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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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    • Privacy
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  • Network Access Rules
    • Rules
      • Table of Contents
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      • PART I - MASTER RULES
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    • Overview
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      • TypeScript
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          • Creating a Simple Transaction
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          • Creating Transactions with Inputs, Outputs and Templates
          • Creating the R-puzzle Script Template
          • Message Encryption and Decryption
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          • Building a Custom Transaction Broadcast Client
          • Verifying Spends with Script Intrepreter
          • BIP32 Key Derivation with HD Wallets
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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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        • Example
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      • Introduction
      • About BSV Blockchain
        • Introduction
        • Safe, Instant Transactions at a Predictably Low Cost
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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 Working Blockchain
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          • A World View Backed by Proof of Work
    • 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
        • BSV Transactions and SHA-256
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        • Proof-of-Work and HASH-256
      • Walkthrough Implementation of SHA-256 in Golang
        • Overview of SHA-256
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      • RIPEMD-160
        • BSV Addresses & WIFs
      • Walkthrough Implementation of RIPEMD-160 in Golang
        • Overview of RIPEMD-160
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        • RIPEMD-160 Final Value Construction and Output
      • Doubla Hashing and BSV's Security
        • Why is Double Hashing Used in BSV
        • Hash Functions and BSV's Security Model
    • Merkle Trees
      • The Merkle Tree
        • What is a Merkle Tree?
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        • Merkle Trees in Action
      • Merkles Trees in BSV
        • The Data Elements
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        • Transaction Merkle Trees in Action
      • Merkle Trees and the Block Header
        • What is the Block Header
        • The Hash Puzzle
        • Proof-of-Work in Action
      • Merkle trees and Verifying Proof of Work
        • Broadcasting the Block
        • The Coinbase Transaction
        • Data Integrity of the Block
        • Saving Disk Space
      • 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
        • Offline Payments
    • Digital Signatures
      • What are Digital Signatures
        • Background
        • Introduction
        • Digital Signatures Protocol
        • Properties of Digital Signatures
      • 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
        • ECDSA (secp256k1) for BSV Transaction
        • Summary
        • Signed Messages
        • Miner Identification and Digital Signatures
    • 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
        • Network Structure
        • Messaging Between Nodes
      • Introduction
        • Commerce on the Internet
        • Non Reversible Transactions
        • Privacy in Commerce
        • The Paradigm of Fraud Acceptance
        • What is Needed...
        • Protecting Sellers From Fraud
        • Proposed Solution
        • Security and Honesty
      • Transactions
        • Electronic Coins
        • Spending a Coin
        • Payee Verification
        • Existing Solutions
        • 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
        • The Majority Decision
        • The Honest Chain
        • 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
    • Join Our Discord
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  1. BSV Academy
  2. Introduction to Bitcoin Script
  3. Chapter 3: The Opcodes

10 - Cryptographic Functions

Previous09 - Bitwise transformations and ArithmeticNext11 - Disabled and Removed Opcodes

Last updated 3 months ago

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Bitcoin script includes a range of cryptographic functions such as hashing functions and ECDSA signature checks.

Hash Functions

There are three hash functions available in Bitcoin script:

  1. RIPEMD160

  2. SHA1

  3. SHA256

There are also opcodes that perform double hash operations using these same base opcodes.

Each hash function consumes the topmost data item on the stack and replace it with the hash of that data item.

Word
Input
Output
Description

OP_RIPEMD160

in

hash

The input is hashed using RIPEMD-160.

OP_SHA1

in

hash

The input is hashed using SHA-1.

OP_SHA256

in

hash

The input is hashed using SHA-256.

OP_HASH160

in

hash

The input is hashed twice: first with SHA-256 and then with RIPEMD-160.

OP_HASH256

in

hash

The input is hashed two times with SHA-256.

ECDSA Signature Check Functions

Bitcoin script provides users with both single and multisignature options based on the Secp256k1 elliptic curve. These functions are core to the Peer to Peer functionality of Bitcoin, allowing users to assert ownership of coins when transacting.

It is important to understand that digital signatures alone cannot be used to establish identity, and there is an implicit requirement for users on each side of a transaction to take responsibility for checking/proving counterparty identity, and then using digital signatures to finalise the transactions.

