Refinements of Miller's algorithm for computing the Weil/Tate pairing

Refinements of Miller's Algorithm for Computing Weil/Tate Pairing

Refinements of Miller's Algorithm over Weierstrass Curves Revisited

In 1986 Victor Miller described an algorithm for computing the Weil pairing in his unpublished manuscript. This algorithm has then become the core of all pairing-based cryptosystems. Many improvements of the algorithm have been presented. Most of them involve a choice of elliptic curves of a special forms to exploit a possible twist during Tate pairing computation. Other improvements involve a ...

Further refinement of pairing computation based on Miller's algorithm

In 2006, Blake, Murty and Xu proposed three refinements to Miller’s algorithm for computing Weil/Tate Pairings. In this paper we extend their work and propose a generalized algorithm, which integrates their first two algorithms. Our approach is to pre-organize the binary representation of the involved integer to the best cases of Blake’s algorithms. Further, our refinement is more suitable for ...

Comparing Implementation Efficiency of Ordinary and Squared Pairings

In this paper, we will implement a standard probabilistic method of computing bilinear pairings. We will compare its performance to a deterministic algorithm introduced in [5] to compute the squared Tate/Weil pairings which are claimed to be 20 percent faster than the standard method. All pairings will be evaluated over pairing-friendly ordinary elliptic curves of embedding degrees 8 and 10 and...

Improved Weil and Tate Pairings for Elliptic and Hyperelliptic Curves

We present algorithms for computing the squared Weil and Tate pairings on elliptic curves and the squared Tate pairing on hyperelliptic curves. The squared pairings introduced in this paper have the advantage that our algorithms for evaluating them are deterministic and do not depend on a random choice of points. Our algorithm to evaluate the squared Weil pairing is about 20% more efficient tha...