Cryptology ePrint Archive: Report 2012/267

Self-pairings on Hyperelliptic Curves

Steven D. Galbraith and Chang-An Zhao

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 (D,\phi(D)) on a curve more efficiently than the general case. The speedup is obtained by requiring a simpler final exponentiation. We also discuss how to use this pairing in cryptographic applications.

Category / Keywords: public-key cryptography / Tate pairing, Weil pairing, Self-pairing, Pairing based cryptography