.

Originally, Bitcoin was released with an algorithm that adjusted its difficulty every 2016 blocks; however, the difficulty adjustment algorithm was changed to calculate a new target after every block. This original algorithm will be restored as part of a future node client system update.