Optimal pairings

In this paper we introduce the concept of an optimal pairing, which by definition can be computed using only log2 r/(k) basic Miller iterations, with r the order of the groups involved and k the embedding degree. We describe an algorithm to construct optimal ate pairings on all parametrized families of pairing friendly elliptic curves. Finally, we conjecture that any non-degenerate pairing on an elliptic curve without efficiently computable endomorphisms different from powers of Frobenius requires at least log2 r/(k) basic Miller iterations.

• Type: Journal
• Year: 2010
• Where: TIT
• Authors: Frederik Vercauteren
• Keywords: Basic Miller Iterations, Education, Elliptic Curve, Optimal Ate Pairings, TIT 2010