{ "contractName": "EllipticCurve", "abi": [ { "inputs": [ { "internalType": "uint256", "name": "x0", "type": "uint256" }, { "internalType": "uint256", "name": "y0", "type": "uint256" } ], "name": "toProjectivePoint", "outputs": [ { "internalType": "uint256[3]", "name": "P", "type": "uint256[3]" } ], "stateMutability": "pure", "type": "function" }, { "inputs": [ { "internalType": "uint256", "name": "x1", "type": "uint256" }, { "internalType": "uint256", "name": "y1", "type": "uint256" }, { "internalType": "uint256", "name": "x2", "type": "uint256" }, { "internalType": "uint256", "name": "y2", "type": "uint256" } ], "name": "addAndReturnProjectivePoint", "outputs": [ { "internalType": "uint256[3]", "name": "P", "type": "uint256[3]" } ], "stateMutability": "pure", "type": "function" }, { "inputs": [ { "internalType": "uint256", "name": "x0", "type": "uint256" }, { "internalType": "uint256", "name": "y0", "type": "uint256" }, { "internalType": "uint256", "name": "z0", "type": "uint256" } ], "name": "toAffinePoint", "outputs": [ { "internalType": "uint256", "name": "x1", "type": "uint256" }, { "internalType": "uint256", "name": "y1", "type": "uint256" } ], "stateMutability": "pure", "type": "function" }, { "inputs": [], "name": "zeroProj", "outputs": [ { "internalType": "uint256", "name": "x", "type": "uint256" }, { "internalType": "uint256", "name": "y", "type": "uint256" }, { "internalType": "uint256", "name": "z", "type": "uint256" } ], "stateMutability": "pure", "type": "function" }, { "inputs": [], "name": "zeroAffine", "outputs": [ { "internalType": "uint256", "name": "x", "type": "uint256" }, { "internalType": "uint256", "name": "y", "type": "uint256" } ], "stateMutability": "pure", "type": "function" }, { "inputs": [ { "internalType": "uint256", "name": "x0", "type": "uint256" }, { "internalType": "uint256", "name": "y0", "type": "uint256" } ], "name": "isZeroCurve", "outputs": [ { "internalType": "bool", "name": "isZero", "type": "bool" } ], "stateMutability": 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"uint256", "name": "x1", "type": "uint256" }, { "internalType": "uint256", "name": "y1", "type": "uint256" } ], "stateMutability": "pure", "type": "function" }, { "inputs": [ { "internalType": "uint256", "name": "scalar", "type": "uint256" } ], "name": "multipleGeneratorByScalar", "outputs": [ { "internalType": "uint256", "name": "", "type": "uint256" }, { "internalType": "uint256", "name": "", "type": "uint256" } ], "stateMutability": "pure", "type": "function" }, { "inputs": [ { "internalType": "bytes32", "name": "message", "type": "bytes32" }, { "internalType": "uint256[2]", "name": "rs", "type": "uint256[2]" }, { "internalType": "uint256[2]", "name": "Q", "type": "uint256[2]" } ], "name": "validateSignature", "outputs": [ { "internalType": "bool", "name": "", "type": "bool" } ], "stateMutability": "pure", "type": "function" } ], "metadata": 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See https://www.nayuki.io/page/elliptic-curve-point-addition-in-projective-coordinates\"},\"isOnCurve(uint256,uint256)\":{\"details\":\"Check if a point in affine coordinates is on the curve.\"},\"isZeroCurve(uint256,uint256)\":{\"details\":\"Check if the curve is the zero curve.\"},\"multipleGeneratorByScalar(uint256)\":{\"details\":\"Multiply the curve's generator point by a scalar.\"},\"multiplyPowerBase2(uint256,uint256,uint256)\":{\"details\":\"Multiply an elliptic curve point by a 2 power base (i.e., (2^exp)*P)).\"},\"multiplyScalar(uint256,uint256,uint256)\":{\"details\":\"Multiply an elliptic curve point by a scalar.\"},\"toAffinePoint(uint256,uint256,uint256)\":{\"details\":\"Transform from projective to affine coordinates.\"},\"toProjectivePoint(uint256,uint256)\":{\"details\":\"Transform affine coordinates into projective coordinates.\"},\"twice(uint256,uint256)\":{\"details\":\"Double an elliptic curve point in affine coordinates.\"},\"twiceProj(uint256,uint256,uint256)\":{\"details\":\"Double an elliptic curve point in projective coordinates. See https://www.nayuki.io/page/elliptic-curve-point-addition-in-projective-coordinates\"},\"validateSignature(bytes32,uint256[2],uint256[2])\":{\"details\":\"Validate combination of message, signature, and public key.\"},\"zeroAffine()\":{\"details\":\"Return the zero curve in affine coordinates.\"},\"zeroProj()\":{\"details\":\"Return the zero curve in projective coordinates.