Lecture 16 - Cryptocurrencies IV

1. The Authentication Problem in a Trustless System

The central issue in decentralised systems is identity verification without trust. In a setting like the Big Book of Transactions (BBT), nothing prevents an agent from impersonating another.

Definition

Trustless system: A system in which participants do not rely on central authority or mutual trust, but instead on verifiable rules and protocols.

  • Without authentication, transactions are meaningless
  • The system must ensure:
    • Messages are verifiable
    • Messages are non-forgeable

This creates a fundamental tension:

  • Everyone must be able to verify a signature
  • No one must be able to replicate it
Theoretical Interpretation

This is a classic mechanism design problem under asymmetric information. Agents must reveal identity credibly without a central verifier. The system must implement a self-enforcing constraint where cheating is technologically infeasible rather than institutionally punished.

2. Digital Signatures and Asymmetric Cryptography

Digital signatures solve the authentication problem using asymmetric cryptography.

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This slide formalises the cryptographic structure of identity:

  • Each agent generates:
    • A private key
    • A public key

These satisfy:

  2. Knowing does not reveal

To sign a message :

  • Compute signature:
  • Send

Verification:

  • Anyone checks
Economic Intuition

Think of the private key as a perfectly secure signature stamp. Everyone can recognise it, but only the owner can produce it. This eliminates impersonation without requiring trust.

Common Mistake

Confusing encryption with signatures:
Encryption ensures secrecy; signatures ensure authenticity. They solve different problems.

Theoretical Interpretation

This creates a credible commitment technology. Agents cannot deny actions ex post because signatures are verifiable and unique. This replaces institutional enforcement with mathematical enforcement.

3. Digital Signatures in Blockchain Systems

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Key implication:

  • A digital signature is a function of the message itself
  • Therefore:
    • It cannot be reused across different messages
    • It prevents forgery

This allows integration into blockchain protocols:

  • Each transaction is tied to a unique identity
  • Each block contains verifiable authorship
Economic Intuition

This ensures property rights over digital assets. Ownership is defined by control over private keys.

Exam Insight

If asked “how does Bitcoin ensure transaction validity?”:
Mention digital signatures as the mechanism ensuring authenticity and non-repudiation.

4. Satoshi’s Protocol (With Hashing and Signatures)

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The protocol defines a valid blockchain structure:

Block Structure

Each block contains:

  1. Hash of previous block

    • Ensures chain integrity

  2. Transaction data:

    • Identity
    • Message
    • Signature such that

  3. Proof-of-work:

    • A number such that the hash begins with zeros

Consensus Rule

  • Always build on the longest valid chain
Theoretical Interpretation

The longest-chain rule acts as a coordination equilibrium. It solves a decentralised coordination problem where agents must agree on a single history of transactions.

Economic Intuition

The cost of producing blocks (proof-of-work) creates a barrier to manipulation. Rewriting history becomes prohibitively expensive.

Common Mistake

Thinking blockchain is immutable by design:
It is only economically immutable because rewriting history is too costly.

5. From BBT to Blockchain: Economic Perspective

The lecture shifts from a toy model (BBT) to real-world Bitcoin.

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Key transition:

  • BBT relied on intrinsic motivation (prestige)
  • Bitcoin relies on extrinsic incentives (profit)

Terminology shift:

  • Pages → Blocks
  • Book → Blockchain
Theoretical Interpretation

This reflects a move from non-pecuniary incentives to market-based incentives. Participation becomes driven by expected returns rather than social recognition.

6. The Economics of Money Creation in Bitcoin

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Two fundamental problems:

(1) Money Creation

  • Traditional systems:
    • Central banks create money via lending
  • Bitcoin:
    • No central authority

(2) Incentives for Participation

  • Block creation is costly
  • Participants must be rewarded
Definition

Decentralised money creation: A process where new currency is issued according to protocol rules rather than a central authority.

Theoretical Interpretation

Bitcoin replaces discretionary monetary policy with a rule-based monetary system. This eliminates time inconsistency but removes stabilisation tools.

7. Mining Rewards and Incentive Compatibility

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Bitcoin solves both problems simultaneously:

  • When a new block is added:
    • A fixed reward is created
    • Paid to the block creator (miner)

This is known as the coinbase transaction.

Economic Intuition

This creates a self-sustaining equilibrium:

  • Miners invest resources
  • They are compensated with new coins
  • This maintains network security
Theoretical Interpretation

This is an example of incentive compatibility:
Profit motive → honest validation → secure network
Deviations (e.g. fraud) reduce expected payoffs.

Exam Insight

If asked “why does Bitcoin work without a central authority?”:
Emphasise aligned incentives via mining rewards and proof-of-work.

8. Complete Satoshi Protocol

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Key Components

Transactions

  • Authenticated transaction:
    such that

  • Coinbase transaction:

    • Creates new money
    • ,

Valid Blockchain

  • Genesis block initialises the system
  • Each block must:
    • Reference previous hash
    • Include valid transactions
    • Respect balance constraints
    • Satisfy proof-of-work

Consensus

  • Follow longest chain
  • Ignore competing chains of equal length
Theoretical Interpretation

The protocol implements a decentralised ledger with endogenous enforcement. Rules are enforced through:

  • Cryptography (identity)
  • Computation (proof-of-work)
  • Incentives (rewards)
Economic Intuition

The system replaces:

  • Banks → protocol rules
  • Courts → cryptographic verification
  • Central bank → algorithmic money supply

9. Synthesis

Summary

Key Takeaways

  • Digital signatures solve the identity problem in trustless systems
  • Blockchain ensures integrity via hashing and proof-of-work
  • The longest-chain rule coordinates decentralised consensus
  • Bitcoin replaces central authority with rules + incentives
  • Mining rewards ensure participation and money creation
  • The system is secured by economic costs, not legal enforcement

10. Exam-Oriented Framing

Exam Insight

For a 10–15 mark answer on Bitcoin:

  1. Define blockchain and decentralisation
  2. Explain digital signatures (authentication)
  3. Explain proof-of-work (security)
  4. Explain incentives (mining rewards)
  5. Conclude with economic interpretation:
    • Credibility
    • Commitment
    • Trade-offs vs central banking

Bibliography

Vigier, A. (2026) Cryptocurrencies Lecture 4. University of Nottingham.