The messages used to generate the signatures are created using reproducible data, which allows the nodes on the network to perform signature checks using only the transaction data itself. This is a key element of Bitcoin's peer-to-peer functionality, and allowing nodes to perform independent signature validations without user input.

Word

Input

Output

Description

sig pubkey

True / false

The entire transaction's outputs, inputs, and script (from the most recently-executed OP_CODESEPARATOR to the end) are hashed. The signature used by OP_CHECKSIG must be a valid signature for this hash and public key. If it is, 1 is returned, 0 otherwise.

OP_CHECKSIGVERIFY

sig pubkey

Nothing / fail

Same as OP_CHECKSIG, but OP_VERIFY is executed afterward.

OP_CHECKMULTISIG

x sig1 sig2 ... <n> pub1 pub2 ... <m>

True / False

Compares the first signature against each public key until it finds an ECDSA match. Starting with the subsequent public key, it compares the second signature against each remaining public key until it finds an ECDSA match. The process is repeated until all signatures have been checked or not enough public keys remain to produce a successful result. All signatures need to match a public key. Because public keys are not checked again if they fail any signature comparison, signatures must be placed in the scriptSig using the same order as their corresponding public keys were placed in the scriptPubKey or redeemScript. If all signatures are valid, 1 is returned, 0 otherwise. Due to a bug, an extra unused value (x) is removed from the stack. Script spenders must account for this by adding a junk value (typically zero) to the stack.

OP_CHECKMULTISIGVERIFY

x sig1 sig2 ... <n> pub1 pub2 ... <m>

Nothing / fail

Same as OP_CHECKMULTISIG, but OP_VERIFY is executed afterward.

OP_CODESEPARATOR

OP_CODESEPARATOR is used in a Bitcoin script to indicate to the node checking the signature exactly which part of the scriptPubKey is being signed. When transactions are submitted to the network, the node inserts OP_CODESEPARATOR at the junction between input and output. When the transaction validation engine reaches an ECDSA checking function, the message that it uses to perform the signature check only includes the script that comes after the most recent OP_CODESEPARATOR in the scriptPubKey being signed. This functionality can be used in complex scripts to allow users to omit parts of the transaction output being signed, which can be useful when building complex functionality such as contracts with signature witness statements

Word

Input

Output

Description

Nothing

Nothing

All of the signature checking words will only match signatures to the data after the most recently-executed OP_CODESEPARATOR.

Example: Masked document for witness signature

scriptSig: <witness_signature> <witness_public_key> <witness_name> <signatory_signature>

scriptPubKey: OP_CODESEPARATOR <hash_contract> OP_DROP <signatory_public_key> OP_CHECKSIGVERIFY OP_CODESEPARATOR <witness_statement> OP_2DROP OP_CHECKSIG In this example, an output is created containing a contract document that is ready to be signed into effect as well as a witness statement allowing a third party to attest that they witnessed the signing party performing the contract signature.

The scriptSig contains 4 elements. First, the witness signature, public key and name are added, then the signing party's signature. The first OP_CODESEPARATOR is inserted by the validation engine when the transaction scriptSig and scriptPubKey are joined. The scriptSig contains both the witness signature and signatory signature. During the validation processs, a hash of the document being signed (<hash_contract>) is pushed onto the stack and dropped before the signatory's public key is pushed onto the stack and their signature checked using OP_CHECKSIGVERIFY. When OP_CHECKSIGVERIFY is processed, the message signed by the signature must include the scriptPubKey all the way back to the first OP_CODESEPARATOR which includes the contract, their public key and the witness statement. After the first OP_CHECKSIGVERIFY, OP_CODESEPARATOR is used.

The script then pushes a witness statement onto the stack, drops it and the witness' name, and then checks their signature against the public key they provided. Again, the message in the signature includes the script as far back as the most recent OP_CODESEPARATOR. This means that the message signed by the witness does not include the contract itself, allowing the witness to act as a witness of the signing party's identity and signature only. This can be likened to showing the witness the signing page of a contract and letting them watch you sign, but keeping the remainder private.

​​

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OP_CHECKSIG
OP_CODESEPARATOR