Mathematics Behind Bitcoin
Bitcoin’s security and functionality rely on cryptography, algorithms, and game theory:
1. Cryptographic Hash Functions (SHA-256):
• Creates unique, irreversible hashes for data security.
• Used in mining and verifying transactions.
2. Public-Key Cryptography (Elliptic Curve Cryptography):
• Private keys generate public keys and Bitcoin addresses.
• Ensures ownership and secures transactions without revealing private keys.
3. Proof of Work (PoW):
• Miners solve complex puzzles to validate transactions and add blocks.
• Prevents manipulation by making attacks computationally expensive.
4. Game Theory:
• Incentivizes honesty with rewards (block rewards/fees).
• Makes attacking the network cost-prohibitive.
5. Finite Supply & Halving:
• Bitcoin’s supply is capped at 21 million.
• Mining rewards halve every 4 years to control issuance and mimic scarcity.
6. Merkle Trees:
• Efficiently verify transactions using a hierarchical structure of hashes.
These principles ensure Bitcoin’s decentralization, security, and trustworthiness.
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