Chapter 12
Cryptocurrencies
Abstract Based on the notion that today monetary exchanges are based on the
transfer of information, this chapter provides a basic introduction into Shannon’s
theory of information, with its central concept—the entropy. After covering different
ways to encode information the relation of Shannon’s entropy to the entropy, known
from thermodynamics, is illustrated with a physical system that has discrete energy
levels. The chapter then discusses the transmission of information across binary
symmetric channels and develops the necessary concepts to establish the maximum
of the mutual information as the channel capacity. After moving information through
continuous channels, limited by the signal-to-noise ratio, a section introduces the
basics of cryptography, which is needed to provide the security when transmitting
sensitive information. Public-key systems, Diffie-Helman and RSA, are discussed
in some detail, before covering the basics of elliptic function cryptography, which
provides the basis for both Bitcoin and Ethereum blockchains, the subject of later
sections in the chapter. An Ethereum smart contract is discussed as an example of a
distributed application—a DApp. The last section touches upon the basics of quantum
computing and illustrates the key concepts of Shor’s algorithm, which might one day
pose a threat to cryptographic systems.
After initial developments from bartering goods, such as pigs and pultry, to coins
and paper money, which we briefly discussed in Sect. 2.4, monetary transactions in
today’s world are predominantly handled electronically. Student loans and salaries
are deposited in our accounts by bank transfer. Likewise, we pay our utility bills for
electricity or gas electronically. Moreover, when eating out or on a shopping spree, we
pay with credit cards or with our smartphones using Google pay, Apple pay, Venmo,
or Swish. None of these methods to transfer funds involve the actual exchange of
coins or paper money. Apparently money has evolved from the exchange of tangible
assets—pigs, coins, or paper money—to the exchange of information about who has
the right to buy things up to a certain value.
In the following we will therefore treat money as an entry in a decentralized
database of who has what purchasing power. Even the ownership of a pig represents
the purchasing power up to the equivalent value of other quantities, and a coin in
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
V. Ziemann, Physics and Finance, Undergraduate Lecture Notes in Physics,
https://doi.org/10.1007/978-3-030-63643-2_12
193
Cryptocurrencies
Abstract Based on the notion that today monetary exchanges are based on the
transfer of information, this chapter provides a basic introduction into Shannon’s
theory of information, with its central concept—the entropy. After covering different
ways to encode information the relation of Shannon’s entropy to the entropy, known
from thermodynamics, is illustrated with a physical system that has discrete energy
levels. The chapter then discusses the transmission of information across binary
symmetric channels and develops the necessary concepts to establish the maximum
of the mutual information as the channel capacity. After moving information through
continuous channels, limited by the signal-to-noise ratio, a section introduces the
basics of cryptography, which is needed to provide the security when transmitting
sensitive information. Public-key systems, Diffie-Helman and RSA, are discussed
in some detail, before covering the basics of elliptic function cryptography, which
provides the basis for both Bitcoin and Ethereum blockchains, the subject of later
sections in the chapter. An Ethereum smart contract is discussed as an example of a
distributed application—a DApp. The last section touches upon the basics of quantum
computing and illustrates the key concepts of Shor’s algorithm, which might one day
pose a threat to cryptographic systems.
After initial developments from bartering goods, such as pigs and pultry, to coins
and paper money, which we briefly discussed in Sect. 2.4, monetary transactions in
today’s world are predominantly handled electronically. Student loans and salaries
are deposited in our accounts by bank transfer. Likewise, we pay our utility bills for
electricity or gas electronically. Moreover, when eating out or on a shopping spree, we
pay with credit cards or with our smartphones using Google pay, Apple pay, Venmo,
or Swish. None of these methods to transfer funds involve the actual exchange of
coins or paper money. Apparently money has evolved from the exchange of tangible
assets—pigs, coins, or paper money—to the exchange of information about who has
the right to buy things up to a certain value.
In the following we will therefore treat money as an entry in a decentralized
database of who has what purchasing power. Even the ownership of a pig represents
the purchasing power up to the equivalent value of other quantities, and a coin in
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
V. Ziemann, Physics and Finance, Undergraduate Lecture Notes in Physics,
https://doi.org/10.1007/978-3-030-63643-2_12
193