Efficient Computation of Miller\u27s Algorithm in Pairing-Based Cryptography

Pairing-based cryptography (PBC) provides novel security services, such as identity-based encryption, attribute-based encryption and anonymous authentication. The Miller\u27s Algorithm is considered one of the most important algorithms in PBC and carries the most computation in PBC. In this thesis, two modified Miller\u27s algorithms are proposed. The first proposed algorithm introduces a right-to-left version algorithm compared to the fact that the original Miller\u27s algorithm works only in the fashion of left-to-right. Furthermore, this new algorithm introduces parallelable computation within each loop and thus it can achieve a much higher speed. The second proposal has the advantage over the original Miller\u27s algorithm not only in parallelable computation but also in resistance to certain side channel attacks based on the new feature of the equilibrium of computational complexities. An elaborate comparison among the existing works and the proposed works is demonstrated. It is expected that the first proposed algorithm can replace the original Miller\u27s if a right-to-left input style is required and/or high speed is of importance. The second proposed algorithm should be chosen over the original Miller\u27s if side channel attack is a concern