Consensus Algorithms

Consensus is a fundamental problem in distributed systems. Since the 1970s, this problem has been researched in the context of distributed systems, but a renewed interest has arisen in developing distributed consensus algorithms that are suitable for blockchain networks. In this chapter, we will explore the underlying techniques behind distributed consensus algorithms, their inner workings, and new algorithms that have been specifically developed for blockchain networks.

In addition, we will introduce various well-known algorithms in a traditional distributed systems arena that can also be implemented in blockchain networks with some modifications, such as Paxos, Raft, and PBFT. We will also explore other mechanisms that have been introduced specifically for blockchain networks such as proof of work (PoW), proof of stake (PoS), and modified versions of traditional consensus such as Istanbul Byzantine Fault Tolerant (IBFT), which is a modified, ‘blockchained...

Introducing consensus

The distributed consensus problem has been studied extensively in distributed systems research since the late 1970s. Distributed systems are classified into two main categories, namely, message passing and shared memory. In the context of blockchain, we are concerned with the message-passing type of distributed systems, where participants on the network communicate with each other via passing messages to each other. Consensus is the process that allows all processes in a network to agree on some specific value in the presence of faults.

As we saw in Chapter 1, Blockchain 101, there are different types of blockchain networks. In particular, two types, permissioned and public (permissionless), were discussed. The consensus problem can also be classified based on these two paradigms. For example, Bitcoin is a public blockchain. It runs PoW, also called Nakamoto consensus. In contrast, many permissioned blockchains tend to run variants of traditional or classical...

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In this chapter, you will be introduced to the concepts and practical aspects of public key cryptography, also called asymmetric cryptography or asymmetric key cryptography. We will continue to use OpenSSL, as we did in the previous chapter, to experiment with some applications of cryptographic algorithms so that you can gain hands-on experience. We will start with the theoretical foundations of public key cryptography and will gradually build on the concepts with relevant practical exercises. After this, we will introduce some new and advanced cryptography constructs.

Before discussing...

Mathematics

As the subject of cryptography is based on mathematics, this section will introduce some basic concepts that will help you understand the concepts presented later.

Modular arithmetic

Also known as clock arithmetic, numbers in modular arithmetic wrap around when they reach a certain fixed number. This fixed number is a positive number called modulus (sometimes abbreviated to mod), and all operations are performed concerning this fixed number.

Modular arithmetic is analogous to a 12-hour clock; there are numbers from 1 to 12. When 12 is reached, the numbers start from 1 again. Imagine that the time is 9:00 now; 4 hours from now, it will be 1:00 because the numbers wrap around at 12 and start from 1 again. In normal addition, this would be 9 + 4 = 13, but that is not the case on a 12-hour clock; it is 1:00.

In other words, this type of arithmetic deals with the remainders after the division operation. For example, 50 mod 11 is 6 because 50 / 11 leaves a remainder of 6.

Sets...

Asymmetric cryptography

Asymmetric cryptography refers to a type of cryptography where the key that is used to encrypt the data is different from the key that is used to decrypt the data. These keys are called private and public keys, respectively, which is why asymmetric cryptography is also known as public key cryptography. It uses both public and private keys to encrypt and decrypt data, respectively. Various asymmetric cryptography schemes are in use, including RSA and ElGamal encryption.

A generic depiction of public-key cryptography is shown in the following diagram:

Figure 4.1: Encryption/decryption using public/private keys

The preceding diagram illustrates how a sender encrypts data P using the recipient's public key and encryption function, and produces an output encrypted data C, which is then transmitted over the network to the receiver. Once it reaches the receiver, it can be decrypted using the receiver's private key by feeding the C encrypted data into decryption...

Cryptographic constructs and blockchain technology

Now, we'll present some advanced topics in cryptography that not only are important on their own but are also relevant to blockchain technology due to their various applications in this space.

Homomorphic encryption

Usually, public key cryptosystems, such as RSA, are multiplicative homomorphic or additive homomorphic, such as the Paillier cryptosystem, and are called partially homomorphic systems. Additive Partially Homomorphic Encryptions (PHEs) are suitable for e-voting and banking applications.

Until recently, there has been no system that supported both operations, but in 2009, a fully homomorphic system was discovered by Craig Gentry. As these schemes enable the processing of encrypted data without the need for decryption, they have many different potential applications, especially in scenarios where maintaining privacy is required, but data is also mandated to be processed by potentially untrusted parties, for example, cloud...

Summary

This chapter started with an introduction to some basic mathematics concepts and asymmetric key cryptography. We discussed various constructs such as RSA and ECC. We also performed some experiments using OpenSSL to see how theoretical concepts can be implemented practically. After this, hash functions were discussed in detail, along with their properties and usage. Next, we covered concepts, such as Merkle trees, that are used extensively in blockchains and in fact are at its core. Other concepts such as Patricia trees and hash tables were also introduced. We also looked at some advanced and modern concepts such as zero-knowledge proofs and relevant constructions, along with different types of digital signatures.

In the next chapter, we will explore the captivating world of distributed consensus, which is central to the integrity of any blockchain and is a very active area of research.