Pairing-based cryptography resources on the web.
Throughout this site are several documents giving some background on pairing-based cryptography such as the PBC Library Manual, my PhD thesis and my notes, including some on cryptography, and programming pairing-based cryptography.
By Alfred J. Menezes, Paul C. van Oorschot and Scott A. Vanstone. Describes many algorithms and techniques that are used in, and ought to be used in PBC. For example: sliding windows, NAF exponentiation, Montgomery representation.
Categorized list of pairing-based cryptography publications. Maintained by Paulo Barreto.
See these projects that use PBC. Other projects of interest:
Mike Scott’s C++ library which also provides pairing-based cryptography primitives. Runs on many Windows versions and Linux x86, and is very quick on those platforms due to tight hand-optimized assembly code for low-level arithmetic. Free for noncommercial use.
Open-source software for Algebra and Geometry Experimentation.
A computer algebra system that includes elliptic curves. While it does not have pairings by default, it is not too difficult to write scripts to compute pairings, e.g: Katherine Stange’s script for computing the Tate pairing via elliptic nets.
A modern cryptographic meta-toolkit with emphasis on efficiency and flexibility. Includes pairings, notably pairings over supersingular curves which PBC does not support.
Information on very old versions of the PBC library.