Bitcoin and Cryptocurrency Technologies: A Comprehensive Introduction - Chapter 1

CHAPTER 1: Introduction to Cryptography and Cryptocurrencies

Cryptocurrencies, like traditional currencies, require mechanisms to control supply and enforce security properties to prevent fraud. While fiat currencies rely on central banks for issuance and anti-counterfeiting features, cryptocurrencies enforce rules purely through technology—without centralized authorities. This chapter explores the cryptographic foundations underpinning cryptocurrencies.

1.1. Cryptographic Hash Functions

Core Properties of Cryptographic Hash Functions:

1. Collision Resistance:

   • Infeasible to find two distinct inputs (x ≠ y) producing the same output (H(x) = H(y)).
   • Example: SHA-256’s 256-bit output makes collisions statistically improbable.

2. Hiding:

   • Given y = H(x), it’s infeasible to determine x.
   • Achieved by concatenating inputs with high-entropy secrets (e.g., H(r ‖ x)).

3. Puzzle Friendliness:

   • No shortcuts to find x for a target y when k is randomized.
   • Essential for mining in cryptocurrencies like Bitcoin.

Applications:

• Message Digests: Verify data integrity (e.g., file storage systems).
• Commitment Schemes: Securely commit to values without revealing them initially.

SHA-256

• Compression Function: Transforms 768-bit inputs into 256-bit outputs.
• Merkle-Damgård Transform: Extends fixed-length hashing to arbitrary-length inputs.

1.2. Hash Pointers and Data Structures

Block Chain:

• Linked list with hash pointers instead of traditional pointers.
• Tamper-evident: Any alteration disrupts hash continuity, detectable via the head pointer.

Merkle Trees:

• Binary trees with hash pointers for efficient membership verification.
• Proof of Membership: Log(n) path verification (e.g., verifying transactions in Bitcoin).

1.3. Digital Signatures

Components:

1. Key Generation: (sk, pk) := generateKeys(keysize).
2. Signing: sig := sign(sk, message).
3. Verification: isValid := verify(pk, message, sig).

Security Properties:

• Unforgeability: Only the secret key holder can sign; signatures are verifiable by pk.
• ECDSA: Bitcoin’s elliptic-curve scheme (secp256k1 curve).

Practical Concerns:

• Randomness: Critical for secure key generation.
• Message Size: Sign hash digests (e.g., SHA-256) for arbitrary-length data.

1.4. Public Keys as Identities

Decentralized Identity Management:

• Generate identities (addresses) as hash(pk).
• No central registration; identities are pseudonymous but linkable via transaction patterns.

1.5. Two Simple Cryptocurrencies

Goofycoin

• Rules:

  1. Goofy creates coins via signed CreateCoin statements.
  2. Owners transfer coins by signing Pay statements.
• Weakness: Double-spending possible without a ledger.

Scroogecoin

• Ledger: Append-only block chain signed by Scrooge.

• Transaction Types:

  • CreateCoins: Minted by Scrooge.
  • PayCoins: Consumes and creates coins of equal value (signed by owners).
• Centralization Issue: Scrooge controls validation, creating trust bottlenecks.

Next Step: Removing centralization (e.g., Bitcoin’s consensus mechanism).

FAQs

Q: Why is collision resistance important in cryptocurrencies?

A: Ensures transaction IDs and coin histories are unique, preventing fraud like double-spending.

Q: How do Merkle trees improve efficiency?

A: They enable log(n)-sized proofs for membership, crucial for scalable validation in block chains.

Q: What’s the role of randomness in ECDSA?

A: Bad randomness leaks keys, compromising security. Secure randomness prevents predictable key generation.

👉 Learn more about cryptographic foundations
👉 Explore Bitcoin’s consensus mechanisms

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