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This chapter examines digital signature schemes, the main cryptographic mechanisms for providing non-repudiation of data. It first looks at general requirements for a digital signature scheme. It then considers the ways in which a digital signature scheme could be realised. It discusses digital signature schemes based on RSA and digital signature schemes in practice.

In this chapter, we discuss digital signature schemes. We start by considering the general requirements of a digital signature scheme. We show first that a digital signature scheme could be established using symmetric techniques. We then consider the more conventional use of public-key cryptography to create digital signature schemes. We compare two different approaches to building a digital signature scheme and illustrate how to manifest these using RSA. We then discuss practical issues concerning digital signature schemes, including different aspects of their security. We close by providing a detailed comparison between digital signatures and handwritten signatures which serves to both illustrate the strengths and vulnerabilities of digital signature schemes.

This chapter examines the gradual crystallization of a cryptographic model for an electronic equivalent to handwritten signatures. It suggests that market demise of public-key infrastructures provided a powerful critique of the digital signature model and contends that the difficulties met in translating this model into a commercially successful technology may be attributed to cryptographers’ problematic relationship with the representational nature of models. It also discusses the trade-offs in the mathematization of cryptography.

This chapter traces the path of a parallel definitional process, that of the legal model for electronic signatures. It explains that this model made its way through a series of political, regulatory and professional bodies in the later part of the 1990s and discusses the influence of a digital signatures on the discussion of what kind of evidence an electronically signed document might provide and how that evidence might be judged reliable. It also considers the debate between academic Lawrence Lessig and Judge Frank Easterbrook over law’s proper role in taming the unruliness of information technologies.

This introductory chapter discusses the theme of this volume which is about the history of cryptographic culture and the place of evidence law in the age of electronic documents. This volume offers a counterpoint to the preference for the analysis of the geometry of the line and describes the deployment of electronic signatures within the very professions entrusted with the production and management of documentary evidence. It also argues against the mathematization of cryptography and proposes a technical foundation for digital signatures based on the mathematics of public-key cryptography.

This chapter provides a very detailed introduction to cryptography. It first explains the cryptographic basics and introduces the concept of public-key encryption which is based on one-way and trapdoor functions, considering the three major public-key encryption families like integer factorization, discrete logarithm and elliptic curve schemes. This is followed by an introduction to hash functions which are applied to construct Merkle trees and digital signature schemes. As modern cryptoschemes are commonly based on elliptic curves, the chapter then introduces elliptic curve cryptography which is based on the Elliptic Curve Discrete Logarithm Problem (ECDLP). It considers the hardness of the ECDLP and the possible attacks against it, showing how to find suitable domain parameters to construct cryptographically strong elliptic curves. This is followed by the discussion of elliptic curve domain parameters which are recommended by current standards. Finally, it introduces the Elliptic Curve Digital Signature Algorithm (ECDSA), the elliptic curve digital signature scheme.

Bitcoin was proposed by Nakamoto (2008) as the first electronic payment system, which fully relies on cryptographic primitives in order to work over a purely peer-to-peer system, where everyone can participate in spending funds to other users without the need for a trusted third party. This chapter first introduces the basic ideas of Satoshi Nakamoto, who defined an electronic coin as a chain of digital signatures. It explains how the addresses in Bitcoin are derived, and how the elliptic curve cryptography (ECC) key pair is used in order to transact funds from one user to another. For this, it shows how the transactions are constructed in Bitcoin, based on the most common transaction, which is the Pay-to-Public-Key-Hash transaction. The last section then shows how the transactions are permanently stored in the public ledger, the blockchain, and how the miners solve the Proof-of-Work in order to safeguard the records.