Ethereum zero knowledge proof
From the current mainstream blockchain projects, blockchain projects are mainly divided into four categories: the first category: currency; The second is platform; The third category: application category; The fourth type: asset token
currencies mainly act as the "exchange media" in the field of blockchain assets, and the exchange media refer to general equivalents, such as gold and silver bills in the past< (currency exchange on trading blockchain assets)
platform projects refer to the establishment of technical platforms to meet the needs of various blockchain application development, which can rece the threshold of application development on blockchain
application projects cover a wide range of fields, including finance, social networking, games, property rights protection, etc., and are also the fastest growing fields of blockchain assets
asset token project refers to the blockchain mapping of physical assets, that is, the physical assets on the chain. At present, there are no more than 10 varieties
01 currency
the first category is currency project, which is also the earliest blockchain project. Currency projects mainly include bitcoin and lightcoin. In addition, there is another kind of asset with the characteristics of anonymity. Its main functions include protecting the privacy of both sides of payment while realizing payment. The well-known ones are dash, monero and zcash. Currency is mainly used as the "exchange medium" in the field of blockchain assets. The exchange medium is the general equivalent you use to exchange goods. For example, gold, silver and silver bills can be used as the exchange medium in the past. At present, there are more than 2100 types of digital assets in the world, and the number of currency blockchain projects has increased rapidly recently. As of June 2018, bitcoin is still the largest market value
02 platform type
the second type is platform type blockchain project. The main function of platform type blockchain project is to establish a technical platform to meet the technical requirements of various blockchain application development; In short, platform applications allow developers to directly issue digital assets and write smart contracts on the blockchain. Smart contract is a computer program running on the blockchain database, which can be automatically executed under the conditions of its source code setting
for example, you develop a smart contract based on the house rent protocol on the blockchain. When the owner receives the rent, it will trigger the automatic execution and give the security key of the apartment to the tenant
the main function of platform blockchain projects is to establish the underlying technology platform, so that developers can do application development on the underlying technology platform. A considerable number of platforms are still in the development state. As of June 2018, Ethereum has the largest market value
03 application
the third category is application blockchain projects. Application projects are blockchain projects based on blockchain development platform (such as Ethereum), which can solve many problems in various fields of the real economy
for example, augur, Golem, vechain, omisego, which provides asset exchange and transfer services. Using blockchain technology, these projects can better solve the problems of trust and cross-border circulation. At the same time, using smart contracts and tokens on the blockchain, they can better realize automatic execution and greatly improve the efficiency of social and economic activities. Application blockchain projects cover a wide range of fields, including finance, social networking, games, property rights protection and so on. It is also the field with the fastest market value increment of blockchain projects at present
04 asset token
the fourth category is the asset token blockchain project. Asset token refers to linking the blockchain assets to physical assets such as gold and US dollars, which is the blockchain mapping of physical assets. As of February 2018, there are no more than 10 varieties. The typical representatives are usdt against US dollars, digix Dao against gold, Digix each token represents 1 gram of Gold Certified by the London Bullion Market Association. Asset token has the advantages of convenient transaction and safekeeping. First of all, asset token is more convenient for transaction. Because blockchain assets can be split, it has better liquidity
for example, at present, real estate needs to be transferred as a whole. If the real estate can be token, it can be split and purchased, which is more convenient for transaction. Secondly, the token of physical assets is more concive to custody. Gold is easy to wear out and cause losses in physical transactions, but there is no need for physical transfer after the token of physical assets, which is more concive to the custody of physical assets
in fact, blockchain uses the basic principles of modern cryptography to ensure its security mechanism. The knowledge system involved in the field of cryptography and security is very complicated. Here, I only introce the basic knowledge of cryptography related to blockchain, including hash algorithm, encryption algorithm, information digest and digital signature, zero knowledge proof, quantum cryptography, etc. Through this lesson, you can learn how to ensure the confidentiality, integrity, authentication and non repudiation of the blockchain using cryptography technology
basic course lesson 7 basic knowledge of blockchain security
1. Hash algorithm (hash algorithm)
hash function (hash), also known as hash function. Hash function: hash (original information) = summary information. Hash function can map any length of binary plaintext string to a shorter (generally fixed length) binary string (hash value)
a good hash algorithm has the following four characteristics:
1. One to one correspondence: the same plaintext input and hash algorithm can always get the same summary information output
2. Input sensitivity: even if the plaintext input changes slightly, the newly generated summary information will change greatly, which is greatly different from the original output
3. Easy to verify: plaintext input and hash algorithm are public, anyone can calculate by themselves, and whether the output hash value is correct
