Learning pairing-based cryptography by hands-on exercises

摘要

Many modem cryptographic schemes, especially those with special functionalities, employ elliptic curves and pairings thereon. While the cryptographic system itself may be quite simple to specify and write down, prototyping such a system to compute examples is often a significant independent challenge connected to understanding the system itself. Elliptic curves come with complicated group laws that rely on finite field arithmetic and depend on the particular instance of the underlying field. To get the grips on a cryptographic system, a student has thus to work out the fundamentals of finite field arithmetic, building elliptic curve group laws upon this, and finally, dig into the rich theory of pairings, before taking the first steps towards the cryptographic system. We report on work in progress on an eLearning system called Sunset/FFapl: Sunset is a development environment for the programming language FFapl (finite field application language), which offers finite fields and elliptic curves as native data types. Operations on those work in infix notation and via built-in functions, ranging up to elliptic curve groups and pairings thereon for cryptography. This work discusses various difficulties and challenges that students face in learning pairing-based cryptography and shows how to address them by hands-on exercises in Sunset/FFapl.