Self-pairings on supersingular elliptic curves with embedding degree three

Self-pairings are a special subclass of pairings and have interesting applications in cryptographic schemes and protocols. In this paper, we speed up the computation of the self-pairing by using a simple final exponentiation on supersingular elliptic curves with embedding degree k=3k=3. We also compare the efficiency of self-pairing computations on different curves over large characteristic. We indicate that supersingular elliptic curves with k=3k=3 may be more attractive for implementing the self-pairings.