4. Irreversibility: if there is only the output hash value, the hash algorithm can never dece the plaintext
5. Conflict avoidance: it is difficult to find two plaintexts with different contents, but their hash values are the same (collision)
for example:
hash (Zhang San lent Li Si 100000 yuan for 6 months) = 123456789012
such a record as 123456789012 is recorded in the account book
it can be seen that hash function has four functions:
simplify information
it is easy to understand, and the information after hashing becomes shorter
identification information
you can use 123456789012 to identify the original information, and summary information is also called the ID of the original information
hidden information
the account book is a record like 123456789012, and the original information is hidden
verification information
if Li Si cheated that Zhang San only lent Li Si 50000 when repaying, both parties can verify the original information with the hash value of 123456789012 recorded before
hash (Zhang San lent Li Si 50000 for 6 months) = 987654321098
987654321098 is completely different from 123456789012, which proves that Li Si lied, Then the information can't be tampered
common hash algorithms include MD4, MD5 and Sha series algorithms, and Sha series algorithms are basically used in mainstream fields. Sha (secure hash algorithm) is not an algorithm, but a group of hash algorithms. At first, it was SHA-1 series, and now the mainstream applications are sha-224, SHA-256, sha-384 and sha-512 algorithms (commonly known as SHA-2). Recently, Sha-3 related algorithms have been proposed, such as keccak-256 used by Ethereum
MD5 is a very classic hash algorithm, but unfortunately, both it and SHA-1 algorithm have been cracked. It is considered by the instry that its security is not enough to be used in business scenarios. Generally, sha2-256 or more secure algorithm is recommended
hash algorithm is widely used in blockchain. For example, in blocks, the latter block will contain the hash value of the previous block, and the content of the later block + the hash value of the previous block will jointly calculate the hash value of the later block, which ensures the continuity and non tamperability of the chain< Encryption and decryption algorithm is the core technology of cryptography, which can be divided into two basic types: symmetric encryption algorithm and asymmetric encryption algorithm. According to whether the key used in the encryption and decryption process is the same or not, the two modes are suitable for different needs, just forming a complementary relationship, and sometimes can be combined to form a hybrid encryption mechanism
symmetric cryptography (also known as common key cryptography) has the advantages of high computational efficiency and high encryption strength; Its disadvantage is that it needs to share the key in advance, which is easy to leak and lose the key. The common algorithms are des, 3DES, AES and so on
asymmetric cryptography (also known as public key cryptography) is different from the encryption and decryption key, and its advantage is that it does not need to share the key in advance; Its disadvantage is that it has low computational efficiency and can only encrypt short content. Common algorithms include RSA, SM2, ElGamal and elliptic curve series. Symmetric encryption algorithm is suitable for the encryption and decryption process of a large number of data; It can't be used in signature scenario: and it often needs to distribute the key in advance. Asymmetric encryption algorithm is generally suitable for signature scenario or key agreement, but it is not suitable for large amount of data encryption and decryption< Third, information digest and digital signature
as the name suggests, information digest is to hash the information content to obtain a unique digest value to replace the original and complete information content. Information digest is the most important use of hash algorithm. Using the anti-collision feature of hash function, information digest can solve the problem that the content has not been tampered
digital signature is similar to signing on paper contract to confirm contract content and prove identity. Digital signature is based on asymmetric encryption, which can be used to prove the integrity of a digital content and confirm the source (or non repudiation)
we have two requirements for digital signature to make it consistent with our expectation for handwritten signature. First, only you can make your own signature, but anyone who sees it can verify its validity; Second, we want the signature to be only related to a specific file and not support other files. These can be achieved by our asymmetric encryption algorithm above
in practice, we usually sign the hash value of information instead of the information itself, which is determined by the efficiency of asymmetric encryption algorithm. Corresponding to the blockchain, it is to sign the hash pointer. In this way, the front is the whole structure, not just the hash pointer itself< Zero knowledge proof means that the verifier can make the verifier believe that a certain conclusion is correct without providing any additional information to the verifier
zero knowledge proof generally meets three conditions:
1. Completeness: authentic proof can make the verifier successfully verify
2. Soundness: false proof can not make the verifier pass the verification
3. Zero knowledge: if you get proof, you can't get any information other than the proof information from the proof process< With more and more attention paid to the research of quantum computing and quantum communication, quantum cryptography will have a huge impact on the information security of cryptography in the future
the core principle of quantum computing is that qubits can be in multiple coherent superposition states at the same time. Theoretically, a large amount of information can be expressed by a small number of qubits and processed at the same time, which greatly improves the computing speed
in this way, a large number of current encryption algorithms are theoretically unreliable and can be cracked, so the encryption algorithm has to be upgraded, otherwise it will be broken by quantum computing
as we all know, quantum computing is still in the theoretical stage, which is far from large-scale commercial use. However, the new generation of encryption algorithms should consider the possibility of this situation.
