Module pairing

Traits for optimal Ate pairing check using intrinsic functions.

Structs

EvaluatedLine

The output of a line function on Fp12 x Fp12 (see UnevaluatedLine). Represents 1 + b w’ + c w’^3 where w’ = w for D-type and w’ = w^-1 for M-type twists.

PairingCheckError

SexticExtField

Sextic extension field of F with irreducible polynomial X^6 - \xi. Elements are represented as c0 + c1 * w + ... + c5 * w^5 where w^6 = \xi, where \xi in F.

UnevaluatedLine

A line function on Fp12 x Fp12 in a sparse representation. Let Fp12 = Fp2[w] / (w^6 - \xi). Then the line function is L(x,y) = 1 + b (x/y) w' + c (1/y) w'^3 where w' = w for D-type and w' = w^{-1} for M-type twists

Traits

Evaluatable

FinalExp

FromLineDType

Convert D-type lines into Fp12 elements

FromLineMType

Convert M-type lines into Fp12 elements

LineMulDType

Trait definition for line multiplication opcodes for D-type lines

LineMulMType

Trait definition for line multiplication opcodes for M-type lines

MillerStep

Trait definition for Miller step opcodes

MultiMillerLoop

PairingCheck

PairingIntrinsics

Functions

exp_check_fallback

shifted_funct7