๐๐ฎ๐น๐ฐ๐๐น๐ฎ๐๐ถ๐ผ๐ป๐
If an attacker strives to create an alternate blockchain thatโs longer than the honest one, it's essential to understand that Bitcoin's security and integrity remain intact. The system has protections against arbitrary alterations, such as generating invalid bitcoin or seizing someone elseโs funds.
The main way for an attacker to exploit #Bitcoin is by modifying one of their recent transactions. In other words, they could buy something with bitcoin, and then undo the transaction. But even this would need to follow the system's rules and withstand scrutiny from honest nodes.
In the realm of Bitcoin's security, there's an ongoing competition between the honest chain (the legitimate blockchain) and an attacker's chain (a potentially malicious blockchain). Satoshi likens this contest to a "Binomial Random Walk", which is a statistical model where something moves unpredictably from one state to another.
Essentially, this description portrays the race between the honest and attacker's chains as a series of random events, with each additional block being a โstepโ in this unpredictable journey. Seeing it this way helps us grasp the probabilistic nature of their competition, and the factors influencing their progress.
Itโs possible to calculate the probability of an attacker catching up to the legitimate chain. Satoshi compared this to a "Gambler's Ruin" problem, in which a hypothetical gambler begins with a deficit and has unlimited resources to continue playing. This mirrors an attacker attempting to catch up to the honest blockchain when the attacker's chain is initially behind.
The probability being calculated is similar to assessing the likelihood of the gambler ever reaching the point of breaking even in their betting game. This provides a formal method to gauge the likelihood of these events happening over time.
As we calculate the probability of an attacker catching up to the honest blockchain, we see that ๐ต๐ฉ๐ฆ๐ช๐ณ ๐ค๐ฉ๐ข๐ฏ๐ค๐ฆ๐ด ๐ฅ๐ช๐ฎ๐ช๐ฏ๐ช๐ด๐ฉ ๐ฆ๐น๐ฑ๐ฐ๐ฏ๐ฆ๐ฏ๐ต๐ช๐ข๐ญ๐ญ๐บ as the number of blocks they need to catch up with increases.
This analysis even gives the attacker the benefit of the doubt, assuming he has greater computational power than the honest nodes. But even then, ๐ถ๐ณ ๐๐ต๐ฒ ๐ฎ๐๐๐ฎ๐ฐ๐ธ๐ฒ๐ฟ ๐ฑ๐ผ๐ฒ๐๐ป'๐ ๐ด๐ฎ๐ถ๐ป ๐ฎ ๐๐๐ฏ๐๐๐ฎ๐ป๐๐ถ๐ฎ๐น ๐น๐ฒ๐ฎ๐ฑ ๐ฎ๐ ๐๐ต๐ฒ ๐ผ๐๐๐๐ฒ๐, ๐๐ต๐ฒ๐ถ๐ฟ ๐ฐ๐ต๐ฎ๐ป๐ฐ๐ฒ๐ ๐ผ๐ณ ๐๐๐ฐ๐ฐ๐ฒ๐๐ ๐ณ๐ฎ๐น๐น ๐ผ๐๐ฒ๐ฟ ๐๐ถ๐บ๐ฒ.
The expanding computational power of the honest network makes it progressively harder for the attacker to overtake it. This beautifully demonstrates the security and robustness of the Bitcoin network.
Next, Satoshi delves into the question of how long a bitcoin recipient may wish to wait, in order to have enough confidence that the transaction can never be altered. He describes a scenario that involves a cautious recipient who wants to guard against a possibly malicious sender who intends to alter the transaction.
As a countermeasure to prevent a dishonest sender from preparing a fraudulent transaction in advance, the recipient can generate a new pair of cryptographic keys and provide the sender with the new public key just before signing the transaction. This approach reduces the window of opportunity for the sender to work on an attacking chain ahead of time.
Then Satoshi explains how waiting for Bitcoin transactions to be confirmed is crucial for transaction security. He estimates the potential progress an attacker might make during this waiting period, using statistical calculations, including Poisson distributions (๐ช.๐ฆ. ๐ข ๐ฎ๐ฆ๐ต๐ฉ๐ฐ๐ฅ ๐ง๐ฐ๐ณ ๐ฑ๐ณ๐ฆ๐ฅ๐ช๐ค๐ต๐ช๐ฏ๐จ ๐ณ๐ข๐ฏ๐ฅ๐ฐ๐ฎ ๐ฐ๐ค๐ค๐ถ๐ณ๐ณ๐ฆ๐ฏ๐ค๐ฆ๐ด ๐ธ๐ช๐ต๐ฉ๐ช๐ฏ ๐ข ๐ด๐ฑ๐ฆ๐ค๐ช๐ง๐ช๐ค ๐ฑ๐ฆ๐ณ๐ช๐ฐ๐ฅ ๐ฐ๐ง ๐ต๐ช๐ฎ๐ฆ, ๐ถ๐ด๐ช๐ฏ๐จ ๐ข๐ท๐ฆ๐ณ๐ข๐จ๐ฆ๐ด), to determine the expected value of the attacker's progress.
When all the mathematical probabilities are taken into account, letโs just say the attacker would be better off just using Bitcoin honestly. ๐
๐งต๐