according to the introction, zcash uses a technology called zero knowledge proof (known as "ZK snark") to verify the authenticity of the transaction. It uses a public blockchain to display the transaction, but it will hide the amount of the transaction. Viewing the owner of the key (i.e. the owner of the coin) allows others to view the information associated with the key
in short, this method of calculation allows users to prove that they have the currency they want without exposing information about where the currency came from or is going. It's like zero knowledge proof allows you to enter a password on a website and verify it by the website's server without actually transmitting the password
in contrast, although bitcoin and other digital currencies are famous for their concealment of transactions, in real life, they can often track transactions through the records of ordinary bitcoin blockchain, so that people can accurately know the sender and sending location of bitcoin. Nowadays, zcash has realized the transaction of original data in the form of encryption, rather than publishing the transaction data to the public like bitcoin. Snowden also said that the anonymous zcash project can solve the monitoring risk of bitcoin
therefore, zcash, an anonymous function that pursues the ultimate privacy protection, is first considered to have great value in the financial instry. Foreign media pointed out that the traditional financial instry has an extraordinary demand for information protection. Although many people think that the privacy requirements of bitcoin and other blockchain systems come from crypto anarchists and liberals, the fact is that the traditional financial instry is promoting the hiding of transaction information on the blockchain
however, the anonymity of digital currency is also a headache for the regulatory authorities, and it is very difficult to popularize it in the world. At most, it is only a niche proct. However, the platform developed by using blockchain technology has great potential. For example, the blockchain content publishing platform decent, Ethereum's intelligent contract and so on.
apart from BCH and BSV, most of the other bifurcated currencies have declined. BTC, BCH and BSV represent the exploration of three different directions respectively. BTC is the most conservative and cautious, BSV is the most radical, and BCH is relatively mild and graal. At present, BTC enjoys the name of bitcoin in fact and has the largest market value< br />
< At the end of 2013, vitalik buterin (V God), a gifted programmer born in 1994, published a white paper on Ethereum, proposing the idea of adding various smart contracts to cryptocurrency, which can be used in social networking, trading, games and other fields. The market value of Ethereum has soared all the way, and it will soon be second only to bitcoin, Ethereum with smart contracts is also known as blockchain 2.0
in 2016, Ethereum encountered a serious hacker coin theft incident (DAO), and God V decided to delete the coin theft record by using rollback method. However, some people who insisted that the blockchain should not be tampered with opposed rollback, so Ethereum also split. Unlike bitcoin, the original Ethereum chain has become a minority, known as the Ethereum classic (etc), and the new chain that has been rolled back has become a majority, the de facto Ethereum (ETH)
stable currency system
stable currency is generally anchored legal currency, which can be used to exchange legal currency 1:1 to the issuer. The currency value is relatively stable, but sometimes there will be a small amount of premium in transactions, which is widely used in cryptocurrency transactions. Now the most common stable currency is the usdt issued by tether company, 1 usdt = 1 dollar. Stable currency is generally issued on other cryptocurrency networks, such as bitcoin Omni protocol, Ethereum erc20 protocol, etc< br />
in anonymous currency
on bitcoin, every transaction is clear and searchable, although we don't know who the person behind the address is. Some people think that the privacy of bitcoin is not enough, so some anonymous coins, such as XmR, dash and zcash, which can cover up user information, have emerged. Monroe coin uses ring signature technology, dasey coin adopts mixed coin technology, and big zero coin uses zero knowledge proof, which can play an anonymous effect in different degrees
platform currency system
some digital currency trading platforms often release their own platform currency, and there are certain discounts for trading with platform currency, such as okb of okex, HT of fire currency, BNB of coin security, etc<
some other mainstream currencies
lightcoin (LTC) has copied the code of bitcoin, replaced the consensus algorithm, and shortened the block out time. When bitcoin wants to upgrade, it often does experiments on bitcoin first. Lightcoin is known as "bitcoin, lightsilver"
XRP is currently the third largest currency in market value. It is an Internet transaction protocol, allowing users to transfer money around the world quickly and cheaply
grapefruit coin (EOS), known as blockchain 3.0 and Ethereum upgrade, attempts to introce more functions and application expansion on it
