Blockchain – Tech Pomelo

Bitcoin is no stranger to anyone. The reason why many people believe in its value is because everyone thinks that it is more reasonable to endorse it by mathematical algorithms than by the government. As for the technology behind Bitcoin, in fact, most people don’t understand it. With the mathematical foundation we learned before, we can talk about Bitcoin or, more broadly, the mathematical foundation of blockchain.

Why is the nature of encryption a mathematical asymmetry?

Mathematically, the reason why all cryptocurrencies can be circulated and not cracked is because of the asymmetric beauty in mathematics. People usually like symmetry, hate asymmetry, and feel that the latter is imperfect. When it comes to obtaining information, everyone wants transparency, because opacity and hiding are always unsettling. However, asymmetry sometimes has its own beauty , such as the golden section is asymmetric.

As far as information security is concerned, complete transparency and complete symmetry will bring many security risks. When we are the owner of the information, we don’t really want others to get our information, especially private information, but often we have to share access to many information for convenience so that the other party can verify the authenticity and know us. It helps identify who we are ,or let the other party make some analysis/ statistics to provide us with better services. In the past, we did not share information, and many things could not be achieved. For example, when you applied for a loan from a bank, you almost shared all personal and financial information to the bank.

In a completely open information society, it is almost impossible to completely protect information security. We have said this many times. If you want to protect private information, especially privacy, you must have an asymmetric mechanism, so that others can use the information without owning it under certain authorization, and you can let them verify the information without granting ownership to the information.

The significance of Bitcoin is that it confirms that we can protect information from being leaked through encryption and authorization, and that some authorized people can still use the information.

Bitcoin does this because the encryption key and the decryption key are not the same. The key used for encryption is the so-called private key, which is only owned by the owner of Bitcoin, and the decryptor uses the public key generated by the private key, which can be given to anyone.

The asymmetry of this encryption lies in the fact that in a limited computation time, the private key cannot be deduced from the public key. Therefore, you can think that the person holding the private key can see all the information, while the person holding the public key can only see part of the information or only verify the authenticity of the information. In order to further understand this asymmetric characteristic, we may wish to look at a specific example.

If we want to sell a house, we must first prove that the house belongs to us and is eligible for sale. In the past, we had to let the buyer see the real estate certificate, and the relevant department or notary agency had to prove that the real estate certificate was genuine. This way you come and go many times, and the buyers will know a lot of information about you, and they can even forge a deed exactly like yours.

In the future, the digital real estate certificate can be stored on the blockchain. As a homeowner, the blockchain algorithm will give us a private key, and all the information is in your hands. Then the corresponding public key can be generated to the buyer to verify the ownership of our homeowner, which is enough, the buyer does not need to know other information about us.

This process of verifying the real estate certificate using the blockchain protocol can be illustrated with a picture:

Of course, it should be noted that the purchaser verified the authenticity of the deed after using the public key. If he buys the house, the deed will be transferred to his name and the private key of the original homeowner will be invalidated, and then the new homeowner can have the new private key, and this process will be recorded in the blockchain’s ledger.

Next, let’s see how this is done mathematically. Let’s use the Bitcoin protocol as an example. It uses a method called elliptic curve encryption. Compared with the currently popular RSA encryption algorithm, the elliptic curve encryption method can achieve a comparable or better encryption effect with a shorter key.

So, what is elliptic curve encryption? We will start with elliptic curves and their properties.

An elliptic curve has nothing to do with an ellipse. It is a set of curves with the following properties: y ² = x³ + ax + b

The shape of this type of curve is shown below:

The principle of elliptic curve encryption

The characteristic of this curve is that it is symmetrical up and down, very smooth, and has many good properties, especially drawing a straight line from any point on the curve (point A in the figure). It has at most three intersections with the curve itself (including the point) itself).

So what does such a curve have to do with encryption? We use the following figure to illustrate.

Process of point multiplication on elliptic curve

In the figure, we start from point A, draw a line through point B, and finally intersect the curve at point C. Using this property, we define an operation called dot multiplication “·”, we use

A · B = C

To represent the relationship between these three points, which means: connecting from point A to point B, and intersecting the curve at point C. Since the elliptic curve is symmetrical with respect to the x-axis, we make C a symmetry point D about the x-axis. Let D be a new point, and then connect a line with point A. Then, we have another intersection point E with the elliptic curve.

A · D = E

We can then repeat this process continuously. Suppose we have finally performed K times of point multiplication and stopped at point Z.

Note: In this process, there are four points that need to be explained:

First of all, the operation of dot multiplication satisfies the laws of commutation and combination, so which step is counted first, and which step is counted afterwards. We do not prove this property.

