At its core, a blockchain is a distributed ledger—a shared, synchronized database of transactions. Unlike a bank's private ledger, copies exist on thousands of computers (nodes) worldwide.

• Immutable Record: Once data is added, it is cryptographically sealed and cannot be altered.
• Transparent History: All participants can verify the entire transaction history.
• Example: Bitcoin's ledger has recorded every transaction since its 2009 genesis block.

Transactions are grouped into blocks, which are linked (chained) together using cryptographic hashes. Each block contains:

• A hash of the previous block, creating a tamper-evident chain.
• A timestamp and a set of recent transactions.
• A nonce used in the Proof-of-Work consensus mechanism.

Altering a single transaction would require re-mining that block and all subsequent blocks, making fraud computationally infeasible.

Think of a blockchain as a public spreadsheet duplicated across a global network. When a new transaction occurs (e.g., 'Alice sends 1 ETH to Bob'), the network validates it and updates all copies simultaneously.

• Consensus Mechanisms like Proof-of-Stake (Ethereum) or Proof-of-Work (Bitcoin) ensure all copies agree on the update.
• No single entity controls the master copy, eliminating central points of failure.
• This model underpins DeFi protocols and NFT ownership records.

Blockchains enable trustless interaction. Parties can transact directly without needing a trusted intermediary like a bank or escrow service. Trust is placed in the code and cryptographic guarantees of the network.

• Smart contracts (e.g., on Ethereum or Solana) automate agreements without human intervention.
• Cryptographic Proofs verify asset ownership and transaction validity.
• This reduces counterparty risk and enables programmable money (DeFi).

A blockchain is a replicated state machine. All nodes begin with the same initial state (genesis). As they process the same ordered set of valid transactions, they deterministically arrive at the same final state.

• State represents current data (account balances, smart contract code).
• Transactions are instructions that trigger a state transition.
• This property is critical for EVM-compatible chains and decentralized applications (dApps).

Unlike a traditional centralized database managed by one entity, a blockchain is a decentralized database maintained by a peer-to-peer network.

• Data Integrity: Uses Merkle trees to efficiently and securely verify large datasets.
• Fault Tolerance: The network remains operational even if many nodes fail.
• Permissionless: Anyone can join the network to read, write, or validate (in public blockchains). This architecture resists censorship and downtime.

A one-way function that takes any input and produces a fixed-size output (hash).

Key Properties:

• Deterministic: Same input always yields same hash.
• Pre-image Resistance: Cannot derive the input from its hash.
• Avalanche Effect: A tiny change in input creates a completely different hash.
• Collision Resistance: Extremely difficult to find two different inputs that produce the same hash.

Blockchain Use:

• Creating block and transaction identifiers (e.g., Bitcoin's SHA-256).
• Linking blocks in a chain via parent block hashes.
• Generating addresses from public keys.

A cryptographic system using a pair of keys: a public key (shared openly) and a private key (kept secret).

How it Works:

• Data encrypted with the public key can only be decrypted with the corresponding private key.
• A digital signature created with a private key can be verified by anyone with the public key.

Blockchain Use:

• Digital Signatures: Prove ownership and authorize transactions (e.g., ECDSA in Ethereum).
• Address Generation: A public key is hashed to create a user's wallet address.
• Node Identity: Used in peer-to-peer network protocols for secure communication.

A mathematical scheme for verifying the authenticity and integrity of a message. It proves a message came from a specific sender and was not altered.

Process:

1. A hash of the transaction/message is created.
2. The hash is signed using the sender's private key, creating a signature.
3. The signature is sent along with the message and the sender's public key.
4. The verifier recomputes the hash and uses the public key to verify the signature matches.

Blockchain Use: Every transaction on a blockchain (e.g., sending ETH) must be signed by the sender's private key. This prevents forgery and ensures non-repudiation.

A hierarchical data structure that efficiently summarizes and verifies large sets of data.

Structure:

• Leaf Nodes: Contain the cryptographic hashes of individual data blocks (e.g., transactions).
• Non-Leaf Nodes: Contain the hash of its child nodes' hashes.
• Root Hash: A single hash at the top (Merkle Root) that represents the entire dataset.

Blockchain Use:

• Light Client Verification: A light client can verify a specific transaction is in a block by checking a small Merkle proof (~log(n) hashes) against the block's Merkle root.
• Data Integrity: Used in Bitcoin and Ethereum blocks to commit to the set of transactions. Changing any transaction invalidates the Merkle root.

