Expand description
This library implements the MNT6_298 curve generated in [BCTV14]. The name denotes that it is a Miyaji–Nakabayashi–Takano curve of embedding degree 6, defined over a 298-bit (prime) field. The main feature of this curve is that its scalar field and base field respectively equal the base field and scalar field of MNT4_298.
Curve information:
- Base field: q = 475922286169261325753349249653048451545124878552823515553267735739164647307408490559963137
- Scalar field: r = 475922286169261325753349249653048451545124879242694725395555128576210262817955800483758081
- valuation(q - 1, 2) = 34
- valuation(r - 1, 2) = 17
- G1 curve equation: y^2 = x^3 + ax + b, where
- a = 11
- b = 106700080510851735677967319632585352256454251201367587890185989362936000262606668469523074
- G2 curve equation: y^2 = x^3 + Ax + B, where
- A = Fq2 = (0, 0, a)
- B = Fq2(b * NON_RESIDUE, 0, 0)
- NON_RESIDUE = 5 is the cubic non-residue used to construct the field extension Fq3