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"bitkangaroo" is the first digital currency financial service platform in the world that allocates theoretical revenue from its own mines and machines without power failure. The platform is mainly based on cloud computing procts, and the theoretical revenue is allocated by "1tash" of Wanyou computing power's professional mine, a strategic partner, on a regular basis every day, integrating high-yield, security, liquidity, transparency and professionalism
High Yield: the platform aims at "increasing users' assets", and customers can choose a variety of derivatives to prevent systemic risks
Security: the team stores the standby digital assets in the cold multi signature wallet, and in case of any accident, the reserve fund will be used to distribute revenue to customers
Liquidity: the platform allocates income every day, and can withdraw as soon as it reaches the minimum currency withdrawal standard
transparency: mine data and mine logs are open and transparent, and users can monitor the actual computing power of the mine at any time through the data center monitoring system
Professional: the mine is operated and managed by professional personnel who have been engaged in deep mining for many years. Each unit is isolated by professional network interruption to prevent virus invasion. Multiple standby networks are used in the computer room to eliminate non systematic risks in an all-round way
there should be key settings over there
but one of the chain mining presets I know seems to press v
in Goldwasser's zero knowledge proof, there must be interaction between the prover and the verifier, which is called "interactive zero knowledge proof". In the late 1980s, Blum and others further proposed the concept of "non interactive zero knowledge proof", using a short random string instead of the interactive process and realizing zero knowledge proof. One of the important applications of non interactive zero knowledge proof is the large-scale network which needs to execute a large number of cryptographic protocols
in zero knowledge proof, a person (or device) can prove that he knows the secret without revealing any secret.. if zero knowledge proof can be used for verification, Will be able to effectively solve many problems..
proof materials
with relevant zero knowledge proof materials:
zero knowledge proof is not proof in terms of mathematical feeling, because there is a fixed possibility P in any zero knowledge proof Peggy can provide the right response to the challenge, that is, she does not know the key. However, if the test is repeated N, timing fraud is reced, and the probability of Peggy fraud is reced to an arbitrary level by increasing the number of test winners
example strategy
Peggy's public key is a large chart, which we will call G. Peggy was organized by G some time ago, and widely then published it. Because she specifically made it for the purpose, Peggy knew about a Hamilton cycle. Peggy will prove her identity to the winner and she knows a Hamilton cycle in G. Even if G is public information, no one can do it, because no one knows a Hamiltonian cycle of G, and it is a difficult problem to find Hamiltonian cycle in graph (see NP completeness)
however, Peggy can't simply tell the winner Hamilton's cycle, because then the winner (or eavesdropper) can pretend to be Peggy. Peggy can't reveal any information in any period, because eavesdroppers may be able to collect information in several different occasions and integrate it, so that eavesdroppers have enough information to play the role of Peggy
to prove her identity, Peggy and the winner play several circles in the following competitions:
Peggy marks the G endpoint with a random number. The edges may then be represented as a pair of these numbers. She lists g edges, and encrypts each edge with an additional key. She then sends the coded edge to the winner
the winner flips the coin
* if the coin comes over the head, Peggy surrenders the key to the random number and maps from the endpoint. The winner decodes the edge and then verifies that the encrypted edge is sent in step 1 to actually do graph. G and no other graph
* if the coin comes over the tail, Peggy surrenders the key only for actually forming the edge of Hamilton's cycle. Winners decode these edges and verify that they do form the right length of cycle
the impostor; Pamela ') Be able to manage to play Peggy, and have a 50% chance of successfully bluffing the winner in any particular round. There are two possible play strategies. Pamela can send Peggy's graph. G to code. In this case, she escaped detection if the winner threw his head; She revealed that it was coded, and the winner verified that the chart was indeed G. But if the winner throws his tail, Pamela is caught. The set of keys she was asked to reveal constituted a Hamilton cycle g edge, and she could not do that because she did not know one
another strategy Pamela can follow is to prepare some other chart. She knows that the h of a Hamilton cycle is coded. She is safe in this case if the winner throws his tail; She reveals the cycle, and, because the winner never looks at the margin of the remainder, he never learns that the chart is h and not g. But if the winner throws the head, Pamela is asked to reveal the whole chart, and the winner sees that this is not g
by playing this game for 20 rounds, the winner can rece the possibility of being fooled by Pamela to only 1 / 2. By playing more circles, the winner can rece the possibility of craving