A specific type of public-key cryptography based on the algebraic structure of elliptic curves over finite fields. It provides equivalent security to RSA with much smaller key sizes.

Key Advantages:

• Smaller Keys: A 256-bit ECC key offers security comparable to a 3072-bit RSA key.
• Faster Operations: Signature generation and verification are generally faster.
• Efficiency: Crucial for blockchain where every byte in a transaction matters.

Blockchain Use:

• secp256k1: The specific elliptic curve used by Bitcoin and Ethereum for key generation and the ECDSA signing algorithm.
• Ed25519: An alternative curve used by chains like Solana and Near, offering different performance characteristics.

Smart contracts are immutable code deployed to a blockchain address. They define a set of rules (e.g., "if X happens, then execute Y") and autonomously perform actions like transferring value or updating state. Key characteristics include:

• Deterministic: Same inputs always produce the same outputs.
• Tamper-proof: Code cannot be altered after deployment.
• Trust-minimized: Execution is verified by the network, not a central party.

Ethereum's Solidity and Solana's Rust are common languages for writing smart contracts.

The Ethereum Virtual Machine (EVM) is the global, sandboxed runtime environment that executes all smart contracts on Ethereum and compatible chains (like Polygon, Arbitrum). It ensures consensus on contract state changes. Alternatives include:

• Solana's Sealevel: A parallel runtime for high throughput.
• CosmWasm: A WebAssembly-based smart contract module for Cosmos chains.
• StarkNet's Cairo VM: A ZK-optimized VM for StarkEx rollups.

Each environment defines the rules for gas, computation, and state access.

Gas is the unit measuring computational work required to execute operations on a blockchain. Users pay gas fees to compensate validators. Key concepts:

• Gas Price: Amount of native token (e.g., ETH, MATIC) per unit of gas, set by the user.
• Gas Limit: Maximum gas a user is willing to spend on a transaction.
• Out of Gas: Transaction fails if execution exceeds the limit; gas is still consumed.

High network demand increases gas prices. Layer 2 solutions and alternative chains like Solana offer lower-cost execution environments.

While smart contract code is immutable, systems can be designed for upgrades. Common patterns include:

• Proxy Pattern: Uses a proxy contract that delegates calls to a logic contract. The proxy's storage is persistent, but the address of the logic contract can be changed by an admin or DAO.
• Diamond Pattern (EIP-2535): A modular system where a single proxy contract can delegate to multiple logic contracts (facets).
• Migration: Deploying a new contract and moving all state and users to it.

Upgrades introduce centralization risks and must be managed via transparent governance.

The foundational application. Blockchains like Bitcoin and Litecoin enable peer-to-peer value transfer without intermediaries. Key features include:

• Censorship-resistant transactions
• Global settlement in minutes, not days
• Reduced fees compared to traditional cross-border payments Ethereum and other smart contract platforms expanded this to programmatic payments and microtransactions.

Recreating financial services—lending, borrowing, trading—using smart contracts on blockchains like Ethereum, Solana, and Avalanche. Users interact directly with protocols, not banks.

• Lending protocols like Aave and Compound automate loans with over-collateralization.
• Decentralized exchanges (DEXs) like Uniswap use automated market makers for permissionless trading.
• Yield farming and staking provide alternative returns on capital.

Blockchains provide verifiable ownership and provenance for unique digital assets. Each NFT is a cryptographically unique token on a ledger.

• Digital Art & Collectibles: Projects like CryptoPunks and Bored Ape Yacht Club.
• Gaming Assets: True ownership of in-game items across platforms.
• Identity & Credentials: Soulbound tokens for diplomas, licenses, and memberships. Standards like ERC-721 and ERC-1155 on Ethereum define the technical specifications.

Member-owned communities without centralized leadership, governed by smart contracts and token-based voting. Treasury management and proposal execution are encoded on-chain.

• Protocol Governance: MakerDAO, which manages the DAI stablecoin.
• Investment Collectives: Groups like The LAO pool capital for early-stage crypto projects.
• Social Clubs: Groups coordinating around shared goals using tools like Snapshot for voting and Gnosis Safe for multisig treasuries.

Self-sovereign identity (SSI) allows individuals to control their verifiable credentials (VCs) without relying on central authorities. Blockchains provide the decentralized registry for public keys and schemas.

• W3C Standards: Verifiable Credentials Data Model.
• Decentralized Identifiers (DIDs): A new type of identifier, like did:ethr:0x....
• Use Cases: KYC/AML compliance, university degrees, professional licenses, and passwordless login systems. Projects include Microsoft Entra Verified ID and the Sovrin Network.