Secondly, it is possible that after such a point multiplication calculation several times, the x value of an intersection point, that is, the abscissa is very large. In order to prevent the calculation results from diverging after continuous iteration, we set a boundary on a place on the right with a large abscissa Max (maximum value), after exceeding Max, let the straight line reflect back.

Secondly, although the curve in the figure is continuous and the value of each point is a real number, when we really use it, we discretize it by some transformation, so all points are integer values.

In the end, some people may worry that after this calculation, they will return to a certain point. Don’t worry about this, this operation is a bit like multiplying two huge prime numbers and then dividing a prime number to take the remainder (also known as modulo operation, Mod), as long as the algorithm is well designed, and it repeats at a certain point. The probability is almost zero.

If we think of the point multiplication in the above curve operation as a multiplication of numbers, after K times of point multiplication, it is equivalent to the power of K, and then given the starting point A and the ending point Z, K is actually equivalent to A is the logarithm of the base Z. Therefore, this calculation process is called discrete logarithm calculation of elliptic curve. Then why should I tell you this process of calculations over and over again?

The calculation of the elliptic curve I mentioned above has a characteristic. If I tell you that it starts with A, then passes from B to C, then to D, to E, etc. After taking a total of K steps, you can calculate that it finally stopped at Z The process is intuitive and simple. However, if I tell you that the starting point is A and the ending point is Z, if you want to guess how many steps I have completed to complete the above process, it is almost impossible, or the amount of calculation is huge. This asymmetry makes it very easy to verify the results, but it is more difficult to crack the password.

Specifically, the encryption protocol used by Bitcoin is a standard called SECP256K1, which uses the following very simple elliptic curve: y ² = x³ + 7

Using the very simple curve in the form above, we have completed encryption that looks very complicated from the outside.

There are many encryption methods for elliptic curves. Although their algorithms and key lengths are different, their principles are similar. The US National Standards and Research Institute has stipulated that the minimum key length for this type of algorithm is 160 bits, and there are 192 bits, 224 bits, and so on. They are much shorter than the shortest 1024 bits required by RSA, which is the advantage of elliptic curve encryption.

So is such a short key safe? In fact, in 2003, a research team spent 10,000 PCs a year and a half to crack a shorter 109-bit key. However, the decryption time increases exponentially with the length of the key. Cracking a 160-bit key requires about 100 million times the calculation amount, and it is even more difficult to crack a 192-bit or 224-bit key. Therefore, it is difficult to decode the information encrypted by elliptic curves unless the speed of the computer is increased by a million times.

Of course, Google has made a breakthrough in quantum computing in 2019. In certain calculations, calculations that previously took tens of thousands of years to complete can be completed in an instant. Therefore, many people are worried about whether the encryption of the blockchain is still safe. It should be said that if Google’s technology can really get out of the laboratory and can be used for more calculations, not just specific calculations, the current blockchain encryption algorithm needs to be modified.

However, the idea of elliptic curve encryption is still secure, because encryption (and the difficulty of verifying passwords) and decryption are always asymmetric. Even if the computing power of a computer has been increased by a trillion times, a more complex encryption can be used, such as quantum computing. To no avail. In short, as long as this asymmetry of mathematics exists, encryption is secure.

Beginning in 2020, a Global battle against the new Coronavirus began. In the race against time, various new technologies have demonstrated their powers. Big data tracks close contacts to analyze the spread. Artificial intelligence is used in remote consultations. Infrared measuring instruments detect the temperature of human groups. Robots deliver meals to isolated people. Epidemic prevention and control is a systematic project of the whole society, and the monitoring and control of technical forces have played an inestimable role. So what role can the same blockchain technology be expected to play in this battlefield?

The characteristics of the blockchain: building an ideal “fortress of trust”

In the information society, we face massive amounts of fragmented information every day. This information comes from different media, through various channels, and may have undergone several “processing”, occupying your senses with unbridled expression. In daily life, you can of course choose to block or selectively obtain, but when you want to pursue the truth of an event and master complete and true information, you will find that this is actually a huge challenge.

Not only that, most people will not give up the need to restore the truth in extraordinary times. Especially in the face of sudden crisis events such as this epidemic, collective anxiety may even exacerbate this impulse, forcing people to use the most primitive ways to stitch fragments when they lack the necessary scientific tools. This also led to rumors at the beginning of the epidemic, about the spread of the epidemic, the number of people infected, the way of transmission, the control methods, various pieces of public opinion, expert advice, and platform information of mainstream and non-mainstream media. Very loud. There are also many questions raised by the Red Cross Society of Hubei Province not long ago. The Red Cross Society, which is responsible for receiving and distributing aid materials, was involved in a storm of public opinion due to the distribution of materials and opacity of information.