\"}},\"title\":\"EllipticCurve\",\"version\":1},\"userdoc\":{\"kind\":\"user\",\"methods\":{},\"notice\":\"Implements elliptic curve math; Parametrized for SECP256R1. 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"source": "pragma solidity ^0.7.4;\n\n/**\n * @title EllipticCurve\n *\n * @author Tilman Drerup;\n *\n * @notice Implements elliptic curve math; Parametrized for SECP256R1.\n *\n * Includes components of code by Andreas Olofsson, Alexander Vlasov\n * (https://github.com/BANKEX/CurveArithmetics), and Avi Asayag\n * (https://github.com/orbs-network/elliptic-curve-solidity)\n *\n * Source: https://github.com/tdrerup/elliptic-curve-solidity\n *\n * @dev NOTE: To disambiguate public keys when verifying signatures, activate\n * condition 'rs[1] > lowSmax' in validateSignature().\n */\ncontract EllipticCurve {\n\n // Set parameters for curve.\n uint constant a = 0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC;\n uint constant b = 0x5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B;\n uint constant gx = 0x6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296;\n uint constant gy = 0x4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5;\n uint constant p = 0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF;\n uint constant n = 0xFFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551;\n\n uint constant lowSmax = 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0;\n\n /**\n * @dev Inverse of u in the field of modulo m.\n */\n function inverseMod(uint u, uint m) internal pure\n returns (uint)\n {\n if (u == 0 || u == m || m == 0)\n return 0;\n if (u > m)\n u = u % m;\n\n int t1;\n int t2 = 1;\n uint r1 = m;\n uint r2 = u;\n uint q;\n\n while (r2 != 0) {\n q = r1 / r2;\n (t1, t2, r1, r2) = (t2, t1 - int(q) * t2, r2, r1 - q * r2);\n }\n\n if (t1 < 0)\n return (m - uint(-t1));\n\n return uint(t1);\n }\n\n /**\n * @dev Transform affine coordinates into projective coordinates.\n */\n function toProjectivePoint(uint x0, uint y0) public pure\n returns (uint[3] memory P)\n {\n P[2] = addmod(0, 1, p);\n P[0] = mulmod(x0, P[2], p);\n P[1] = mulmod(y0, P[2], p);\n }\n\n /**\n * @dev Add two points in affine coordinates and return projective point.\n */\n function addAndReturnProjectivePoint(uint x1, uint y1, uint x2, uint y2) public pure\n returns (uint[3] memory P)\n {\n uint x;\n uint y;\n (x, y) = add(x1, y1, x2, y2);\n P = toProjectivePoint(x, y);\n }\n\n /**\n * @dev Transform from projective to affine coordinates.\n */\n function toAffinePoint(uint x0, uint y0, uint z0) public pure\n returns (uint x1, uint y1)\n {\n uint z0Inv;\n z0Inv = inverseMod(z0, p);\n x1 = mulmod(x0, z0Inv, p);\n y1 = mulmod(y0, z0Inv, p);\n }\n\n /**\n * @dev Return the zero curve in projective coordinates.\n */\n function zeroProj() public pure\n returns (uint x, uint y, uint z)\n {\n return (0, 1, 0);\n }\n\n /**\n * @dev Return the zero curve in affine coordinates.\n */\n function zeroAffine() public pure\n returns (uint x, uint y)\n {\n return (0, 0);\n }\n\n /**\n * @dev Check if the curve is the zero curve.\n */\n function isZeroCurve(uint x0, uint y0) public pure\n returns (bool isZero)\n {\n if(x0 == 0 && y0 == 0) {\n return true;\n }\n return false;\n }\n\n /**\n * @dev Check if a point in affine coordinates is on the curve.\n */\n function isOnCurve(uint x, uint y) public pure\n returns (bool)\n {\n if (0 == x || x == p || 0 == y || y == p) {\n return false;\n }\n\n uint LHS = mulmod(y, y, p); // y^2\n uint RHS = mulmod(mulmod(x, x, p), x, p); // x^3\n\n if (a != 0) {\n RHS = addmod(RHS, mulmod(x, a, p), p); // x^3 + a*x\n }\n if (b != 0) {\n RHS = addmod(RHS, b, p); // x^3 + a*x + b\n }\n\n return LHS == RHS;\n }\n\n /**\n * @dev Double an elliptic curve point in projective coordinates. See\n * https://www.nayuki.io/page/elliptic-curve-point-addition-in-projective-coordinates\n */\n function twiceProj(uint x0, uint y0, uint z0) public pure\n returns (uint x1, uint y1, uint z1)\n {\n uint t;\n uint u;\n uint v;\n uint w;\n\n if(isZeroCurve(x0, y0)) {\n return zeroProj();\n }\n\n u = mulmod(y0, z0, p);\n u = mulmod(u, 2, p);\n\n v = mulmod(u, x0, p);\n v = mulmod(v, y0, p);\n v = mulmod(v, 2, p);\n\n x0 = mulmod(x0, x0, p);\n t = mulmod(x0, 3, p);\n\n z0 = mulmod(z0, z0, p);\n z0 = mulmod(z0, a, p);\n t = addmod(t, z0, p);\n\n w = mulmod(t, t, p);\n x0 = mulmod(2, v, p);\n w = addmod(w, p-x0, p);\n\n x0 = addmod(v, p-w, p);\n x0 = mulmod(t, x0, p);\n y0 = mulmod(y0, u, p);\n y0 = mulmod(y0, y0, p);\n y0 = mulmod(2, y0, p);\n y1 = addmod(x0, p-y0, p);\n\n x1 = mulmod(u, w, p);\n\n z1 = mulmod(u, u, p);\n z1 = mulmod(z1, u, p);\n }\n\n /**\n * @dev Add two elliptic curve points in projective coordinates. See\n * https://www.nayuki.io/page/elliptic-curve-point-addition-in-projective-coordinates\n */\n function addProj(uint x0, uint y0, uint z0, uint x1, uint y1, uint z1) public pure\n returns (uint x2, uint y2, uint z2)\n {\n uint t0;\n uint t1;\n uint u0;\n uint u1;\n\n if (isZeroCurve(x0, y0)) {\n return (x1, y1, z1);\n }\n else if (isZeroCurve(x1, y1)) {\n return (x0, y0, z0);\n }\n\n t0 = mulmod(y0, z1, p);\n t1 = mulmod(y1, z0, p);\n\n u0 = mulmod(x0, z1, p);\n u1 = mulmod(x1, z0, p);\n\n if (u0 == u1) {\n if (t0 == t1) {\n return twiceProj(x0, y0, z0);\n }\n else {\n return zeroProj();\n }\n }\n\n (x2, y2, z2) = addProj2(mulmod(z0, z1, p), u0, u1, t1, t0);\n }\n\n /**\n * @dev Helper function that splits addProj to avoid too many local variables.\n */\n function addProj2(uint v, uint u0, uint u1, uint t1, uint t0) private pure\n returns (uint x2, uint y2, uint z2)\n {\n uint u;\n uint u2;\n uint u3;\n uint w;\n uint t;\n\n t = addmod(t0, p-t1, p);\n u = addmod(u0, p-u1, p);\n u2 = mulmod(u, u, p);\n\n w = mulmod(t, t, p);\n w = mulmod(w, v, p);\n u1 = addmod(u1, u0, p);\n u1 = mulmod(u1, u2, p);\n w = addmod(w, p-u1, p);\n\n x2 = mulmod(u, w, p);\n\n u3 = mulmod(u2, u, p);\n u0 = mulmod(u0, u2, p);\n u0 = addmod(u0, p-w, p);\n t = mulmod(t, u0, p);\n t0 = mulmod(t0, u3, p);\n\n y2 = addmod(t, p-t0, p);\n\n z2 = mulmod(u3, v, p);\n }\n\n /**\n * @dev Add two elliptic curve points in affine coordinates.\n */\n function add(uint x0, uint y0, uint x1, uint y1) public pure\n returns (uint, uint)\n {\n uint z0;\n\n (x0, y0, z0) = addProj(x0, y0, 1, x1, y1, 1);\n\n return toAffinePoint(x0, y0, z0);\n }\n\n /**\n * @dev Double an elliptic curve point in affine coordinates.\n */\n function twice(uint x0, uint y0) public pure\n returns (uint, uint)\n {\n uint z0;\n\n (x0, y0, z0) = twiceProj(x0, y0, 1);\n\n return toAffinePoint(x0, y0, z0);\n }\n\n /**\n * @dev Multiply an elliptic curve point by a 2 power base (i.e., (2^exp)*P)).\n */\n function multiplyPowerBase2(uint x0, uint y0, uint exp) public pure\n returns (uint, uint)\n {\n uint base2X = x0;\n uint base2Y = y0;\n uint base2Z = 1;\n\n for(uint i = 0; i < exp; i++) {\n (base2X, base2Y, base2Z) = twiceProj(base2X, base2Y, base2Z);\n }\n\n return toAffinePoint(base2X, base2Y, base2Z);\n }\n\n /**\n * @dev Multiply an elliptic curve point by a scalar.\n */\n function multiplyScalar(uint x0, uint y0, uint scalar) public pure\n returns (uint x1, uint y1)\n {\n if(scalar == 0) {\n return zeroAffine();\n }\n else if (scalar == 1) {\n return (x0, y0);\n }\n else if (scalar == 2) {\n return twice(x0, y0);\n }\n\n uint base2X = x0;\n uint base2Y = y0;\n uint base2Z = 1;\n uint z1 = 1;\n x1 = x0;\n y1 = y0;\n\n if(scalar%2 == 0) {\n x1 = y1 = 0;\n }\n\n scalar = scalar >> 1;\n\n while(scalar > 0) {\n (base2X, base2Y, base2Z) = twiceProj(base2X, base2Y, base2Z);\n\n if(scalar%2 == 1) {\n (x1, y1, z1) = addProj(base2X, base2Y, base2Z, x1, y1, z1);\n }\n\n scalar = scalar >> 1;\n }\n\n return toAffinePoint(x1, y1, z1);\n }\n\n /**\n * @dev Multiply the curve's generator point by a scalar.\n */\n function multipleGeneratorByScalar(uint scalar) public pure\n returns (uint, uint)\n {\n return multiplyScalar(gx, gy, scalar);\n }\n\n /**\n * @dev Validate combination of message, signature, and public key.\n */\n function validateSignature(bytes32 message, uint[2] memory rs, uint[2] memory Q) public pure\n returns (bool)\n {\n\n // To disambiguate between public key solutions, include comment below.\n if(rs[0] == 0 || rs[0] >= n || rs[1] == 0) {// || rs[1] > lowSmax)\n return false;\n }\n if (!isOnCurve(Q[0], Q[1])) {\n return false;\n }\n\n uint x1;\n uint x2;\n uint y1;\n uint y2;\n\n uint sInv = inverseMod(rs[1], n);\n (x1, y1) = multiplyScalar(gx, gy, mulmod(uint(message), sInv, n));\n (x2, y2) = multiplyScalar(Q[0], Q[1], mulmod(rs[0], sInv, n));\n uint[3] memory P = addAndReturnProjectivePoint(x1, y1, x2, y2);\n\n if (P[2] == 0) {\n return false;\n }\n\n uint Px = inverseMod(P[2], p);\n Px = mulmod(P[0], mulmod(Px, Px, p), p);\n\n return Px % n == rs[0];\n }\n}", "sourcePath": "/home/arachnid/Dropbox/projects/enssec/contracts/algorithms/EllipticCurve.sol", "ast": { "absolutePath": "/home/arachnid/Dropbox/projects/enssec/contracts/algorithms/EllipticCurve.sol", "exportedSymbols": { "EllipticCurve": [ 5243 ] }, "id": 5244, "nodeType": "SourceUnit", "nodes": [ { "id": 3887, "literals": [ "solidity", "^", "0.7", ".4" ], "nodeType": "PragmaDirective", "src": "0:23:8" }, { "abstract": false, "baseContracts": [], "contractDependencies": [], "contractKind": "contract", "documentation": { "id": 3888, "nodeType": "StructuredDocumentation", "src": "25:585:8", "text": " @title EllipticCurve\n @author Tilman Drerup;\n @notice Implements elliptic curve math; Parametrized for SECP256R1.