• Administrivia

• Money as a social construct

• The network model

• The non-eclipsing assumption

• The gossip protocol

• Setting up a TypeScript project

• TypeScript basics

• Building your project

• The adversary A

• The security parameter κ

• The honest protocol Π

• The adversarial model

• Probabilistic polynomial-time adversaries

• Negligible functions

• Game-based security

• Security proofs by computation reduction

• Proofs by contradiction and forward proofs

• TCP/IP socket connections

• Establishing a connection

• Receiving and parsing data

• The hash function: H

• Preimage resistance, second preimage resistance, collision resistance

• Collision resistance implies preimage resistance

• Preimage resistance implies second preimage resistance

• Public/private keys

• Signature schemes

• Signature correctness

• Existential unforgeability

• Ledgers

• The grader will test your node for you to get feedback. This is not graded. Please check out the PSETs tab for more information.

• Transactions

• Inputs and outputs

• The transaction graph

• Change

• Multiple inputs

• Multiple outputs

• The UTXO model

• The law of conservation

• Verifying a transaction

• The grader will test your node and give you a grade. Please check out the PSETs tab for more information.

• JavaScript promises

• Async/await

• Event emitters

• Views in disagreement

• Double spending

• The network delay Δ

• Simple ideas don't work!

• Rare events

• Blocks

• Proof-of-work

• The mining target T

• The proof-of-work equation

• The mining algorithm

• Block freshness

• The genesis block G

• Chains

• The grader will test your node for you to get feedback. This is not graded. Please check out the PSETs tab for more information.

• Hash chains

• The number n of parties

• The number t of adversarial parties

• The hashing power q

• Rare events are irregular

• Convergence opportunities and periods of silence

• The honest majority assumption

• The longest chain rule

• Coinbase

• Fees

• Mempools

• The grader will test your node and give you a grade. Please check out the PSETs tab for more information.

• Temporary forks

• Convergence

• The Nakamoto race

• Chain Growth, Common Prefix, Chain Quality

• Censorship

• Majority attacks

• The grader will test your node for you to get feedback. This is not graded. Please check out the PSETs tab for more information.

• Healing

• Macroeconomic supply

• Selfish mining

• Mining pools

• The grader will test your node and give you a grade. Please check out the PSETs tab for more information.

• CPU, GPU, ASIC mining

• Incentive compatibility

• Block size limits

• Transaction prioritization by fees

• Macroeconomic policy, reward adjustment

• The difficulty adjustment equation Τ_{j+1} = T_{j} (t_2 - t_1) / (mη)

• Mining pools, the light PoW equation: H(B) ≤ 2^z T

• The pooled mining protocol

• Cold, hot, and hardware wallets

• Wallet seeds, deterministic wallets

• TBD

• The account model

• Transactions in the account model

• Balances

• Nonces

• The generic transition function δ

• Blockchain as a State Machine Replication mechanism

• UTXO vs accounts

• The file storage problem

• The Merkle Tree: compress, prove, verify

• Proofs of inclusion, succinctness

• Merkle Tree security proof by reduction from collision-resistant hashes

• This will be a short theory exercise to help you practice for the exam. Please check out the PSETs tab for more information.

• More information available on Ed

• TBD

• The problem of scalability in blockchains: Scaling computation, communication, and storage

• From x-bar to x using Merkle Trees

• The Simple Payment Verification (SPV) protocol

• The header chain

• Miners, Full Nodes, Light Nodes

• Chain virtues for light nodes

• Privacy concerns for light nodes

• Random Oracles, formally

• The synchrony assumption Δ = 1

• This will be a short theory exercise to help you practice for the exam. Please check out the PSETs tab for more information.

• The Environment and the Execution

• The Rushing Adversary

• The Sybil Adversary

• The Network model, the gossiping model

• The Non-Eclipsing Assumption

• The honest backbone protocol

• Maintaining, adopting, and having chains

• Proof-of-work

• The q-bounded Random Oracle

• The Static Difficulty assumption

• Chain validation; the δ* function

• Successful rounds

• Convergence opportunities

• Formal definition of Chain Virtues

• Common Prefix, the parameter k

• Chain Quality, the parameters μ and ℓ

• Chain Growth, the parameters τ and s

• The formal honest majority assumption: t < (1 - δ)(n - t)

• The honest advantage δ

• Convergence Opportunities are useful: The Pairing Lemma and its proof

• The grader will test your node for you to get feedback. This is not graded. Please check out the PSETs tab for more information.

• Ledger Safety and Liveness, formally. The liveness parameter u.

• Proof of Safety from Common Prefix

• Proof of Liveness from Chain Quality and Chain Growth; u = max((ℓ + k) / τ, s)

• The Chain Growth Lemma and its proof

• The successful round indicator X

• The convergence opportunity indicator Y

• The adversarial success indicator Z

• The expectations of X, Y, and Z

• Bernoulli's inequality

• Lower and upper bounds on the expectation of X

• Lower bounds on the expectation of Y

• Good things converge: The Chernoff bound

• The world is good, usually: Typical executions

• The Chernoff duration λ

• The Chernoff error ε

• Proof of Typicality Theorem

• The Balancing Equation: 3ε + 3f ≤ δ

• A plot of X, Y, and Z with 3f, 3ε and δ

• The grader will test your node and give you a grade. Please check out the PSETs tab for more information.

• Reminder of bounds on the expectations of X and Y

• Upper bound on the expectation of Z

• Typical bounds, and proof that Z ≤ Y

• Chains grow: The Chain Growth theorem and its proof

• The Patience Lemma and its proof

• The Common Prefix theorem and its proof

• Discussion on the relationship between ε and λ

• You can't have it all: Discussion on the parametrization options for ε, f, δ

• The grader will test your node for you to get feedback. This is not graded. Please check out the PSETs tab for more information.

• The grader will test your node and give you a grade. Please check out the PSETs tab for more information.

• Proof of Work's perils and environmental impact

• Proof of Work vs Proof of Stake

• Dangers of Proof of Stake

• The Proof of Stake equation

• Lecture notes

• The grader will test your node for you to get feedback. This is not graded. Please check out the PSETs tab for more information.

• Proof of Work's perils and environmental impact

• Proof of Work vs Proof of Stake

• Dangers of Proof of Stake

• The Proof of Stake equation

• Lecture notes

• Everything is a Race and Nakamoto Always Wins

• Verifiable Random Functions

• VRF correctness

• The unpredictability game

• Towards instant finality

• Lecture notes

• The grader will test your node and give you a grade. Please check out the PSETs tab for more information.

• TBD

• The Streamlet protocol and its proof of safety

• Accountability and slashing

• Lecture notes

• This will be a short theory exercise to help you practice for the exam. Please check out the PSETs tab for more information.

• Permissioned vs Proof of Stake: static vs dynamic stake

• Stake grinding attacks and their mitigations

• Stake unbonding and long range attacks and their mitigations

• Lecture notes

• TBD

• This will be a short theory exercise to help you practice for the exam. Please check out the PSETs tab for more information.

• More information will be posted soon.