Type I Internals

Type I pairings is symmetric, constructed on a supersingular curve y2 = x3 - x + 1 over a ternary extension field F_{3m}. The embedding degree k is 6. Both G1 and G2 are the group of points E(F_{3m}). GT is a subgroup of F_{36*m}. The group order is a prime number.


m, t:
  The ternary extension field is F(3)[x]/(x^m^ + x^t^ + 2).
  the order of G1
  n * n2 = number of points in E(F_{3^m^})

Introduced by Barreto et al, "Efficient Pairing Computation on Supersingular Abelian Varieties", Designs, Codes and Cryptography, vol. 42, no. 3, pp. 239-271, Mar. 2007.