úÎ!hF^Jš      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghij k l m n o p q r s t u v w x y z { | } ~  €  ‚ ƒ „ … † ‡ ˆ ‰ Š ‹ Œ  Ž   ‘ ’ “ ” • – — ˜ ™ š › œ  ž Ÿ  ĄąŁ€„Š§None"#.479=>?@AMSX_gk j   None"#.479=>?@AMSX_gk úpairingISum all the elements of some container according to its group structure.None"#.479=>?@AMSX_gkź pairingElliptic curve coefficent pairingElliptic curve coefficent!pairingEmbedding degreešpairing&BN parameter that determines the prime"pairing0Characteristic of the finite fields we work with#pairingxOrder of elliptic curve E(Fq) G1, and therefore also the characteristic of the prime field we choose our exponents from$pairingNParameter used to define the twisted curve over Fq, with xi = xi_a + xi_b * i%pairingNParameter used to define the twisted curve over Fq, with xi = xi_a + xi_b * i&pairingQuadratic nonresidue in Fq !"#$%& "#!&$%None"#.479=>?@AMSX_gk~6pairing%Picks the postive square root only |'()*+,-./0123456789:'()*+,-./0123456789:None"#.479=>?@AMSX_gkă;pairing Prime field Fr with characteristic _r>pairingÁCompute primitive roots of unity for 2^0, 2^1, ..., 2^28. (2^28 is the largest power of two that divides _r - 1, therefore there are no primitive roots of unity for higher powers of 2 in Fr.);<=>?;<=>?None"#%.479=>?@AMSX_gk2@pairingQuadratic extension field of Fq6 defined as Fq12 = Fq6[w]/ h(w)©pairing'Quadratic irreducible monic polynomial h(w) = w^2 - vApairingCubic extension field of Fq2 defined as  Fq6 = Fq2[v]/ g(v)Șpairing#Cubic irreducible monic polynomial g(v) = v^3 - (9 + u)BpairingQuadratic extension field of Fq defined as  Fq2 = Fq[u]/ f(u)«pairing'Quadratic irreducible monic polynomial f(u) = u^2 + 1Cpairing Prime field Fq with characteristic _qEpairing$Square root of Fq2 are specified by  $https://eprint.iacr.org/2012/685.pdf,% Algorithm 9 with lots of help from  Hhttps://docs.rs/pairing/0.14.1/src/pairing/bls12_381/fq2.rs.html#162-222q This implementation appears to return the larger square root so check the return value and negate as necessaryHpairingQuadratic non-residueIpairingCubic non-residue in Fq2Jpairing Multiply by xi (cubic nonresidue in Fq2) and reorder coefficientsKpairing ConjugationLpairingMultiplication by a scalar in FqMpairing ConjugationNpairingCreate a new value in Fq120 by providing a list of twelve coefficients in Fq , should be used instead of the Fq12 constructor.OpairingDeconstruct a value in Fq12' into a list of twelve coefficients in Fq.PpairingIterated Frobenius automorphismŹpairingFast Frobenius automorphism@ABCDEFGHIJKLMNOPCBA@DEFGHIJKLNOMPNone"#.479=>?@AMSX_gk9bZpairingPoints on a curve over a field aE represented as either affine coordinates or as a point at infinity.[pairing Affine point\pairingPoint at infinity]pairinghPoint addition, provides a group structure on an elliptic curve with the point at infinity as its unit.^pairingPoint doubling_pairing#Negation (flipping the y component)`pairingMultiplication by a scalarZ[\]^_`Z[\^]_`None"#.479=>?@AMSX_gk=‰gpairingBJacobian coordinates for points on an elliptic curve over a field k.hpairing2Convert affine coordinates to Jacobian coordinatesipairing2Convert Jacobian coordinates to affine coordinatesghighi None"#.479=>?@AMSX_gkE1jpairingÿ€Encodes a given byte string to a point on the BN curve. The implemenation uses the Shallue van de Woestijne encoding to BN curves as specifed 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 Definiton 2 of the paper is sent to an arbitrary point on the curvejj None"#.479=>?@AMSX_gkGspairing9The serialisation may fail if y cannot be obtained from x klmnopqrstuv rsopqmnkltuv None"#.479=>?@AMSX_gkHOwxwx None"#.479=>?@AMSX_gkI5}~}~ None"#.479=>?