Roadmap

How Hashing Works

What a cryptographic hash is, how SHA-256 digests a block, and why the avalanche effect makes hashes tamper-evident.

Nonces & Mining Math

The nonce field, the astronomical odds of finding a valid hash, and why miners iterate quintillions of guesses.

Merkle Trees

How hashing transactions into a tree yields a compact root, and how SPV wallets prove inclusion without the full block.

Merkle Patricia Tries

Ethereum's state structure — how Merkle tries store accounts, storage, and receipts and enable fast state proofs.

Hash Commitments & Preimages

How committing to a hash hides a value until reveal, and where commitments underpin protocols and proofs.

Bloom Filters

How light clients probabilistically request relevant transactions without revealing which addresses they own.

Key Derivation (BIP32/39/44)

From mnemonic seed to master key to child keys — the HD wallet derivation paths behind every modern wallet.

The Quantum Threat

How Shor's and Grover's algorithms threaten ECDSA and hashes, and the post-quantum signature migration ahead.

ECDSA vs. Schnorr

The math behind Bitcoin's signatures, why Schnorr is simpler and linear, and what batch verification unlocks.

Elliptic Curve Cryptography

secp256k1, point addition and scalar multiplication, and why the discrete log problem secures your keys.

Threshold Signatures & MPC

Splitting a key across parties so no single custodian holds the full private key — how MPC custody works.

BLS Signatures

Pairing-based signatures that aggregate across thousands of validators, enabling Ethereum's committee efficiency.

Signature Aggregation & M-of-N

How multisig, threshold, and aggregate signatures differ, and the trade-offs between them.

Proof of Work Mechanics

Difficulty adjustment, the longest-chain rule, orphaned blocks, and how selfish mining exploits propagation.

Proof of Stake & Finality

Slashing, checkpointing, and how Casper FFG + LMD-GHOST give Ethereum economic finality.

Verkle Trees

The next-gen state structure whose compact witnesses let stateless clients verify blocks without storing state.

Fork Choice Rules

How nodes agree on the chain head across PoW and PoS, and why the rule matters more than the mechanism.

Long-Range Attacks & Nothing-at-Stake

The PoS attack vectors that don't exist in PoW, and how weak subjectivity and finality defend against them.

MEV & Proposer-Builder Separation

How block construction became a market, and why PBS aims to decentralize the proposer role.

UTXO vs. Account Model

The two accounting paradigms — Bitcoin's parallelizable UTXOs vs. Ethereum's serial accounts — and their trade-offs.

Bitcoin Script

The stack-based opcode set, why it's deliberately non-Turing-complete, and what it can and can't express.

EVM Internals

Gas, stack, memory, and storage; opcode pricing; and the 26.5k gas floor that shapes every contract.

Transaction Lifecycle

From mempool submission to inclusion, fee estimation, and RBF/CPFP replacement strategies.

Taproot & Scriptless Scripts

Key-path vs. script-path spends, MAST, and how Schnorr enables smarter spending without revealing logic.

Account Abstraction (ERC-4337)

Paymasters, bundlers, and how smart-contract wallets make accounts first-class programmable objects.

P2P Gossip Protocols

How blocks and transactions propagate through libp2p/devp2p, and why latency decides who wins block rewards.

Ethereum Client/Consensus/Execution Split

The post-Merge architecture — how the execution and consensus clients talk over the Engine API.

Light Client Protocols

Sync committees and proof systems that let a phone verify the chain without storing it.

Data Availability Sampling (DAS)

How nodes verify block data is available without downloading it all — the foundation of danksharding.

P2P DHTs & BitTorrent Origins

The distributed hash table lineage from BitTorrent to modern crypto networking.

Rollup Mechanics

How optimistic and ZK rollups post state roots to L1, and what execution moves off-chain.

Fraud Proofs & Challenge Windows

The 7-day optimistic rollup withdrawal delay, and how fraud proofs keep the sequencer honest.

Validity Proofs (SNARKs/STARKs)

Polynomial commitments and the prover/verifier asymmetry that makes ZK rollups trustless.

Data Availability Layers

Celestia and EigenDA — what 'availability' means versus storage, and why it's its own problem.

State Channels & Payment Channels

How Lightning and Raiden move state off-chain and settle on-chain in a single transaction.

Zero-Knowledge Proofs

zk-SNARK vs. zk-STARK, trusted setups, and the math of proving without revealing.

Ring Signatures & Stealth Addresses

Monero's decoy outputs and one-time addresses, and how they obscure sender and receiver.

Federated Chaumian E-Cash

CoinJoin coordination without a trusted party — how Wasabi and Whirlpool mix coins.

Homomorphic Encryption

Computing on encrypted data — where it's used in crypto today and where it's still promise.

Differential Privacy in Analytics

How chain-analysis firms de-anonymize, and how protocols add noise to resist it.

Reentrancy & Exploit Classes

The bug families — reentrancy, integer overflow, access control — and how each famously went wrong.

Formal Verification

Mathematically proving contracts correct, and the tools (K-framework, Coq) that do it.

51% Attacks & Reorgs

Deep chain reorganizations, exchange confirmation thresholds, and what a majority hashrate can do.

Address Collisions & Vanity Addresses

The birthday-problem math behind vanity prefixes, and why a collision is computationally out of reach.

Transaction Malleability

What malleability is, how SegWit fixed it, and the Mt. Gox excuse that wasn’t.

Derivatives & Perpetuals

How crypto futures, options and perpetual swaps work, from funding rates to liquidations, and why leverage magnifies losses.

Restaking & Liquid Staking

How liquid staking tokens and restaking reuse staked ETH, and the extra layers of risk each adds.

Airdrops & Token Distribution

How projects hand out tokens, from airdrops to vesting and unlock schedules, and how fake airdrops exploit the hype.

Account Abstraction

How smart-contract wallets add recovery, spending limits and gas sponsorship, and what ERC-4337 changes.

Standards & EIPs

How improvement proposals change Bitcoin and Ethereum, and the token standards (ERC-20, ERC-721 and more) behind what you hold.

On-chain Analytics

How to read public blockchain data such as flows, holder concentration and exchange balances, and the limits of what it tells you.

How to Verify a Receive Address

Check an address and its network before you send, so a typo or a swapped address can't take your funds.

How to Set Up a Hardware Wallet

Initialize the device, write down the seed phrase and test a small recovery before moving real funds.

How to Read a Transaction on a Block Explorer

Find a transaction by its ID and read its inputs, outputs, fee and confirmations.

How to Choose a Fee and Unstick a Transaction

Pick a fee for the speed you need, and use replace-by-fee or CPFP when a transaction stalls.

How to Move Tokens Between Chains Safely

Choose the right network, bridge or exchange route, and send a test amount first.

How to Set Up a 2-of-3 Multisig

Split control of shared funds across three keys, so losing one doesn't lose everything.

How to Keep Crypto Tax Records

Record the date, cost basis and value of every trade, swap and spend as it happens.