Daily Productive Sharing 120 - What Is Bitcoin From A Math Perspective?
(The English version follows)
#finance/crypto
比特币在近期突破了四万美金的历史高位，吸引了不少关注。如果你想现在投资比特币或者其他加密货币，不妨先了解一下这些加密货币的原理。今天的分享非常浅显地介绍了比特币背后用到的数学知识和加密学知识，非常推荐。它回答了以下几个主要问题：
- 如何保证比特币的价值？
- 如何在没有国家机构背书的情况下，大家对比特币达成共识？
- 如何方便地验证比特币交易？
- 如何从技术上杜绝作弊？
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原链
# A technical introduction to Bitcoin for non-technical people
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Bitcoin has attracted a lot of attention as it recently surpassed an all-time high of $40,000. If you want to invest in Bitcoin or other cryptocurrencies now, you might want to learn a little bit about how these cryptocurrencies work. Today's share is a very detailed introduction to the math and cryptography used behind Bitcoin and is highly recommended. It answers several key questions such as:
- how do you guarantee the value of bitcoin?
- how to reach a consensus on bitcoin without the endorsement of a national institution?
- how to easily verify bitcoin transactions?
- how to technically eliminate cheating?
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# A technical introduction to Bitcoin for non-technical people
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Excerpt
Have no fear: although it’s a complicated system, there are no individual parts to it that are terribly difficult to understand.
Cryptography underpins digital security: it helps software architects build and wield a kind of asymmetry: constructing digital structures and operations that are expensive to attack, and cheap to defend.
This math problem has a useful property for us: it is hard to do, but easy to verify.
This math problem has a useful property for us: it is hard to do, but easy to verify.
A hash function, at its simplest, goes “for any input, we’re going to process it with a certain rule, and generate a deterministic output which doesn’t reveal what the input number was.”
Good hash algorithms, like one we’ll see later on called SHA-256 (“Secure Hash Algorithm”), have a useful set of properties in common. For any given input of a string of characters: 1) the outputs will be unique, to a sufficiently high degree of probability, 2) they’ll all be the same length, so they can be easily stored and compared, and 3) small changes in the input will lead to huge changes in the output.
If you don’t have Howie’s private key (if you’re trying to spy on them, for instance) there is mathematically no way to break the encryption other than brute force trying every key combination; the difficulty level of modern encryption services is sufficiently high as to make unauthorized decryption effectively impossible.
In general, cryptography is useful whenever we want to make a technical system robust against attack at little cost to the defender.
That’s good news for us: identity and ownership are important aspects of money and payments!
It’s easy for me to prove I possess a certain key, but it’s much harder for me to prove that I am the only person who possesses this key.
We can take advantage of cryptography to create a kind of task that serves no useful purpose aside from being deliberately computationally expensive, and impossible to cheat.
When used correctly, proof of work can be used to impose a genuine kind of scarcity and skin in the game: “You’re serious about this? Prove it by showing me how much work you’re willing to do for it.”
Their value derives dually from 1) the fact that your peers also assign it value, and 2) that it has some inherent scarcity which prevents inflationary devaluation.
Creating a successful digital currency means figuring out a way to create “un-forgeable, costly bits” where transactions between parties cannot be faked, nor can they be stopped or censored by anyone.
We can define a little digital object called a coin that says, “I am a coin. I live inside a wallet. There’s only one thing you can do with me if I am in your wallet, which is specify a new wallet to send me to. If you so choose to do that, I will no longer be your wallet’s coin, I’ll become the new wallet’s coin.”
If you can successfully create unforgeable costly bits, then a peer to peer network would be a good way for those bits to get recognized, traded and stored.
The safest way to know for sure that people aren’t cheating is to have a historical record of all transactions that have ever taken place, so that the identity and integrity of every single coin can be traced back to its source.
But with internet money that has to be able to function anywhere in the world, we don’t want to trust banks; in fact we don’t want to trust anyone.
Instead, we’re going to try a new idea: put the ledger of transactions in public, out in the open, on the peer to peer network where anyone can read it and consult it.
On the contrary, if the book is a matter of public record, and is maintained by the group collectively rather than by any one individual, censorship is harder.
Repeat this to yourself one more time to let it sink in: the challenge isn’t figuring out how to choose one transaction over another based on which one is “correct” or more deserving. The challenge is on getting everyone to agree on an order of transactions.
The Byzantine Generals Problem: The challenge is: can you come up with a system that will allow the generals to know, with absolute certainty, whether they’ve reached real consensus – even if any given message is susceptible to tampering or any general could be a bad actor?
Byzantine Fault Tolerance generally means: “suppose you have a system that contains a bunch of components, and the components need to communicate together in order to avoid some sort of failure. How do you engineer the system to avoid failure even if the components themselves are individually unreliable?
The first critical breakthrough idea in the Bitcoin protocol is the following: Asking people to collaborate to maintain our transaction ledger seems like a losing battle. Collaboration is too susceptible to tampering; it’s too susceptible to stalemate; it’s too vulnerable to bad actors, no matter how you structure it. Specifically, there’s no way to fully safeguard against double spending. So what if instead of getting people tocollaborateto maintain the book, we had themcompetefor the opportunity to maintain the book?
It’s worth repeating that idea one more time: instead of asking people to collaborate, make them compete. Specifically, make them compete on some task where 1) it’s impossible to cheat; 2) it costs them real resources so that they have skin in the game, 3) where the outcome of the task turns writing in the book into a kind of one-way function: it’s effectively impossible to undo once done.
With Bitcoin, this reward comes in two forms: first, as a small “tax” that the winner of the competition gets to levy off of everyone whose transactions were processed in that batch. Second, the winner of the competition gets to assign themselves some newly created Bitcoin as a reward specifically for them.
For the time being, just remember that 1) everybody who’s engaging in this proof of work competition is pursuing a real reward, and 2) the total number of Bitcoin in circulation will ultimately be restricted, to prevent runaway inflation.
This is important to remember, because we can understand how someone who’s writing in the ledger book cannot fake transactions by other people and other coins that they don’t have; not without knowing the private keys.
What I’ll do is broadcast my solution to the group: I’ll publicly post my whole block, including the header and whatever the correct nonce happens to be. Then, the group will check my work; they can do this pretty quickly.
Each time someone successfully solves the proof of work challenge and mines a block, it’s like time freezes; we get to all look together to make sure the block is valid; once we agree and commit to begin the next block, time starts back up again.o repeat that one more time: true consensus means not only are we all 100% in agreement today, but we have to be certain that no one in the future can retrospectively go back and change their answer, in any way, no matter how talented of a hacker they might be or how much coercion they have on anybody.
Mining has a real cost, and and it’s only worth it if you have a chance at gaining a bitcoin reward for your troubles.
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