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- q = 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab
- F1 = GF(q)
- # F₂ is constructed as F(u) / (u² + 1)
- # F₆ is constructed as F₂(v) / (v³- (u + 1))
- # F₁₂ is constructed as F₆(w) / (w²- v)
- # we can't do extension field towers in sage...
- # https://ask.sagemath.org/question/49663/efficiently-computing-tower-fields-for-pairings/
- K2.<x> = PolynomialRing(F1)
- F2.<u> = F1.extension(x^2 + 1)
- # The last line in this section will hang forever
- #K6.<y> = PolynomialRing(F2)
- #F6.<v> = F2.extension(y^3 - (u + 1))
- #K12.<z> = PolynomialRing(F6)
- #F12.<w> = F6.extension(z^2 - v)
- # Alternative construction
- R.<y> = PolynomialRing(F2)
- # w is a root of a(y) = y^6 - (u + 1) and also b(y) = y^2 - v
- # v is a root of c(y) = y^3 - (u + 1), so to enlarge F2 -> F12, we use a(y)
- F12.<w> = F2.extension(y^6 - (u + 1))
- v = w^2
- assert u^2 + 1 == 0
- assert v^3 - (u + 1) == 0
- assert w^2 - v == 0
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