Miller applies Miller's algorithm, which is a bilinear function from the source groups to F_p^12.

Pair calculates an Optimal Ate pairing.

PairingCheck calculates the Optimal Ate pairing for a set of points.

RandomG1 returns x and g₁ˣ where x is a random, non-zero number read from r.

RandomG2 returns x and g₂ˣ where x is a random, non-zero number read from r.

Order is the number of elements in both G₁ and G₂: 36u⁴+36u³+18u²+6u+1.

P is a prime over which we form a basic field: 36u⁴+36u³+24u²+6u+1.

G1 is an abstract cyclic group.

G2 is an abstract cyclic group.

GT is an abstract cyclic group.