Lecture 14 - Cryptocurrencies II
Decentralised Ledgers and Satoshi’s Protocol
These notes explain the core conceptual problem behind cryptocurrencies: how to maintain a shared transaction ledger without relying on a trusted central authority. The lecture develops an intuitive model that illustrates the economic and strategic logic behind Bitcoin’s blockchain protocol.
1. The Core Problem of Cryptocurrencies
Modern monetary systems operate through ledgers. Banks, payment networks, and clearing systems maintain records of transactions which determine who owns what.
Ledger
A registry that records all transactions and determines the ownership of assets within a monetary system.
In conventional systems:
- Banks maintain account balances.
- Central banks regulate monetary infrastructure.
- Payment networks coordinate transfers.
This means trust is centralised.
Cryptocurrencies attempt to remove this requirement.
Decentralised ledger
A transaction record maintained collectively by a distributed network of participants rather than by a trusted central authority.
Satoshi Nakamoto’s objective was therefore to design a system satisfying two key properties:
-
Equality of decision power
- No user or authority should control the ledger.
- Any participant should be able to submit transactions.
-
Immutability
- Once recorded, transactions cannot be removed or altered.
The fundamental challenge is therefore:
How can a decentralised system maintain a reliable ledger when participants may have incentives to cheat?
The problem is essentially a mechanism design problem under decentralisation.
Participants have private incentives and may attempt to manipulate the ledger to benefit themselves.
The protocol must therefore be self-enforcing, meaning that following the rules is the best strategy for each participant given the behaviour of others.
2. A Simplified Model of the Problem
To isolate the strategic logic of decentralised consensus, the lecture introduces an analogy.
The Book of Brilliant Thoughts (BBT)
Imagine:
- There are n intellectuals.
- They want to create an eternal book of brilliant ideas.
- Each intellectual can share documents via fax machines (1972 setting, no internet).
The goal is to create a book satisfying:
- No participant has more authority than others
- Once written, pages cannot be modified or deleted
This book is essentially a decentralised ledger analogue.
Incentives of Participants
Each intellectual seeks to maximise prestige.
Prestige increases with the share of pages they authored in the book.
This creates a strategic conflict:
- Participants prefer to add their own pages.
- They may want to remove others’ pages.
The analogy mirrors the incentives in cryptocurrency systems.
If participants could rewrite the ledger, they could:
- reverse payments,
- double-spend coins,
- or erase others’ transactions.
Therefore, the system must make tampering prohibitively costly.
3. Translation as a Computational Cost
The model introduces a clever mechanism: translation work.
Assumptions:
- There are infinitely many languages.
- Each intellectual has a sequence of unique languages:
where:
All participants can translate between languages.
However:
- Translation takes 24 hours + ε minutes
Verification of a translation is instantaneous.
Translation work is an abstraction of computational work in cryptocurrency mining.
In Bitcoin, miners perform computational hashing rather than translation tasks.
The key property is that producing a valid block is costly but verifying it is cheap.
4. Structure of a Valid Book
A book is considered valid if it satisfies strict structural rules.
Page 0
The first page contains a fixed reference text:
- an excerpt from The End of History by Francis Fukuyama.
This acts as a genesis block analogue.
For every page
Each page must contain:
-
An integer
identifying the contributor. -
A translation of page
-
A new brilliant thought written in English.
Protocol
A predefined set of rules determining how participants interact within a decentralised system.
5. Satoshi’s Protocol
Participants follow three simple rules.
Rule 1 – Validity
Only books satisfying the structural requirements are considered valid.
Rule 2 – Work on the Longest Valid Book
At any time:
- Work on translating the last page of the longest valid book known.
If two books are equally long:
- Ignore the new one and continue working.
Rule 3 – Broadcast Updates
After completing a translation:
- Add a new page
- Fax the updated book to everyone.
This rule mimics the longest-chain rule in blockchain systems.
Nodes accept the longest valid chain of blocks as the authoritative ledger.
6. Why the Protocol Works
If everyone follows the protocol:
- At time
- If the book contains
Thus the book grows monotonically.
Self-enforcing protocol
A set of rules where following the protocol is individually rational given the behaviour of others.
7. Attempting to Modify Past Pages
Suppose an intellectual tries to alter page
Because each page contains a translation of the previous one:
- Page
Thus changing page
To create a valid alternative book, the participant must redo:
translations.
Each translation takes about one day.
Time Constraint
While the attacker is rewriting the book:
- Other participants continue adding pages.
Therefore:
- By the time rewriting finishes, the honest chain has already grown.
This is analogous to the 51% attack problem in Bitcoin.
Rewriting transaction history requires recomputing all subsequent blocks faster than the rest of the network combined.
The cost of rewriting the past grows with:
- the length of the ledger
- the amount of computational work embedded in it
This creates path dependence and security through accumulated work.
8. Ignoring Updates
Another potential deviation is to ignore newly received updates.
Imagine a participant is almost finished translating when they receive a longer book.
Continuing might seem tempting because:
- They are only minutes away from completing their translation.
However:
- In expectation, the longer book will grow faster than the shorter one.
Thus continuing work on the old chain is risky.
This corresponds to fork competition in blockchain networks.
Rational miners follow the longest chain because:
- expected rewards are higher
- the probability of producing an orphan block is lower.
9. Key Properties of the Protocol
Satoshi’s protocol satisfies the desired objectives:
Decentralisation
- All participants follow identical rules.
- No central authority coordinates the system.
Immutability
- Past entries become effectively impossible to modify.
Consensus
- Participants converge on the same ledger through the longest-chain rule.
Core mechanism behind decentralised ledgers:
- costly production of new entries
- easy verification
- longest-chain consensus rule
- incentives aligned with honest behaviour
10. Testing the Model
The model relies on several assumptions.
Removing them can break the system.
Example Questions
-
What if participants only translated their new page instead of the previous page?
- Past pages would no longer be embedded in future pages.
- Rewriting history would become easier.
-
What if the number of languages were finite?
- Eventually translation sequences would repeat.
- This could weaken the security structure.
If asked to explain how blockchain prevents ledger manipulation, structure your answer around:
- Decentralised validation
- Computational work (proof-of-work)
- Longest-chain consensus
- Increasing cost of rewriting history
11. Connection to Bitcoin
The analogy corresponds directly to Bitcoin’s architecture.
| Model Concept | Bitcoin Equivalent |
|---|---|
| Translation work | Hash computations |
| Pages | Blocks |
| Book | Blockchain |
| Faxing updates | Peer-to-peer network broadcast |
| Longest book rule | Longest chain consensus |
The key insight behind Bitcoin is that economic incentives and computational work can replace trust in central institutions.
References
Nakamoto, S. (2008) Bitcoin: A Peer-to-Peer Electronic Cash System.
Vigier, A. (2026) Cryptocurrencies – Lecture 2. University of Nottingham.