1 Pairings over elliptic curves in cryptography

I first became interested in elliptic curve cryptography (ECC) in the mid-1990s. I was involved with an activist organization working to legalize marijuana, and we wanted to ensure our member list was secure and that we could email each other with encrypted messages. While I was aware of pretty good privacy (PGP), as a scientist at Argonne National Laboratory, I wanted something more state of the art. So I dug into the papers and went to a few Cryptographic Hardware and Embedded Systems (CHES) conferences to learn how to write my own code.

Today, ECC is ubiquitous. For example, Europay, Mastercard, and Visa (EMVCo) support ECC in their cryptographic interface for credit card transactions. In addition to sharing secret keys as in an SSL/TLS handshake, it is also used for signing certificates to authenticate web pages and HIPAA documents. A blockchain holds globally accessible information shared among many peers.

The blockchain has found use for elliptic curve pairings to enable aggregate group signatures and zero-knowledge proofs. The impetus for blockchain may be cryptocurrency, but the technology has many more uses. Blockchain ledgers are used in healthcare and supply chain environments.

1.1 What is elliptic curve cryptography?

1.2 Why use elliptic curve cryptography?

1.3 Elliptic curves come to public key cryptography

1.3.1 General description of key exchange

1.3.2 Digital signature algorithms explained

1.3.3 How multiple people can sign the same document

1.3.4 Zero knowledge, or how to keep a secret and prove you have one

1.4 Who this book is for

Summary