information revealed by Peggy provides winner any information in all not g's Hamilton cycles. Look at this, notice that the winner can make transcripts of the game without talking to Peggy at all. He was able to select the sequence head and tail, and then prepare the hypothetical reply from Peggy, who had never known Hamilton's cycle, by engaging the appropriate impostor strategy in each circle. Transcripts, and it doesn't contain, cable legitimate information about Peggy's identity. Peggy proved her identity not because she could base her answer on the right one, but because she could base her answer on the right one, she didn't know what the problem would be
the so-called zero knowledge proof refers to a method that the demonstrator does not disclose any information when proving his own identity, and the verifier can not get any private information of the demonstrator, but can effectively prove the identity of the other party. It seems a bit awkward. I'll give you two examples to understand
several examples of zero knowledge proof [original]
proof examples
1) a wants to prove to B that he has the key of a room, assuming that the room can only be opened with the key, but no other method can. At this time, there are two methods:
① a shows B the key, and B uses the key to open the lock of the room, so as to prove that a has the correct key of the room
② B confirms that there is an object in the room. A opens the door of the room with his own key, and then shows the object to B, so as to prove that he really has the key of the room
the following method belongs to zero knowledge proof. The advantage is that in the whole process of proof, B can't see the appearance of the key, so as to avoid the leakage of the key
2) a owns B's public key. A has never seen B, but B has seen a picture of A. one day, two people meet and B recognizes a, but a is not sure whether the person in front of him is B. at this time, B has two ways to prove to a that he is B
① B gives its private key to a. a encrypts some data with the private key, and then decrypts it with B's public key. If it is correct, it proves that the other party is B
② a gives a random value, B encrypts it with its own private key, and then gives the encrypted data to a, a decrypts it with B's public key, and if the original random value can be obtained, it proves that the other party is B
the latter method belongs to zero knowledge proof
3) there is a ring-shaped corridor with a gap. The exit and entrance are very close (within the eye distance), but there is a door in the middle of the corridor that can only be opened with a key. A has to prove to B that he has the key to the door. Using zero knowledge proof, B watches a enter the corridor from the entrance, and then walk out of the corridor from the exit. At this time, B does not get any information about the key, but it can prove that a has the key.
in essence, zero knowledge proof is a protocol. The so-called protocol is a series of steps taken by two or more participants to complete a specific task, including the following three characteristics:
1. Protocol is an orderly process from beginning to end, and each step must be executed in turn. Before the previous step is finished, the latter step cannot be executed
2. An agreement requires at least two participants. One person can complete a task by performing a series of steps, but it does not constitute an agreement
3. A task must be completed by executing the protocol
although the reasoning based on mathematics is very complex, the idea is simple
the so-called zero knowledge proof refers to a method that the demonstrator does not disclose any information when proving his own identity, and the verifier can not get any private information of the demonstrator, but can effectively prove the identity of the other party. It seems a bit awkward, give a few examples: (from the network)
1) a wants to prove to B that he has the key of a room, assuming that the room can only be opened with the key, but no other method can. At this time, there are two methods:
(1) a shows B the key, and B uses the key to open the lock of the room, so as to prove that a has the correct key of the room
(2) B determines that there is an object in the room. A opens the door of the room with his own key, and then shows the object to B, so as to prove that he does have the key of the room
the latter method belongs to zero knowledge proof. The advantage is that in the whole process of proof, B can't see the appearance of the key, so as to avoid the leakage of the key
2) a owns B's public key. A has never seen B, but B has seen a picture of A. one day, two people meet and B recognizes a, but a can't be sure whether the person in front of him is B. at this time, B has two ways to prove to a that he is B
(1) B gives its private key to a. a encrypts a certain data with the private key, and then decrypts it with B's public key. If it is correct, it proves that the other party is B
(2) a gives a random value, B encrypts it with its own private key, and then gives the encrypted data to a, a decrypts it with B's public key, and if the original random value can be obtained, it is proved that the other party is B
the latter method belongs to zero knowledge proof
