International Association for Cryptologic Research

International Association
for Cryptologic Research


Augusto Jun Devegili


Implementing Cryptographic Pairings over Barreto-Naehrig Curves
Augusto Jun Devegili Michael Scott Ricardo Dahab
In this paper we describe an efficient implementation of the Tate and Ate pairings using Barreto-Naehrig pairing-friendly curves, on both a standard 32-bit PC and on a 32-bit smartcard. First we introduce a sub-family of such curves with a particularly simple representation. Next we consider the issues that arise in the efficient implementation of field arithmetic in $\F_{p^{12}}$, which is crucial to good performance. Various optimisations are suggested, including a novel approach to the `final exponentiation', which is faster and requires less memory than the methods previously recommended.
Multiplication and Squaring on Pairing-Friendly Fields
Pairing-friendly fields are finite fields that are suitable for the implementation of cryptographic bilinear pairings. In this paper we review multiplication and squaring methods for pairing-friendly fields $\fpk$ with $k \in \{2,3,4,6\}$. For composite $k$, we consider every possible towering construction. We compare the methods to determine which is most efficient based on the number of basic $\fp$ operations, as well as the best constructions for these finite extension fields. We also present experimental results for every method.