@AMSX_gkR[ ƒpairingKGT is subgroup of _r-th roots of unity of the multiplicative group of Fq12„pairing+G2 is E'(Fq2) defined by y^2 = x^3 + b / xi…pairing$G1 is E(Fq) defined by y^2 = x^3 + b†pairingGenerator for G1‡pairingGenerator for G2ˆpairingFTest whether a value in G1 satisfies the corresponding curve equation‰pairingFTest whether a value in G2 satisfies the corresponding curve equationŠpairing.Test whether a value is an _r-th root of unity‹pairingParameter for curve on FqŒpairing$Parameter for twisted curve over Fq2ƒ„…†‡ˆ‰Š‹ŒŽ‘…„ƒ‹Œ†‡ŽŠˆ‰‘None"#.479=>?@AMSX_gk] pairing9Optimal Ate pairing (including final exponentiation step)Ąpairing9Optimal Ate pairing without the final exponentiation stepąpairingXBinary expansion (missing the most-significant bit) representing the number 6 * _t + 2. Z29793968203157093288 = 0b11001110101111001011100000011100110111110011101100011101110101000­pairing*Miller loop with precomputed values for G2ŁpairingQIterated frobenius morphisms on fields of characteristic _q, implemented naively€pairing5Naive implementation of the final exponentiation step„pairing8A faster way of performing the final exponentiation step ĄąŁ€„ Ą„€ŁąNone"#.479=>?@AMSX_gk^%źŻ°±ČłŽ”¶ !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghiijklmnopqrstuvw x y z { | } ~  €  ‚ ƒ „ … … † ‡ ˆ ‰ Š Š ‹ Œ  Ž   ‘ ’ “ ” • – — ˜ ™ š › œ  ž Ÿ   Ą ą Ł € „ Š § š © Ș «Ź­źŻ°±ČłŽ”¶·žčș»ŒœŸżÀÁÂ$pairing-0.4.2-Dg7e1zic3JIKO8OuLYhCM0Pairing.ByteReprPairing.CyclicGroupPairing.ParamsPairing.Modular Pairing.Fr Pairing.Fq Pairing.PointPairing.Jacobian Pairing.HashPairing.Serialize.TypesPairing.Serialize.MCLWasmPairing.Serialize.Jivsov Pairing.GroupPairing.Pairing Paths_pairingByteReprmkReprfromReprcalcReprLengthByteOrderLength byteOrder lenPerElement ByteOrderMostSignificantFirstLeastSignificantFirsttoBytes toPaddedBytesfromBytesToIntegerValidateisValidElementFromXyFromXisOdd CyclicGroup generatororderexpninverserandom AsInteger asIntegersumG$fAsIntegerPrimeField$fAsIntegerInteger$fAsIntegerInt_b_a_k_q_r_xiA_xiB_nqrwithModwithModMwithQwithQMwithRwithRMnewMod toIntegermodUnOpmodBinOp multInversemodUnOpM modUnOpMTupthreeModFourCongruenceisSquaresqrtOf bothSqrtOflegendre randomMod fromBytesFr isRootOfUnityisPrimitiveRootOfUnityprimitiveRootOfUnityprecompRootOfUnityFq12Fq6Fq2FqfqSqrtfq2SqrtfqYforXfq2YforXfqNqrximulXifq2Conj fq2ScalarMulfq12Conj construct deconstruct fq12Frobenius$fByteReprPrimeField$fFromXPrimeField'$fIrreducibleMonicPrimeFieldPolynomialU$fByteReprExtensionField$fFromXExtensionField+$fIrreducibleMonicExtensionFieldPolynomialV$fByteReprExtensionField0+$fIrreducibleMonicExtensionFieldPolynomialW$fByteReprExtensionField1PointInfinitygAddgDoublegNeggMul $fEqPoint $fOrdPoint $fShowPoint$fFunctorPoint$fGenericPoint $fNFDataPointJPoint toJacobian fromJacobianswEncBNFromUncompressedForm unserializeFromSerialisedFormunserializePointMkUncompressedFormserializePointUncompressedserializeUncompressedMkCompressedFormserializeCompressed minReprLength buildPointparseBSMCLWASM$fFromSerialisedFormMCLWASM$fMkCompressedFormMCLWASM $fEqMCLWASM $fShowMCLWASMJivsov$fFromUncompressedFormJivsov$fFromSerialisedFormJivsov$fMkUncompressedFormJivsov$fMkCompressedFormJivsovGTG2G1g1g2 isOnCurveG1 isOnCurveG2isInGTb1b2hashToG1 groupFromXfromByteStringG1fromByteStringG2fromByteStringGT$fArbitraryPoint$fValidatePoint$fCyclicGroupPoint $fMonoidPoint$fSemigroupPoint$fArbitraryPoint0$fValidatePoint0$fCyclicGroupPoint0$fMonoidPoint0$fSemigroupPoint0$fValidateExtensionField$fCyclicGroupExtensionField$fMonoidExtensionField$fSemigroupExtensionFieldreducedPairing atePairingateLoopCountBinaryfrobeniusNaivefinalExponentiationNaivefinalExponentiation$fShowEllCoeffs $fEqEllCoeffs_t PolynomialW PolynomialV PolynomialU fastFrobenius ateMillerLoopversion getBinDir getLibDir getDynLibDir getDataDir getLibexecDir getSysconfDirgetDataFileName