Fast formulas for computing cryptographic pairings

Costello, Craig (2012) Fast formulas for computing cryptographic pairings. PhD thesis, Queensland University of Technology.


The most powerful known primitive in public-key cryptography is undoubtedly elliptic curve pairings. Upon their introduction just over ten years ago the computation of pairings was far too slow for them to be considered a practical option.

This resulted in a vast amount of research from many mathematicians and computer scientists around the globe aiming to improve this computation speed. From the use of modern results in algebraic and arithmetic geometry to the application of foundational number theory that dates back to the days of Gauss and Euler, cryptographic pairings have since experienced a great deal of improvement. As a result, what was an extremely expensive computation that took several minutes is now a high-speed operation that takes less than a millisecond.

This thesis presents a range of optimisations to the state-of-the-art in cryptographic pairing computation. Both through extending prior techniques, and introducing several novel ideas of our own, our work has contributed to recordbreaking pairing implementations.

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ID Code: 61037
Item Type: QUT Thesis (PhD)
Supervisor: Boyd, Colin & Nieto, Juan Gonzalez
Keywords: tate pairing, ate pairing, explicit formulas, elliptic curves, weierstrass curves,, Miller’s algorithm, precomputation, twists, pairing-friendly curves, subfamilies,, pairing implementation, high-security pairings, hyperelliptic curves, group law,, Jacobian arithmetic, genus 2
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Institutes > Information Security Institute
Institution: Queensland University of Technology
Deposited On: 01 Jul 2013 03:46
Last Modified: 05 Jul 2017 14:44

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