The Bitcoin Revolution

The paper that I’ll be discussing today is perhaps the most famous that has come out in recent years- Bitcoin: A Peer-to-Peer Electronic Cash System, by Satoshi Nakamoto. It was a surprisingly short paper packed with the most amazing ideas for creating an alternate banking system. This paper has gone a long way in upending the finance industry.

Introduction

We all deal with digital money, for example when we make a payment through a credit card. There are some features of such transactions that are relevant to this discussion:

  1. We depend on trustworthy financial institutions to facilitate this transaction.
  2. Double spending, which is spending the same money multiple times, cannot always be prevented. Someone may buy a product using a credit card, use it, and then claim that his card was fraudulently used. In many such cases, because of lack of evidence, this money is refunded to the complainant, although he is clearly defrauding the system. Credit card companies consider this part and parcel of being in the business. Such transactions are called reversible transactions.
  3. These costs are added up for credit card companies, which then increase the price of transaction. Credit card companies approximate the amount of money they spend each year in hiring employees, advertising, and also in returning money to fraudulent customers. These costs are ultimately transferred to buyers and sellers.

In order to remove the need for third parties to moderate transactions, Nakamoto says that what is needed is an electronic payment system based on cryptographic proof. When you agree to pay me for a service that I’ve rendered to you, the proof of this exchange of money will be recorded in the public domain. Hence if I claim that you have not paid me, you can show me, and everyone else the proof of payment.

Transactions

How does it all work though? Everyone has a public key, and a private key. A key here stands for an ID number, like your Driver’s License number. When I make a payment to you, I verify this transaction with my public key, and sign the transaction with my private key. The money is then transferred to you, and the electronic details of your transaction, which contain details of both our public keys and also the time and amount, is hidden through hashing. What hashing does is that it takes all the details of a transaction, and converts it into an alphanumeric code like 000a234bfu344. This code can never be reserved back into the details of the payment. This is to ensure that both the payer and payee retain their privacy. The only thing that can be verified by everyone else is that the payment did indeed take place.

Bitcoin Network

This system of payments works by employing a set of CPUs/nodes to process and store the information of transactions. But what purpose does it serve? Let us demonstrate that with an example:

If you have a physical $10 note, you can clearly only spend it once. However, with digital money being a set of codes instead of a physical entity, people may try to use the $10 they have in digital money multiple times. Can they get away with it? If I try to spend my $10 digital money multiple times, the details of all these multiple transactions go to all nodes that are connected to the Bitcoin network. They only accept the first such transaction, and all other transactions are considered void. Now you can’t spend that $10 anymore, and the only person who can now spend that money is the person you paid.

Timestamp server

Details of each transaction are converted into an alphanumeric code, or a hash. Many such hashes form a block. When a block has been created by the network, a stamp of time is put on it, and every time the server sees that block in the “blockchain” it puts a timestamp on it. So for instance, if a block is created at 12 noon. Then it will have a timestamp of 12 noon. If the timestamp server processes the “blockchain” (literally chain of blocks) again at 12:05 PM, that particular block will have two time stamps- 12 noon and 12:05 PM, and so on. The nodes keep making chains will all the blocks that they receive, and keep exchanging each others blockchains to ensure that they haven’t missed out on any details or transactions.

Proof-of-Work

The recording of transactions, the hashing, the verification, all of this is done by CPUs connected to the Bitcoin network. But why should I connect my CPU to this network? This is what happens: every new transaction is broadcast to all nodes (or CPUs) in the network. Each node collects many such transactions into a block. Each node now tries to find a “proof-of-work” for this block, which is basically finding an appropriate hash code for the block with an appropriate number of 0‘s in front. The first node that finds such a code broadcasts it to all other nodes, who verify that that is indeed an appropriate code for that block. Now they add that block to the blockchain, and continue processing other transactions and blocks. The finding of this appropriate hash code is probabilistic, and each node is equally likely to find it, assuming equal computational power.

But why should I connect my CPU to the network for this? Because whatever I spend in the form of processing time and electricity costs, I get back in the form of Bitcoin. This Bitcoin essentially is a form of money that I can now spend online.

