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Constructing Tower Extensions for the implementation of Pairing-Based Cryptography
Authors: Naomi Benger, Michael ScottAbstract:
A cryptographic pairing evaluates as an element in an 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 irreducible polynomials for the implementation of pairing-based cryptosystems. We introduce a method for automatically constructing efficient towers for more congruency classes than previous methods, some of which allow faster arithmetic.
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