This book is devoted to efficient pairing computations and implementations, useful tools for cryptographers working on topics like identity-based cryptography and the simplification of existing protocols like signature schemes.

As well as exploring the basic mathematical background of finite fields and elliptic curves, Guide to Pairing-Based Cryptography offers an overview of the most recent developments in optimizations for pairing implementation. Each chapter includes a presentation of the problem it discusses, the mathematical formulation, a discussion of implementation issues, solutions accompanied by code or pseudocode, several numerical results, and references to further reading and notes.

Intended as a self-contained handbook, this book is an invaluable resource for computer scientists, applied mathematicians and security professionals interested in cryptography.

chapter 1

Pairing-Based Cryptography

BySébastien Canard, Jacques Traoré

chapter 2

Mathematical Background

ByJean-Luc Beuchat, Nadia El Mrabet, Laura Fuentes-Castañeda, Francisco Rodríguez-Henríquez

chapter 3


BySorina Ionica, Damien Robert

chapter 4

Pairing-Friendly Elliptic Curves

BySafia Haloui, Edlyn Teske

chapter 5

Arithmetic of Finite Fields

ByJean Luc Beuchat, Luis J. Dominguez Perez, Sylvain Duquesne, Nadia El Mrabet, Laura Fuentes-Castañeda, Francisco Rodríguez-Henríquez

chapter 6

Scalar Multiplication and Exponentiation in Pairing Groups

ByJoppe Bos, Craig Costello, Michael Naehrig

chapter 7

Final Exponentiation

ByJean-Luc Beuchat, Luis J. Dominguez Perez, Laura Fuentes-Castaneda, Francisco Rodriguez-Henriquez

chapter 8

Hashing into Elliptic Curves

ByEduardo Ochoa-Jiménez, Francisco Rodríguez-Henríquez, Mehdi Tibouchi

chapter 9

Discrete Logarithms

ByAurore Guillevic, François Morain

chapter 10

Choosing Parameters

BySylvain Duquesne, Nadia El Mrabet, Safia Haloui, Damien Robert, Franck Rondepierre

chapter 11

Software Implementation

ByDiego F. Aranha, Luis J. Dominguez Perez, Amine Mrabet, Peter Schwabe

chapter 12

Physical Attacks

ByNadia El Mrabet, Louis Goubin, Sylvain Guilley, Jacques Fournier, Damien Jauvart, Martin Moreau, Pablo Rauzy, Franck Rondepierre