Abstract
Pairing-based protocols are getting popular in many cryptographic applications. Pairing algorithms involve computations on elements in all three pairing groups, G_1, G_2 and G_3; however, most protocols usually require additional scalar multiplication and exponentiation in any of these three groups. The Gallant-Lambert-Vanstone (GLV) method is an elegant technique to accelerate the scalar multiplication which can reduce the number of elliptic curve doubling by using Straus-Shamir simultaneous multi-scalar multiplication technique. However, efficiently computable endomorphisms are required to apply GLV for the elliptic curves. This paper shows the GLV technique by deriving efficiently computable endomorphism for Kachisa-Schaefer-Scott (KSS) curve defined over degree 16 extension field. In addition, the authors show explicit formulas to compute the GLV method together with Straus-Shamir simultaneous multi-scalar multiplication technique for 2, 4 and 8 dimensions in G2 group. The comparative implementation shows that dimension 4 gives faster computational time than dimension 8 and 2.
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