Quadratic extension of the base field of BN254.
The quadratic extension Fq2 is defined as Fq[u] / (u^2 + 1). Fq2 is the base field of the twist of BN254, thus points in G2 have coordinates in Fq2.
Inside this struct we define the parameters of the twist:
- the coefficient twist_b = 3 / (9 + u) defining the equation of the twist: y^2 = x^3 + twist_b. The coefficient is derived as b / \xi, where b = 3 is the coefficient of BN254 in short-Weierstrass form, and \xi = 9 + u is not a sixth residue in Fq2.
- the coefficients required to compute the frobenius map on the twisted curve: if \Psi : E' --> E is the isomorphism between the twist E' and the base curve E, then the frobenius map on E' is \Psi^{-1} \circ Frobenius \circ \Psi. This map is given by (x, y) --> (\xi^{(q-1)/3} * x^q, \xi^{(q-1)/2}} * y^q). We precompute the two powers of \xi and store them as frobenius_on_twisted_curve_x and frobenius_on_twisted_curve_y.
Definition at line 29 of file fq2.hpp.
1.9.8