@MISC{Sanyal_anovel, author = {Sutirtha Sanyal}, title = {A Novel Proof on Weil Pairing}, year = {} }

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Abstract

In this paper we will prove a basic property of weil pairing which helps in evaluating its value. We will show that the weil pairing value as computed from the definition is equivalent with the ratio formula based on the miller function. We prove a novel theorem (Theorem 2) and use it to establish the equivalence. We further validate our claims with actual random examples. I. INTRODUCTION AND PRELIMINARIES We will use basic concepts and usual notations from [1]. In general case, the equation of the elliptic curve E, defined over a finite field K and given in the Weierstrass form, is y 2 + a1xy + a3y = x 3 + a2x 2 + a4x + a6 where ai ∈ K. We consider two points in it, S and T of order n, co-prime to char(K). The weil pairing en(S, T) can be defined in the following manner. Let the function f O T ∈ ¯ K(E) has the divisor n(T) − n(O) ( ¯ K(E) is the function field associated