Hash Functions

• •Definition: A mathematical function that takes any input and produces a fixed-size output (the hash or digest).
• •One-way: Easy to compute the hash from input, impossible to reverse (find input from hash).
• •Deterministic: Same input always produces the same output.
• •Avalanche effect: Changing one bit in the input completely changes the output.
• •Collision resistance: Nearly impossible to find two different inputs that produce the same hash.

• •Full name: Secure Hash Algorithm 256-bit
• •Output: Always 256 bits (64 hexadecimal characters)
• •Example: SHA256("Hello") = 185f8db32271fe25f561a6fc938b2e264306ec304eda518007d1764826381969
• •Security: No known attacks; considered secure for decades to come.
• •Speed: Fast enough to compute billions per second, slow enough to make brute force impractical.
• •Uses in Bitcoin: Addresses, mining, transaction IDs, Merkle roots, block hashing.

• •SHA-256: Bitcoin's primary hash function (256-bit output).
• •RIPEMD-160: A 160-bit hash function used in creating Bitcoin addresses.
• •Double SHA-256: Hashing the output of SHA-256 again (SHA256(SHA256(x))). Bitcoin uses this in many places.
• •Hash rate: In mining context, the number of hashes per second miners compute.
• •Merkle root: A single hash representing all transactions in a block (created by hashing pairs of hashes).
• •Collision: When two different inputs produce the same hash (should be nearly impossible).

1. Mining (Proof of Work)

• •Miners hash block headers repeatedly to find a hash below the target.
• •Example: Find nonce such that SHA256(SHA256(block header)) < target.

2. Addresses

• •Public key → SHA-256 → RIPEMD-160 → Base58Check = Bitcoin address.

3. Transaction IDs

• •Each transaction's data is hashed to create a unique transaction ID (txid).

4. Merkle Trees

• •All transactions in a block are hashed into a single Merkle root.

5. Block Hashes

• •Each block's header is hashed to create a unique block ID.

6. Script verification

• •Hash locks (like in Lightning) use hashes to lock funds until a secret (preimage) is revealed.

• •Huge output space: 2²⁵⁶ possible hashes (more than atoms in the universe).
• •No shortcuts: Only way to find a specific hash is trial and error (brute force).
• •Avalanche effect: Can't predict output by tweaking input.
• •No known breaks: SHA-256 has been thoroughly analyzed for decades with no practical attacks.
• •Quantum resistance: SHA-256 is believed to be resistant to quantum computers (unlike ECDSA).

• •Address security: Even if someone knows your public key, they only see the hashed version (your address). This adds an extra layer of security.
• •Transaction immutability: Once a transaction is hashed into a block, changing it would change the block hash, breaking the chain.
• •Chain integrity: Each block includes the previous block's hash, creating an immutable chain.
• •Simplified Payment Verification (SPV): Light clients can verify transactions using Merkle proofs without downloading the full blockchain.

• •RIPEMD-160: Used alongside SHA-256 in address generation (smaller 160-bit output).
• •SHA-1: Older, broken hash function (collisions found). Not used in Bitcoin.
• •MD5: Even older, completely broken. Never use for security.
• •SHA-3: Newer NIST standard. Not used in Bitcoin, but secure.
• •BLAKE3: Modern, fast hash function. Not used in Bitcoin, but interesting for future systems.