P(z) = \sum_{k=0}^{\infty} \frac{\lambda^k e^{-\lambda}}{k!} \left( \frac{q}{p} \right)^k
where: * $$q$$ = attacker's hashrate * $$p$$ = honest hashrate * $$\lambda = z \cdot \frac{q}{p}$$ For $$q < 0.5$$, the probability becomes negligible after 6 confirmations. *** ### 2.2. Multilayer security Bitcoin has **5 layers of security**: 1. **Cryptographic** → signatures, hashes 2. **Economic** → incentives, rewards 3. **Energy** → PoW 4. **P2P Network** → antiseptic topology 5. **Social / consensus** → independent nodes *** ## 3. Classic attacks on the blockchain ### 3.1. 51% attack Attacker obtains >50% of the hashrate. Can: * reorganize N blocks * reverse their own payments * temporarily censor transactions Cannot: * forge bitcoins * steal others' funds * break ECDSA * change rules Estimated cost of the attack:\text{Costo} \approx \text{Hashrate global} \times \text{Precio electricidad} \times \text{Tiempo}
Conclusion: **economically suicidal**. *** ### 3.2. Double-spend attacks Type A: **Race attack**\ Type B: **Finney attack**\ Type C: **Vector 76**\ Type D: **Deep reorg** (requires massive PoW) Bitcoin mitigates through: * successive confirmations * accumulated PoW * honest nodes * fast propagation *** ### 3.3. Eclipse attacks (node isolation) Goal: isolate a node and control all the information it receives. Mitigation: * redundant connections * geographic diversity * random addressing * anti-Sybil rules * P2P protocol improvements (BIP155) *** ### 3.4. Censorship attacks Miners may attempt to exclude transactions: But: * pools are replaceable * individual miners switch pools * market competition * economic incentives (fees) * node relay Outcome: large-scale censorship → impractical. *** ## 4. Economic attacks ### 4.1. Selfish mining (Eyal & Sirer, 2013) Theory: a miner hides blocks to amplify their reward. Requires >33% of the hashrate to be profitable. Mitigated by: * faster block propagation * natural penalty * improved network topology * against honest strategies *** ### 4.2. Spying / pool-hopping Miners jump between pools based on reward probability. Effect: reduces efficiency of poorly designed pools.\ The global system is not affected. *** ### 4.3. State-level economic attack A State could attempt to: * subsidize electricity * buy massive hardware * censor blocks internationally Problems: * astronomical cost * specialized hardware hard to manufacture * detectable attacks * difficult political coordination * nodes can reject invalid blocks *** ## 5. Network and P2P layer attacks ### 5.1. Sybil attacks Create thousands of fake nodes to influence the network. Mitigations: * PoW limits useful identities * random topology * full nodes verify everything * no voting → multiple identities do not grant power *** ### 5.2. DDoS attacks Attempt to saturate nodes: * rate limiting * automatic disconnection * protected mempool * dynamic TTL Bitcoin Core incorporates defenses by design. *** ## 6. Cryptographic attacks ### 6.1. Breaking SHA-256 Currently: **impractical**. Even with quantum computing: * Grover reduces the complexity of $$2^{256}$$ to $$2^{128}$$ * still impossible to break in reasonable times *** ### 6.2. Breaking ECDSA Theoretical quantum threat (Shor's algorithm). Natural mitigation: * public keys not revealed until spent * possible future transition to post-quantum signatures * soft-fork for new schemes Bitcoin is prepared to upgrade if necessary. *** ## 7. Consensus security Bitcoin is not democratic.\ Rules are not voted on.\ Nodes **verify** immutable rules. ### 7.1. Who decides the rules? 1. **Users run full nodes** 2. Nodes accept or reject blocks 3. Miners *cannot* impose invalid rules 4. Developers do not control nodes 5. Exchanges also do not control rules It is a system of **emergent consensus**, not imposed. *** ### 7.2. Hard forks vs soft forks * **Soft fork** → restrictive, compatible changes * **Hard fork** → changes rules, creates new chain Bitcoin favors soft forks (BIP9, BIP8, Speedy Trial). *** ## 8. Game theory applied Bitcoin implements a game of incentives: | Player | Goal | Strategy | | -------------- | ---------------- | ------------------------- | | Miners | Maximize revenue | Mine honestly | | Nodes | Security | Reject invalid blocks | | Users | Ownership | Choose honest nodes | | Pool operators | Fees | Coordinate work | | Attackers | Profit | Attack → prohibitive cost | Nash equilibrium: > Mining honestly is the dominant strategy. *** ## 9. Mathematical models of security ### 9.1. Probability of deep reorgP = \left( \frac{q}{p} \right)^z
If $$q = 0.1$$ and $$z = 6$$:P = (0.1)^6 = 10^{-6}
*** ### 9.2. Energy cost of the attackCosto = H_{red} \cdot E \cdot t
Where: * $$H\_{red}$$ hashrate * $$E$$ cost per hash * $$t$$ time Cost far exceeds possible benefits. *** ## 10. Social and political attacks The most dangerous: * anti-Bitcoin propaganda * regulatory pressure * attempts at prohibition * intimidation of miners * blocking exchanges But Bitcoin resists: * private nodes → impossible to shut down * mobile miners → global relocation * liquidity outside exchanges * extreme decentralization *** ## 11. Emergent security of the ecosystem ### 11.1. Full nodes Nodes enforce: * block size * valid signatures * correct scripts * consensus rules * accumulated PoW * heaviest chain * valid timestamps Miners **do not command**; nodes verify. *** ### 11.2. Mempool: defense against invalid transactions The mempool discards: * double spends * transactions without fees * out-of-range transactions * malformed data *** ## 12. Chapter conclusion Bitcoin's security is the combination of: * unbreakable cryptography, * alliances of economic incentives, * physical costs of attack, * distributed consensus, * independent verifying nodes, * adversarial game theory, * emergent immutability. Bitcoin is not secure by “luck”:\ it is secure because **it designs incentives so that attacking is more expensive than defending**. *** > Bitcoin's security is not based on trusting anyone.\ > It is based on that, even if someone wanted to attack, **they could not afford it**. *** --- # Agent Instructions This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com. ## Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter: ``` GET https://www.notbank.com/learn/academy/en/bitcoin/security.md?ask=