Blockchain Fundamentals

Understanding Hash Functions

Hash functions are mathematical algorithms that convert input data of any size into a fixed-size string of characters.

Key Properties:

• Deterministic: Same input always produces same output
• Fixed Output Size: Always produces same length hash
• Avalanche Effect: Small input change = drastically different output
• One-way Function: Easy to compute forward, impossible to reverse
• Collision Resistant: Extremely difficult to find two inputs with same hash

Common Hash Functions:

• SHA-256: Used in Bitcoin, produces 256-bit hash
• Keccak-256: Used in Ethereum
• Blake2: Fast and secure, used in various blockchains

Blockchain Applications:

• Block identification and linking
• Transaction verification
• Merkle tree construction
• Proof of Work mining
• Digital signatures

Digital Signature Cryptography

Digital signatures provide authentication, integrity, and non-repudiation for digital messages.

How Digital Signatures Work:

1. Key Generation: Create public/private key pair
2. Signing: Use private key to sign message hash
3. Verification: Use public key to verify signature

Elliptic Curve Cryptography (ECC):

Most blockchains use ECC for efficient digital signatures:

• secp256k1: Used by Bitcoin and Ethereum
• Ed25519: Used by Solana for faster verification
• Smaller keys: 256-bit keys vs 2048-bit RSA
• Faster operations: Efficient signing and verification

Blockchain Applications:

• Transaction authorization
• Wallet authentication
• Smart contract execution
• Multi-signature schemes

Proof of Work Consensus

PoW requires miners to solve computationally expensive puzzles to validate transactions and create new blocks.

How PoW Works:

1. Transaction Collection: Miners gather pending transactions
2. Block Creation: Form a block with transactions and metadata
3. Nonce Search: Find a nonce that makes block hash meet difficulty target
4. Block Broadcast: Share valid block with network
5. Verification: Other nodes verify and accept the block

Mining Process:

Block Hash = SHA256(
  Previous Block Hash +
  Merkle Root +
  Timestamp +
  Difficulty Target +
  Nonce
)

// Goal: Find nonce where hash starts with required zeros
// Example: 0000a1b2c3d4e5f6... (4 leading zeros = difficulty)

Advantages:

• Proven security model
• Decentralized and permissionless
• Resistant to attacks
• Simple to understand and verify

Disadvantages:

• High energy consumption
• Slow transaction throughput
• Mining centralization risks
• Environmental concerns

Proof of Stake Consensus

PoS selects validators to create new blocks based on their stake (ownership) in the network.

How PoS Works:

1. Staking: Validators lock up tokens as collateral
2. Selection: Algorithm chooses validator based on stake and randomness
3. Block Creation: Selected validator creates and proposes block
4. Attestation: Other validators vote on block validity
5. Finalization: Block becomes final after sufficient attestations

Validator Selection Methods:

• Randomized Block Selection: Higher stake = higher probability
• Coin Age Selection: Considers how long tokens have been staked
• Delegated Proof of Stake: Token holders vote for delegates

Slashing Conditions:

Validators lose staked tokens for malicious behavior:

• Double signing (creating two blocks at same height)
• Surround voting (contradictory attestations)
• Offline penalties for extended downtime

Advantages:

• Energy efficient (99% less than PoW)
• Faster finality
• Economic security through slashing
• Scalable to higher throughput

CAP Theorem

The CAP theorem states that distributed systems can only guarantee two of three properties simultaneously.

The Three Properties:

• Consistency (C): All nodes see the same data simultaneously
• Availability (A): System remains operational and responsive
• Partition Tolerance (P): System continues despite network failures

Blockchain Trade-offs:

• Bitcoin (CP): Prioritizes consistency and partition tolerance over availability
• Ethereum (CP): Similar to Bitcoin, eventual consistency model
• Some DeFi protocols (AP): May sacrifice consistency for availability

Network Partitions in Blockchain:

When network splits occur:

• Different parts of network may have different views
• Consensus mechanisms handle partition recovery
• Longest chain rule resolves conflicts
• Some transactions may be reversed (reorganization)

Practical Implications:

• Transaction finality takes time
• Higher confirmation counts = higher security
• Network upgrades require careful coordination
• Emergency procedures for major partitions

Tokenomics Fundamentals

Tokenomics combines token design with economic incentives to create sustainable blockchain ecosystems.

Token Types:

• Utility Tokens: Access to network services (ETH for gas)
• Governance Tokens: Voting rights in protocol decisions
• Security Tokens: Represent ownership or debt
• Stablecoins: Price-stable cryptocurrencies
• NFTs: Non-fungible tokens for unique assets

Supply Mechanisms:

• Fixed Supply: Bitcoin's 21M cap creates scarcity
• Inflationary: New tokens minted for rewards
• Deflationary: Token burning reduces supply
• Elastic: Supply adjusts based on demand

Incentive Alignment:

• Staking Rewards: Encourage network security
• Transaction Fees: Prevent spam and reward validators
• Liquidity Mining: Bootstrap DeFi protocols
• Governance Participation: Reward active community members

Economic Security:

The cost of attacking the network must exceed potential gains:

• PoW: Cost of 51% hash power
• PoS: Cost of 33% stake + slashing penalties
• Economic finality through stake at risk