Abstract. We describe efficient formulas for computing pairings on ordinary elliptic curves over prime fields. First, we generalize lazy reduction techniques, previously considere...
Diego F. Aranha, Koray Karabina, Patrick Longa, Ca...
Abstract. This paper proposes new explicit formulae for the point doubling, tripling and addition on ordinary Weierstrass elliptic curves with a point of order 3 over finite fiel...
Research on efficient pairing implementation has focussed on reducing the loop length and on using high-degree twists. Existence of twists of degree larger than 2 is a very restric...
This paper presents efficient formulas for computing cryptographic pairings on the curve y2 = cx3 + 1 over fields of large characteristic. We provide examples of pairing-friendly...
Edwards recently introduced a new normal form for elliptic curves. Every elliptic curve over a non-binary field is birationally equivalent to a curve in Edwards form over an exten...