One of Ethereum’s foundational technologies is cryptography, which is a branch of mathematics used extensively in computer security. Cryptography means “secret writing” in Greek, but the study of cryptography encompasses more than just secret writing, which is referred to as encryption. Cryptography can, for example, also be used to prove knowledge of a secret without revealing that secret (e.g., with a digital signature), or to prove the authenticity of data (e.g., with digital fingerprints, also known as “hashes”). These types of cryptographic proofs are mathematical tools critical to the operation of the Ethereum platform (and, indeed, all blockchain systems), and are also extensively used in Ethereum applications.

Note that, at the time of publication, no part of the Ethereum protocol involves encryption; that is to say all communications with the Ethereum platform and between nodes (including transaction data) are unencrypted and can (necessarily) be read by anyone. This is so everyone can verify the correctness of state updates and consensus can be reached. In the future, advanced cryptographic tools, such as zero knowledge proofs and homomorphic encryption, will be available that will allow for some encrypted calculations to be recorded on the blockchain while still enabling consensus; however, while provision has been made for them, they have yet to be deployed.

In this chapter we will introduce some of the cryptography used in Ethereum: namely public key cryptography (PKC), which is used to control ownership of funds, in the form of private keys and addresses.