\n Includes components of code by Andreas Olofsson, Alexander Vlasov\n (https://github.com/BANKEX/CurveArithmetics), and Avi Asayag\n 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"ElementaryTypeName", "src": "6257:4:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "6221:44:8" }, "returnParameters": { "id": 4645, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 4640, "mutability": "mutable", "name": "x2", "nodeType": "VariableDeclaration", "scope": 4800, "src": "6296:7:8", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 4639, "name": "uint", "nodeType": "ElementaryTypeName", "src": "6296:4:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 4642, "mutability": "mutable", "name": "y2", "nodeType": "VariableDeclaration", "scope": 4800, "src": "6305:7:8", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": 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"mutability": "mutable", "name": "z0", "nodeType": "VariableDeclaration", "scope": 4839, "src": "7115:7:8", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 4816, "name": "uint", "nodeType": "ElementaryTypeName", "src": "7115:4:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "id": 4818, "nodeType": "VariableDeclarationStatement", "src": "7115:7:8" }, { "expression": { "id": 4831, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "components": [ { "id": 4819, "name": "x0", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4803, "src": "7134:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 4820, "name": "y0", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4805, "src": "7138:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 4821, "name": "z0", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4817, "src": "7142:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "id": 4822, "isConstant": false, "isInlineArray": false, "isLValue": true, "isPure": false, "lValueRequested": true, "nodeType": "TupleExpression", "src": "7133:12:8", "typeDescriptions": { "typeIdentifier": "t_tuple$_t_uint256_$_t_uint256_$_t_uint256_$", "typeString": "tuple(uint256,uint256,uint256)" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "arguments": [ { "id": 4824, "name": "x0", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4803, "src": "7156:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 4825, "name": "y0", "nodeType": "Identifier", 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"typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 5047, "nodeType": "IfStatement", "src": "8724:109:8", "trueBody": { "id": 5046, "nodeType": "Block", "src": "8742:91:8", "statements": [ { "expression": { "id": 5044, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "components": [ { "id": 5032, "name": "x1", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4939, "src": "8761:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 5033, "name": "y1", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4941, "src": "8765:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 5034, "name": "z1", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4983, "src": "8769:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": 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"typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 5036, "name": "addProj", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4626, "src": "8775:7:8", "typeDescriptions": { "typeIdentifier": "t_function_internal_pure$_t_uint256_$_t_uint256_$_t_uint256_$_t_uint256_$_t_uint256_$_t_uint256_$returns$_t_uint256_$_t_uint256_$_t_uint256_$", "typeString": "function (uint256,uint256,uint256,uint256,uint256,uint256) pure returns (uint256,uint256,uint256)" } }, "id": 5043, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "names": [], "nodeType": "FunctionCall", "src": "8775:43:8", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_tuple$_t_uint256_$_t_uint256_$_t_uint256_$", "typeString": "tuple(uint256,uint256,uint256)" } }, "src": "8760:58:8", "typeDescriptions": { "typeIdentifier": "t_tuple$__$", "typeString": "tuple()" } }, "id": 