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

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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 the authors consider criteria that apply when choosing the best towering construction, and the associated choice of irreducible polynomials for the implementation of pairing-based cryptosystems. They introduce a method for automatically constructing efficient towers for more classes of finite fields than previous methods, some of which allow faster arithmetic.