Guide to Pairing-Based Cryptography (Chapman & HallCRC Cryptography and Network Security Series) by Nadia El Mrabet & Marc Joye

Author:Nadia El Mrabet & Marc Joye
Language: eng
Format: azw3
Publisher: CRC Press
Published: 2017-01-05T16:00:00+00:00

parametrized by selecting an arbitrary x ∈ Z such that

are both prime.

Constant-time hashing to

In Latincrypt 2012, Fouque and Tibouchi [25] presented a specialization of the procedure proposed by Shallue and van de Woestijne [50] applied to Barreto–Naehrig curves, which are defined over the finite field , with p ≡ 7 mod 12, or p ≡ 1 mod 12. The mapping covers a 9/16 fraction of the prime group size r = #E(Fp). In a nutshell, the procedure proposed in [25] consists in the following.

Let t be an arbitrary nonzero element in the base field such that x1,x2,x3 are defined as

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