3) there is a ring-shaped corridor with a gap. The distance between the exit and the entrance is very close (within the eye distance), but there is a door that can only be opened with a key somewhere in the middle of the corridor. A has to prove to B that he has the key to the door. Using zero knowledge proof, B watches a enter the corridor from the entrance, and then walk out of the corridor from the exit. At this time, B does not get any information about the key, but it can prove that a has the key< In my understanding, zero knowledge proof is an authentication protocol. A proves to B that he has "something" (such as identity) instead of giving B the opportunity to use his own characteristics. That is to say, B can't have the ability to prove to others that he is a. in real life, for example, ID card, You can show your ID card to others to prove yourself, but you don't have to give him your ID card, otherwise he can impersonate you. This is the zero knowledge proof agreement
zero knowledge proof protocol usually consists of three protocol steps:
witness: the prover selects a random number and gives the verifier a secret number of knowledge. This number is related to a series of questions that the prover can answer<
challenge: the verifier randomly selects a question in these question sets and sends it to the verifier
reply: the verifier uses his secret number to solve this problem and sends it to the verifier
or an example of ID card:
A: I am a and tell B I have an ID card
b: can I have a look at the ID card
A: show your ID card< The zero knowledge proof should be to prove how much information a divulges to B. for example, my ID card example must be based on the premise that B can't and forge the ID card, otherwise, we still divulge the information to B. the curve model established should take these into account
let me give another example of authentication (a checks b):
method 1:
A generates a random message and sends it to B, B encrypts it with its private key and sends it to a, and a decrypts and verifies the message with B's public key
there is a problem here, B sometimes doesn't know what message he encrypts, and a can impersonate B with the encrypted message, Or decrypt (though hard). The zero knowledge of this kind of verification is not good
improvement: on the premise that Party A determines Party B's public key, Party B finds an unimportant message and sends two messages to Party A. one message first uses the message digest and then encrypts it with the private key, and the other message is not encrypted. In this way, Party a can still verify Party B, but zero knowledge is good< There are many interesting stories about zero knowledge proof on the Internet.
Yes
blockchain can solve the problem of mutual trust in transactions
< H2 > smart contract solves the problem of mutual trust in transactionssince the beginning of bitcoin, blockchain technology has been developing continuously. In 2014, Ethereum further developed a variety of new functions of smart contract technology. Smart contract is linked in the form of digital, & quot; Once generated, the information recorded in the blockchain will be permanently recorded and cannot be tampered with; It can solve the trust problem of "strange trust"
ulord has the property of smart contract, which introces the design concept of gas, but different from Ethernet gas, every operation consumes gas. Compared with the gas concept of ether, ulord adopts a more simplified and abstract method. The resources and sites that users publish on the ulord consume the resources on the ulord network. Therefore, when users publish resources or sites, they need to bind a certain amount of ulordtoken. With the growth of block height, the ulordtoken will be consumed graally. Users need to fill in a new ulordtoken at the address corresponding to the consumed site to ensure the ownership of the domain name. At the same time, through the side chain technology, it can be compatible with the Ethernet virtual machine, publish smart contracts, and allow users to publish their own tokens. There is a certain proportion of exchange relationship between tokens and ulordtoken. Ulord allows users to customize the release of their own site services, and by issuing their own tokens, they can operate their own site
< H2 > ZK snark technology to protect transaction privacyulord will adopt the most mainstream privacy protection ZK snark technology to protect transaction privacy. In the ulord blockchain, creating an effective transaction includes the following three things:
1
2. The sender proves that he is the "holder" of the currency by means of authorized signature
The input of transaction is equal to its outputthe work of proving that money has not been spent before is done by the ledger itself, which does not require the sender to do any work. The sender only needs to prove that he is the holder of these currencies, and he wants to send these currencies by means of electronic signature through the private key corresponding to the address. In order for the signature to be verified, the sender's address must be public. Correspondingly, the receiver must disclose the receiving address to complete the transaction process. In the use of ulord, it is simple to verify that the input and output of the transaction are equal, because the number of transmissions is fully revealed