When uneven pieces of information are rushed together, those parts that can’t fit and join can easily become the focus of attention, especially when guessing can’t fill the cracks in logic and imagination, those parts may become Group panic breeds soil. Once the trust crisis breaks out, it is undoubtedly more difficult to rebuild trust. The seeds of doubt are always endless. In addition, in this epidemic, in addition to being authentic and credible, real-time nature is also one of the requirements of the public for information. The lagging information obviously cannot satisfy the public’s grasp of the situation, neither can it serve the implementation of the solution, nor can it facilitate the implementation of public supervision.

In response to this crisis, blockchain technology can make a difference in the construction of “credibility”.

1. Integrate information fragments and present data panorama. To respond to the epidemic, we need multisectoral, full-process, real-time data and information. At the same time, this information can be made available to the public to ensure the public’s right to know. The blockchain can improve the ability to respond to crisis events by sharing data among all participants, and can automate data sharing and storage in different levels of organizations, thereby realizing data integration throughout the process and showing a panoramic view of the data.

2. Open and transparent, not tamperable.
Based on the data structure in the block, any data in the block is modified, so that the lower layer and the upper layer hash value in this block cannot correspond. In addition, any read, write, delete, and retrieve activities on the chain will leave marks. From this perspective, blockchain technology achieves openness and transparency of information and cannot be tampered with. If the infection cases in this epidemic are chained, information such as the onset time, disease changes, and treatment progress will be recorded on the chain, so that medical personnel and scientific researchers around the world can also grasp the trends in the non-infected areas to conduct research. It is also very beneficial to be able to break through the virus attack as soon as possible. At the same time, because the blockchain uses multi-party node authentication, each authenticated node must bear certain responsibilities, and it will also promote the collaboration efficiency of various departments. In the framework, at least each department, as a node on the chain, can clarify its own job responsibilities and responsibilities, rather than perfunctory responsibility on the ambiguous edge.

3. The whole process can be traced, which is easy for accountability.
The introduction of the blockchain traceability mechanism, the accountability of this accountability, and the improvement of this improvement are conducive to the establishment of a society-wide prevention and control system. To the outbreak of material donations and distributed, for example, if the block in the chain which provides technical support, all the money and materials can be the first to achieve information on the chain of time. This can effectively get rid of the intermediary role of the middleman as a transfer channel for a large amount of assistance, thereby reducing problems such as misappropriation and theft. Because no matter how many links the material goes from the donor to the recipient, there are records to follow, and the problem of information breakage between logistics, warehousing, and distribution will not occur. Where is the donated material, whether it is distributed in a timely manner, where is the stall, and who is the ultimate beneficiary of the donated money, whether it has become a bucket of water, a bag of instant noodles, or a protective clothing, as a donor can be clear, no information is in the black box.

Many issues of trust were exposed during the public health crisis. “Credibility” is not only a moral concept of justice, but also a cornerstone of social affairs management. Increasing the public’s trust in the government, so as to cooperate with the government to do a good job in epidemic prevention and control, is the right way. Only through transparent and open information, clear coordination of powers and responsibilities, and active and traceable policy implementation can the government’s macro-coordination role be better exerted.

The reality of blockchain: large-scale application is still a long way to go

Blockchain as a cutting-edge technology toolbox is still in the early stages of development, and there is application in large scale. The popularity of the blockchain is relatively low. From a practical point of view, to promote the reality of the blockchain, certain conditions must also be met. From the perspective of epidemic prevention and control, the support and cooperation of multiple parties are still needed.

First, because blockchain requires the cooperation of participants, for example, donors and hospitals must have corresponding terminals. At the same time, in order to ensure the authenticity of the on-chain information, verifying the authenticity of the information is also a major challenge.

Second, because the links involved in the blockchain are extremely complex, its applications must be supported by infrastructure such as big data and cloud computing. This requires the government to coordinate the cooperation of various departments and open the corresponding big data interface, which requires that it be reflected in the top-level design.

Third, because the nature of distributed storage block chain requirements, the design of distributed nodes need to have professionals come to support. Relevant talent reserves still need to accumulate for a period of time.

Fourth, because world has a vast geographical area and regional economic and social development is still unbalanced, in the process of implementing the blockchain, the popularity of hardware facilities needs to wait for the opportunity. For example, to trace the trajectory of the infected person, a large number of cameras and local network connections are needed. At present, these infrastructures need to be improved, especially in relatively remote areas.