Self-pairings on hyperelliptic curves

Steven D. Galbraith 1  and Chang-An Zhao 2
  • 1 Mathematics Department, University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
  • 2 Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, P. R. China


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.

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JMC is a forum for original research articles in the area of mathematical cryptology. Works in the theory of cryptology and articles linking mathematics with cryptology are welcome. Submissions from all areas of mathematics significant for cryptology are published, including but not limited to, algebra, algebraic geometry, coding theory, combinatorics, number theory, probability and stochastic processes.