5045, "nodeType": "ExpressionStatement", "src": "8760:58:8" } ] } }, { "expression": { "id": 5052, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 5048, "name": "scalar", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4936, "src": "8847:6:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 5051, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 5049, "name": "scalar", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4936, "src": "8856:6:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "31", "id": 5050, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "8866:1:8", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "src": "8856:11:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "8847:20:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 5053, "nodeType": "ExpressionStatement", "src": "8847:20:8" } ] }, "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 5015, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 5013, "name": "scalar", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4936, "src": "8623:6:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 5014, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "8632:1:8", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "8623:10:8", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 5055, "nodeType": "WhileStatement", "src": "8617:261:8" }, { "expression": { "arguments": [ { "id": 5057, "name": "x1", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4939, "src": "8909:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 5058, "name": "y1", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4941, "src": "8913:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 5059, "name": "z1", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4983, "src": "8917:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 5056, "name": "toAffinePoint", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4143, "src": "8895:13:8", "typeDescriptions": { "typeIdentifier": "t_function_internal_pure$_t_uint256_$_t_uint256_$_t_uint256_$returns$_t_uint256_$_t_uint256_$", "typeString": "function (uint256,uint256,uint256) pure returns (uint256,uint256)" } }, "id": 5060, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "names": [], "nodeType": "FunctionCall", "src": "8895:25:8", "tryCall": false, "typeDescriptions": { "typeIdentifier": 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"internal" } ], "src": "8079:31:8" }, "returnParameters": { "id": 4942, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 4939, "mutability": "mutable", "name": "x1", "nodeType": "VariableDeclaration", "scope": 5063, "src": "8140:7:8", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 4938, "name": "uint", "nodeType": "ElementaryTypeName", "src": "8140:4:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 4941, "mutability": "mutable", "name": "y1", "nodeType": "VariableDeclaration", "scope": 5063, "src": "8149:7:8", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 4940, "name": "uint", "nodeType": "ElementaryTypeName", "src": "8149:4:8", "typeDescriptions": { 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"nodeType": "TupleExpression", "src": "1742:39:8", "typeDescriptions": { "typeIdentifier": "t_tuple$_t_int256_$_t_int256_$_t_uint256_$_t_uint256_$", "typeString": "tuple(int256,int256,uint256,uint256)" } }, "src": "1723:58:8", "typeDescriptions": { "typeIdentifier": "t_tuple$__$", "typeString": "tuple()" } }, "id": 3992, "nodeType": "ExpressionStatement", "src": "1723:58:8" } ] }, "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 3963, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 3961, "name": "r2", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3955, "src": "1675:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "!