Self-pairings on hyperelliptic curves

Abstract

A self-pairing is a pairing computation where both inputs are the same group element. Self-pairings are used in some cryptographic schemes and protocols. In this paper, we show how to compute the Tate–Lichtenbaum pairing on a curve more efficiently than the general case. The speedup is obtained by using a simpler final exponentiation. We also discuss how to use this pairing in cryptographic applications.

Keywords

• tate pairing
• weil pairing
• self-pairing
• pairing based cryptography