On finite fields for pairing based cryptography

Constructing Tower Extensions of Finite Fields for Implementation of Pairing-Based Cryptography

A cryptographic pairing evaluates as an element of a finite extension field, and the evaluation itself involves a considerable amount of extension field arithmetic. It is recognised that organising the extension field as a “tower” of subfield extensions has many advantages. Here we consider criteria that apply when choosing the best towering construction, and the associated choice of irreducibl...

Report on Pairing-based Cryptography.

This report summarizes study results on pairing-based cryptography. The main purpose of the study is to form NIST's position on standardizing and recommending pairing-based cryptography schemes currently published in research literature and standardized in other standard bodies. The report reviews the mathematical background of pairings. This includes topics such as pairing-friendly elliptic cu...

Pairing-based Cryptography

Acknowledgements I would like to take this opportunity to express my gratitude to some people who were involved in this project. First of all, I owe thanks to Henk van Tilborg for being my overall supervisor and arranging current and previous projects. I would like to thank Benne de Weger, who was closely involved in the writing of this report, for the fruitful discussions and useful advises. T...

On the Disadvantages of Pairing-based Cryptography

Pairing-based cryptography (PBC) has many elegant properties. It is claimed that PBC can offer a desired security level with smaller parameters as the general elliptic curve cryptography (ECC). In the note, we remark that this view is misleading. Suppose that an elliptic curve E is defined over the field Fq. Then ECC is working with elements which are defined over Fq. But PBC is working with th...

Fault Attacks on Pairing-Based Cryptography