Blockchain architecture is a distributed ledger system consisting of several key components:

• Blocks: Data containers holding transaction records, timestamps, and cryptographic hashes
• Hash Functions: Create unique digital fingerprints for data integrity (commonly SHA-256)
• Merkle Trees: Binary tree structures that efficiently summarize all transactions in a block
• Digital Signatures: Cryptographic proofs of transaction authenticity
• Consensus Mechanism: Protocol ensuring network agreement on valid transactions
• Peer-to-Peer Network: Distributed nodes maintaining synchronized copies of the ledger
  The architecture ensures immutability, transparency, and decentralization without requiring a central authority.

Public Blockchains: Fully open networks where anyone can participate, read, and write transactions. Examples: Bitcoin, Ethereum. They offer maximum decentralization but have slower performance.
Private Blockchains: Restricted networks controlled by a single organization. Only authorized participants can access and validate transactions. They provide faster performance and privacy but sacrifice decentralization.
Consortium Blockchains: Semi-decentralized networks controlled by a group of organizations. Validation rights are restricted to pre-selected nodes. They balance performance, privacy, and partial decentralization. Common in supply chain and banking consortiums.

Hash functions are mathematical algorithms that convert input data of any size into fixed-length output strings (hash values).
Key Properties:

• Deterministic: Same input always produces same output
• Avalanche Effect: Small input change drastically changes output
• One-way: Computationally infeasible to reverse
• Collision Resistant: Nearly impossible to find two inputs with same output
  Blockchain Applications:
  Block Linking: Each block contains hash of previous block, creating an immutable chain.
  Transaction Integrity: Merkle trees use hashes to efficiently verify transaction data.
  Mining: PoW consensus requires finding hashes meeting difficulty targets.
  Address Generation: Public keys are hashed to create wallet addresses.
  Example (SHA-256):

Input: "Hello" → Hash: 2cf24dba4f21d4288fd4c8c...
Input: "hello" → Hash: aec070645fe53ee3b3763059...

A Merkle tree is a binary tree structure where:

• Leaf nodes contain hashes of individual transactions
• Internal nodes contain hashes of their child nodes
• Root node (Merkle root) represents the entire block's data
  Importance:
• Efficient Verification: Can verify any transaction without downloading the entire block
• Data Integrity: Any change in transactions changes the Merkle root
• Scalability: Enables light clients to verify transactions with minimal data
• Quick Synchronization: Nodes can quickly identify differences between block versions
  Example: With 4 transactions [T1, T2, T3, T4], the tree structure allows verifying T1 by only knowing Hash(T2), Hash(T3,T4), making verification O(log n) instead of O(n).