Information Loss

What about information loss? It is entirely possible that some node does not receive details of a certain transaction. However, we can be almost certain that at least one node will. And eventually, when the first node receives the block containing details of the missing transaction, it will rectify its mistake.

Now here’s an important caveat: as we’ve seen before, all these blocks are arranged in a chain. However, when these blocks are broadcast by one node (which could successfully come up with a good hash for the block) to all the other nodes, some nodes may have missed out on this. Let us suppose node A missed out on a block, but it successfully receives the next block. It creates a chain that is one block short. However, when it receives the block chains that other nodes have created, it discards the previous chain, and chooses the longer chain. This process of choosing the longer chain removes the errors that creep in when certain nodes do not receive all the blocks. This works on the assumption that at least some nodes receive all the information of all blocks in a small interval of time. This is likely, as there are thousands of nodes in the network.

Another caveat is that nodes only accept information of transactions that are valid. As a node receives all the information of all transactions, if I try to spend my digital $latex 10 twice, the nodes (which successfully receive this information) will not process my second transaction.

Reclaiming disk space

All the CPUs store all the information of each transaction on the network. That sure sounds like a lot of space. In order to clear space, blocks only store information pertaining to the fact that the transaction happened, and erase the details of old transactions. If a transaction can be thought of as a tree with roots (proof of transaction) and branches (details of transaction), the branches of the trees are cut off so that only the roots remain. Nakamoto calculates that a CPU would need only 4.2 MB of storage space in a year to store all information of all transactions.

Payment Verification

How do I verify that a certain transaction took place at 12 noon on Saturday? I ask the nodes for the longest blockchain (which is the correct one with no missing information), access the relevant block by using the right block header, and then verify that some payment indeed took place at that time. I cannot find out the parties involved, or the amount. However, the fact that this payment took place is public information.

Beating the network

What does beating the network mean here? I can either spend my $10 multiples times and force the network to accept it, or I can go into history, and erase the record of me paying someone money so that I can keep it for myself. Because no other codes will accept multiple transactions, the first option is infeasible. Hence, the only way I can do that is go back into history, erase the record of my payment, and then build blocks faster than other nodes so that I can make a longer chain than them.

Suppose there are 10,000 CPUs/nodes in the network, and I have managed to capture 100 of them. Suppose that the transaction that I want to erase was recorded z blocks ago. I need to go back z blocks, which means I need to erase z-1 blocks, erase my transaction from the zth block, and now hash blocks faster than the “honest” nodes so as to form a longer chain. Remember that only the longest blockchain will be thought to be the correct one, and will be accepted by all parties involved. This act of erasing blocks may stop all exchange of blocks between the “honest” nodes and the “evil” nodes under my control. Hence, the only way to legalize my fraud is to quickly build a longer blockchain, so that everyone will have to accept that my version of events is the correct one.

Coming up with the right hash or code for a block is probabilistic. Hence, the honest nodes, which are much greater in number, have a much higher chance of forming the longer blockchain. The author calculates that if the number of “honest” nodes h is greater than the number of “evil” nodes e, the probability of the evil nodes ever making a longer chain than the honest nodes is (\frac{e}{h})^z. Hence, if the number of honest nodes is much greater than the number of evil nodes, which is likely to be the case in the real world, then it is extremely unlikely that an evil person will be able to overpower the system.

Another incentive for people not to overpower the system is that if they spend the CPU power that they’re using for evil in hashing transactions and blocks instead, the monetary value of the bitcoin that they’ll earn will be far greater than any monetary reward that they might earn by trying to break the system.

Thanks for reading!

References

  1. Bitcoin: A Peer-to-Peer Electronic Cash System
  2. Hash

Published by ayushkhaitan3437

Hello! My name is Ayush Khaitan, and I'm a graduate student in Mathematics. I am always excited about talking to people about their research. Please please set up a meeting with me if you feel that I might have an interesting perspective to offer- https://calendly.com/ayushkhaitan/meeting-with-ayush

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