G1 is an abstract cyclic group. The zero value is suitable for use as the output of an operation, but cannot be used as an input.

G2 is an abstract cyclic group. The zero value is suitable for use as the output of an operation, but cannot be used as an input.

GT is an abstract cyclic group. The zero value is suitable for use as the output of an operation, but cannot be used as an input.

curvePoint implements the elliptic curve y²=x³+3. Points are kept in Jacobian form and t=z² when valid. G₁ is the set of points of this curve on GF(p)

gfP12 implements the field of size p¹² as a quadratic extension of gfP6 where ω²=τ.

For details of the algorithms used, see "Multiplication and Squaring on Pairing-Friendly Fields, Devegili et al. http://eprint.iacr.org/2006/471.pdf.

For details of the algorithms used, see "Multiplication and Squaring on Pairing-Friendly Fields, Devegili et al. http://eprint.iacr.org/2006/471.pdf.

twistPoint implements the elliptic curve y²=x³+3/ξ over GF(p²). Points are kept in Jacobian form and t=z² when valid. The group G₂ is the set of n-tor