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1.INTRODUCTIONThe purpose of blockchain technology is to solve the trust problem between people or institutions and make the communication data and network communication of the Internet. In real, especially in some fields, the authenticity of data is very important. In daily life, data fraud is a problem that people are very worried about. For example, when a country elects a president, we should ensure that the data is not tampered with. At present, there is no foolproof way. However, if the voting process is published on the blockchain, it can ensure that the data is true and reliable because the blockchain scheme directly isolates the tamperability of the data from the technical level. Everyone’s voting records are open and traceable, saved into the blockchain, they cannot be modified. Through blockchain, This is the result we want, decentralization. We can make this truth in everyone’s hands at the same time. Everyone can monitor and supervise the voting process. Everyone has saved a backup, so everyone directly becomes the maintainer and manager of data. Fate of these data will be decided by everyone. This is the core logic of blockchain decentralization. As mentioned above, the popularity of blockchain technology will completely break the centralized pattern, indicating the advent of a new era in the future - Web3.0. In Figure 1, each block consists of its hash, the hash of the previousblock, a timestamp and some other block fields. In a brief history of security, blockchain is compared to a family tree. It’s equivalent to holding a tweeter on the square when ispeak, and what i say has been heard by many people. When someone wants to repent, as long as there are enough people to prove the truth, no one can repent The core cryptographic primitives of bitcoin are signature algorithm (ECDSA) and hash algorithm (hash). In fact, there are many cryptographic primitives used in blockchain, such as hash, digital signature, etc. Moreover, digital signature not only uses standard digital signature, but also uses ring signature, connectable ring signature, one-time signature, borromer ring signature, multi signature, homomorphic encryption, homomorphic commitment, accumulator, zero knowledge proof,etc. As well as the recently popular password signature toss. 2.RELATED CRYPTOGRAPHY2.1Hash functionHash functions are among the cryptographic primitives, which typically don’t encrypt or decrypt messages and can be used to ensure the data integrity [2]. A method to extract tiny digital “fingerprints” (also called as abstractions) from any type of data is the hash function, also known as hash function and hash algorithm. The hash function will produce a result with a set length and fixed format if data of any length and content are input, this result is comparable to the fingerprint of input data. The fingerprint will change as long as the input varies. For various contents, the hash function yields distinct fingerprints. Hash functions play an important role in blockchain security. Generally speaking, it is very safe. For example, if an attacker wants to crack a 256 bit private key, he must exhaust 2256 key possibilities. If a typical super computer that executes 1018 keys per second is used to crack such a system, it will take 3x1051 years to find the key [4]. The hash function has three main uses in the blockchain:
2.2Evolution of hash function in blockchain
Table 1.Fraction of SHA256d outputs with respective target value[1].
2.3One time digital signatureIn the blockchain version of bitcoin, digital signatures are used to protect data integrity throughout the system and to veri fy the identities of both parties to a transaction. A digital signature employs asymmetric encryption and digital digest tec hnology to guarantee the accuracy of the sender’s identity and the integrity of the material being transmitted. Digital sum marization is to use hash function to change information of any length into information of fixed length. Hash function is a one-way generation system, which generates input value to the generation through the generated hash value irreversibl y. In addition, hash function is a compression mapping, and the output is fixed length information. Digital signature can mainly realize as below:
2.4Ring SignatureRivest et al[5]first introduced the ring signature algorithm, a type of digital signature scheme, in 2001. Ring signatures are a type of group signature that leaks information covertly, or a simpler group signature [6]. The ring signature lists only ring members, not management. The signer randomly selects the public keys of multiple ringmembers, combining their public and private keys, random integers, and other technologies [7], in order to complete a ring signature. The signature verifier can only confirm that the signature is part of the signature set; they are unable to determine who signed the signature. For submitting complaints, casting ballots in elections, using electronic money, and other purposes, ring signature works quite well. The blockchain offers cross-parent transactions, data privacy disclosure, and an open and transparent record ledger. To achieve complete anonymity of users and defend their right to privacy, the technique uses the ring signature transaction signing scheme [7]. Ring signature implementation includes the following rules:
2.5Multi signature and aggregate signatureMany signatures on a digital item are what is commonly referred to as “multiple signatures.” Several signatures show that multiple persons may manage and control digital assets. This fund requires several private key signatures, which is referred to as multi-signature. Usually, a multisignature address or account will be used to hold this money or digital assets. It is comparable to a real-life document that must be signed by several departments in order to become enforceable. Multi signature is an improvement to the digital signature that enables the use of blockchain-related technologies in various spheres of life. An actual operation technique allows for the association of a multisignature address with n private keys. When transfer and other operations are required, as long as m private keys are signed, the funds can be transferred, where m should be less than or equal to N, that is, m/n is less than 1, and can be 2/3, 3/5, etc., which should be determined when establishing this multi signature address. If a couple needs to reserve a sum of money for their children to go to college. Before that, no one can move. Changing the signature mode to 2/2 not only limits the couple, but also increases the difficulty of hacker attacks. The design of multi signature makes it possible to decentralize various businesses. 2.6Homomorphic encryptionBy enabling a specific kind of calculation to be made on the ciphertext and producing an encrypted result that is also the ciphertext, homomorphic encryption facilitates the encryption process[8]. The operation that was carried out on the plaintext produced the result[8]. For instance, no one can determine the precise value of a single number by adding two encrypted numbers and waiting until the other person decrypts the result. This procedure is therefore quite secure. The application of privacy protection technology in blockchain is still in its early stage. For the process of realizing homomorphic encryption of FISCO bcos chain:all data on the chain can be encrypted by calling the Paillier library, and the ciphertext data on the chain can realize homomorphic encryption of ciphertext by calling the Paillier precompiled contract. After the ciphertext is returned to the business layer, it can be decrypted by calling the Paillier library to get the execution result. 2.7Homomorphic commitmentThe function of accumulator is to construct ring signatures on the one hand, and directly use it in blockchain on the other hand.Monroe coins are useful.As for the accumulator, it is also translated into aggregator in China, which is a good concept. It can compress many objects into one space, and the compressed space is almost as large as the original space of each object. 2.8Zero knowledge proofEarly in the 1980s, S. Goldwasser, S. Micali, and C. Rackoff proposed the zero knowledge proof. It means that the verifier can influence the verifier to believe that a certain conclusion is accurate without giving the verifier any valuable information. Zero knowledge proof is simply a contract between two or more parties, or a set of actions that two or more parties must execute in order to complete a task. The certifier convinces the verifier that he understands or is the owner of a certain message by proving it to him, but the verifier cannot learn anything about the proven message throughout the certification process. Zero knowledge proof has been demonstrated to be extremely beneficial in cryptography by a huge number of facts.If zero knowledge proof can be used for verification, many problems can be effectively solved. There are two types of zero-knowledge proof. First one is interactive zero-knowledge proof. It is the firstinvention and requires multiple messages between prover and verifier. The second one is non-interactivezero-knowledge proof. It requires less interaction between the prover and verifier[9]. Figure 3 shows the working principle of the whole zero knowledge proof. 3.CONCLUSIONBlockchain is built with cryptographic algorithm. The chain of digital signatures ensures that the transaction is correct, and then the hash function ensures the integrity and tamperability, ensuring that the data can be verified and its credibility. The unidirectionality of hash function can be used to control the generation speed of money, which is one aspect. On the other hand, the formation of blockchain has made new contributions to cryptography and done something we could not do in the past. With blockchain, cryptography is “valuable”. In the past, cryptography lost money. Passwords are used to protect data, and the cost is relatively high. But with blockchain, cryptography becomes valuable. Because we generate hash codes that meet certain conditions, and after some cryptographic functions, the results become money. At the same time, with blockchain and applications such as bitcoin, these cryptographers suddenly seem to be able to eat, so cryptography is “valuable”. In the past, cryptography could not achieve non repudiation. After the blockchain came out, it became interesting. It will be found that the blockchain itself provides a platform for non repudiation, because blockchain is now a trusted third party, and everyone obeys it. What is said on the chain can naturally play a role in repudiation, which is also the double flower problem in bitcoin. In fact, without the flexible and powerful security provided by public key encryption technology, e-commerce transactions relying on the Internet will be difficult to achieve. In the future, public key encryption technology will become an integral part of all kinds of information systems. Cryptography can guarantee the security of all virtual networks. Security is the basis of all transactions. Blockchain networks cannot be separated from encryption algorithms. Moreover, with the rapid development of science and technology, our encryption algorithm will continue to improve. REFERENCESRaikwar, Mayank & Gligoroski, Danilo & Kralevska, Katina,
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