Reducing the Complexity of the Weil Pairing Computation

In this paper, we present some new variants based on the Weil pairing for efficient pairing computations. The new pairing variants have the short Miller iteration loop and simple final exponentiation. We then show that computing the proposed pairings is more efficient than computing the Weil pairing. Experimental results for these pairings are also given

Twisted Ate Pairing on Hyperelliptic Curves and Applications

In this paper we show that the twisted Ate pairing on elliptic curves can be generalized to hyperelliptic curves, we also give a series of variations of the hyperelliptic Ate and twisted Ate pairings. Using the hyperelliptic Ate pairing and twisted Ate pairing, we propose a new approach to speed up the Weil pairing computation, and obtain an interested result: For some hyperelliptic curves with high degree twist, using this approach to compute Weil pairing will be faster than Tate pairing, Ate pairing etc. all known pairings

On the Efficiency and Security of Cryptographic Pairings

Pairing-based cryptography has been employed to obtain several advantageous cryptographic protocols. In particular, there exist several identity-based variants of common cryptographic schemes. The computation of a single pairing is a comparatively expensive operation, since it often requires many operations in the underlying elliptic curve. In this thesis, we explore the efficient computation of pairings. Computation of the Tate pairing is done in two steps. First, a Miller function is computed, followed by the final exponentiation. We discuss the state-of-the-art optimizations for Miller function computation under various conditions. We are able to shave off a fixed number of operations in the final exponentiation. We consider methods to effectively parallelize the computation of pairings in a multi-core setting and discover that the Weil pairing may provide some advantage under certain conditions. This work is extended to the 192-bit security level and some unlikely candidate curves for such a setting are discovered. Electronic Toll Pricing (ETP) aims to improve road tolling by collecting toll fares electronically and without the need to slow down vehicles. In most ETP schemes, drivers are charged periodically based on the locations, times, distances or durations travelled. Many ETP schemes are currently deployed and although these systems are efficient, they require a great deal of knowledge regarding driving habits in order to operate correctly. We present an ETP scheme where pairing-based BLS signatures play an important role. Finally, we discuss the security of pairings in the presence of an efficient algorithm to invert the pairing. We generalize previous results to the setting of asymmetric pairings as well as give a simplified proof in the symmetric setting