úÎ!=T9j=      !"#$%&'()*+,-./0123456789:;<None"#.479=>?@AMSX_gk!Ÿ#pairingGT is subgroup of r2-th roots of unity of the multiplicative group of Fq12.pairing"G2' is G2 in Jacobian coordinates.pairingG2 is E'(Fq2) defined by y^2 = x^3 + b / xi.pairingG1 is E(Fq) defined by  y^2 = x^3 + b.pairing Prime field Fr.pairingQuadratic extension field of Fq6 defined as Fq12 = Fq6[w]/ w^2- v.pairingCubic extension field of Fq2 defined as  Fq6 = Fq2[v]/ v^3 - (9 + u).pairingQuadratic extension field of Fq defined as  Fq2 = Fq[u]/ u^2+ 1.pairing Prime field Fq. pairingGenerator of G1. pairingGenerator of G2. pairingGenerator of GT. pairing Order of G1. pairing Order of G2.pairing Order of GT.pairingElliptic curve E(Fq) coefficient A, with y = x^3 + Ax + B.pairingElliptic curve E(Fq2) coefficient A', with y = x^3 + A'x + B'.pairingElliptic curve E(Fq) coefficient B, with y = x^3 + Ax + B.pairingElliptic curve E(Fq2) coefficient B', with y = x^3 + A'x + B'.pairingEmbedding degree.pairingQuadratic nonresidue in Fq.pairing Characteristic of finite fields.pairing;Order of G1 and characteristic of prime field of exponents.pairing'BN parameter that determines the prime _q.pairing Parameter of twisted curve over Fq.pairing Conjugation.pairingGGet Y coordinate from X coordinate given a curve and a choice function.pairingScalar multiplication.pairing Multiply by _xi (cubic nonresidue in Fq2) and reorder coefficients.pairing#Iterated Frobenius automorphism in Fq12.=pairingFast Frobenius automorphism in Fq12.pairing'Check if an element is a root of unity.pairing1Check if an element is a primitive root of unity. pairingÁCompute primitive roots of unity for 2^0, 2^1, ..., 2^28. (2^28 is the largest power of two that divides _r - 1, therefore there are no primitive roots of unity for higher powers of 2 in Fr.)!pairingPrecompute roots of unity."  !"  !None"#.479=>?@AMSX_gk#…"#$%&'()*+,-./*+,&'()"#$%/-.None"#.479=>?@AMSX_gk+™4pairingÿ©Encodes a given byte string to a point on the BN curve. The implementation uses the Shallue-van de Woestijne encoding to BN curves as specified in Section 6 of Indifferentiable Hashing to Barreto Naehrig Curves by Pierre-Alain Fouque and Mehdi Tibouchi. This function evaluates an empty bytestring or one that contains NUL to zero, which according to Definition 2 of the paper is sent to an arbitrary point on the curve.44None"#.479=>?@AMSX_gk5µ5pairing9Optimal Ate pairing (including final exponentiation step)6pairing9Optimal Ate pairing without the final exponentiation step7pairingXBinary expansion (missing the most-significant bit) representing the number 6 * _t + 2. Z29793968203157093288 = 0b11001110101111001011100000011100110111110011101100011101110101000>pairing*Miller loop with precomputed values for G28pairingQIterated frobenius morphisms on fields of characteristic _q, implemented naively9pairing5Naive implementation of the final exponentiation step:pairing8A faster way of performing the final exponentiation step56789:56:987None"#.479=>?@AMSX_gk6»None"#.479=>?@AMSX_gk7‘None"#.479=>?@AMSX_gk8gNone"#.479=>?@AMSX_gk9E?@ABCDEFG      !"#$%&'()*+,-.//0123456789:;<=>?@ABCDEFGHIJKLMNO$pairing-0.5.0-8DWcGM5V2ba4cr0zttpZEv Pairing.CurvePairing.ByteRepr Pairing.HashPairing.PairingPairing.Serialize.JivsovPairing.Serialize.MCLWasmPairing.Serialize.Types Paths_pairingGTG2'G2G1FrFq12Fq6Fq2FqgG1gG2gGTrG1rG2rGT_a_a'_b_b'_k_nqr_q_r_t_xiconj getYfromXscalemulXi fq12Frobenius isRootOfUnityisPrimitiveRootOfUnityprimitiveRootOfUnityprecompRootOfUnityByteReprmkReprfromReprcalcReprLengthByteOrderLength byteOrder lenPerElement ByteOrderMostSignificantFirstLeastSignificantFirsttoBytes toPaddedBytesfromBytesToInteger$fByteReprExtensionField$fByteReprExtensionField0$fByteReprExtensionField1$fByteReprPrimeFieldswEncBNreducedPairing atePairingateLoopCountBinaryfrobeniusNaivefinalExponentiationNaivefinalExponentiation$fShowEllCoeffs $fEqEllCoeffs fastFrobenius ateMillerLoopversion getBinDir getLibDir getDynLibDir getDataDir getLibexecDir getSysconfDirgetDataFileName