=", "rightExpression": { "hexValue": "30", "id": 3962, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "1681:1:8", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "1675:7:8", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 3994, "nodeType": "WhileStatement", "src": "1668:124:8" }, { "condition": { "commonType": { "typeIdentifier": "t_int256", "typeString": "int256" }, "id": 3997, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 3995, "name": "t1", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3944, "src": "1806:2:8", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } }, "nodeType": "BinaryOperation", "operator": "<", "rightExpression": { "hexValue": "30", "id": 3996, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "1811:1:8", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "1806:6:8", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 4007, "nodeType": "IfStatement", "src": "1802:46:8", "trueBody": { "expression": { "components": [ { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 4004, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 3998, "name": "m", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3914, "src": "1834:1:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "-", "rightExpression": { "arguments": [ { "id": 4002, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "UnaryOperation", "operator": "-", "prefix": true, "src": "1843:3:8", "subExpression": { "id": 4001, "name": "t1", 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"typeString": "uint256" } }, "src": "1834:13:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "id": 4005, "isConstant": false, "isInlineArray": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "TupleExpression", "src": "1833:15:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "functionReturnParameters": 3918, "id": 4006, "nodeType": "Return", "src": "1826:22:8" } }, { "expression": { "arguments": [ { "id": 4010, "name": "t1", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3944, "src": "1871:2:8", "typeDescriptions": { "typeIdentifier": "t_int256", "typeString": "int256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_int256", "typeString": "int256" } ], "id": 4009, "isConstant": false, "isLValue": false, "isPure": true, "lValueRequested": false, "nodeType": "ElementaryTypeNameExpression", "src": "1866:4:8", "typeDescriptions": { "typeIdentifier": "t_type$_t_uint256_$", "typeString": "type(uint256)" }, "typeName": { "id": 4008, "name": "uint", "nodeType": "ElementaryTypeName", "src": "1866:4:8", "typeDescriptions": {} } }, "id": 4011, "isConstant": false, "isLValue": false, "isPure": false, "kind": "typeConversion", "lValueRequested": false, "names": [], "nodeType": "FunctionCall", "src": "1866:8:8", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "functionReturnParameters": 3918, "id": 4012, "nodeType": "Return", "src": "1859:15:8" } ] }, "documentation": { "id": 3910, "nodeType": "StructuredDocumentation", "src": "1314:62:8", "text": " @dev Inverse of u in the field of modulo m." }, "id": 4014, "implemented": true, "kind": "function", "modifiers": [], "name": "inverseMod", "nodeType": "FunctionDefinition", "parameters": { "id": 3915, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 3912, "mutability": "mutable", "name": "u", "nodeType": "VariableDeclaration", "scope": 4014, "src": "1401:6:8", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 3911, "name": "uint", "nodeType": "ElementaryTypeName", "src": "1401:4:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 3914, "mutability": "mutable", "name": "m", "nodeType": "VariableDeclaration", "scope": 4014, "src": "1409:6:8", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 3913, "name": "uint", "nodeType": "ElementaryTypeName", "src": "1409:4:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "1400:16:8" }, "returnParameters": { "id": 3918, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 3917, "mutability": "mutable", "name": "", "nodeType": "VariableDeclaration", "scope": 4014, "src": "1448:4:8", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 3916, "name": "uint", "nodeType": "ElementaryTypeName", "src": "1448:4:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "1447:6:8" }, "scope": 5243, "src": "1381:500:8", "stateMutability": "pure", "virtual": false, "visibility": "internal" }, { "body": { "id": 4060, "nodeType": "Block", "src": "2069:111:8", "statements": [ { "expression": { "id": 4034, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "baseExpression": { "id": 4026, "name": "P", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4024, "src": "2079:1:8", "typeDescriptions": { "typeIdentifier": "t_array$_t_uint256_$3_memory_ptr", "typeString": "uint256[3] memory" } }, "id": 4028, "indexExpression": { "hexValue": "32", "id": 4027, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "2081:1:8", "typeDescriptions": { "typeIdentifier": "t_rational_2_by_1", "typeString": "int_const 2" }, "value": "2" }, "isConstant": false, "isLValue": true, "isPure": false, "lValueRequested": true, "nodeType": "IndexAccess", "src": "2079:4:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "arguments": [ { "hexValue": "30", "id": 4030, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "2093:1:8", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, { "hexValue": "31", "id": 4031, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "2096:1:8", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, { "id": 4032, "name": "p", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3903, "src": "2099:1:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 4029, "name": "addmod", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": -2, "src": "2086:6:8", "typeDescriptions": { "typeIdentifier": "t_function_addmod_pure$_t_uint256_$_t_uint256_$_t_uint256_$returns$_t_uint256_$", "typeString": "function (uint256,uint256,uint256) pure returns (uint256)" } }, "id": 4033, "isConstant": false, "isLValue": false, "isPure": true, "kind": "functionCall", "lValueRequested": false, "names": [], "nodeType": "FunctionCall", "src": "2086:15:8", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "2079:22:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 4035, "nodeType": "ExpressionStatement", "src": "2079:22:8" }, { "expression": { "id": 4046, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "baseExpression": { "id": 4036, "name": "P", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4024, "src": "2111:1:8", "typeDescriptions": { "typeIdentifier": "t_array$_t_uint256_$3_memory_ptr", "typeString": "uint256[3] memory" } }, "id": 4038, "indexExpression": { "hexValue": "30", "id": 4037, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "2113:1:8", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "isConstant": false, "isLValue": true, "isPure": false, "lValueRequested": true, "nodeType": "IndexAccess", "src": "2111:4:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "arguments": [ { "id": 4040, "name": "x0", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4017, "src": "2125:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "baseExpression": { "id": 4041, "name": "P", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4024, "src": "2129:1:8", "typeDescriptions": { "typeIdentifier": "t_array$_t_uint256_$3_memory_ptr", "typeString": "uint256[3] memory" } }, "id": 4043, "indexExpression": { "hexValue": "32", "id": 4042, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "2131:1:8", "typeDescriptions": { "typeIdentifier": "t_rational_2_by_1", "typeString": "int_const 2" }, "value": "2" }, "isConstant": false, "isLValue": true, "isPure": false, "lValueRequested": false, "nodeType": "IndexAccess", "src": "2129:4:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 4044, "name": "p", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3903, "src": "2135:1:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 4039, "name": "mulmod", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": -16, "src": "2118:6:8", "typeDescriptions": { "typeIdentifier": "t_function_mulmod_pure$_t_uint256_$_t_uint256_$_t_uint256_$returns$_t_uint256_$", "typeString": "function (uint256,uint256,uint256) pure returns (uint256)" } }, "id": 4045, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "names": [], "nodeType": "FunctionCall", "src": "2118:19:8", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "2111:26:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 4047, "nodeType": "ExpressionStatement", "src": "2111:26:8" }, { "expression": { "id": 4058, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "baseExpression": { "id": 4048, "name": "P", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4024, "src": "2147:1:8", "typeDescriptions": { "typeIdentifier": "t_array$_t_uint256_$3_memory_ptr", "typeString": "uint256[3] memory" } }, "id": 4050, "indexExpression": { "hexValue": "31", "id": 4049, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "2149:1:8", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "isConstant": false, "isLValue": true, "isPure": false, "lValueRequested": true, "nodeType": "IndexAccess", "src": "2147:4:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "arguments": [ { "id": 4052, "name": "y0", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4019, "src": "2161:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "baseExpression": { "id": 4053, "name": "P", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4024, "src": "2165:1:8", "typeDescriptions": { "typeIdentifier": "t_array$_t_uint256_$3_memory_ptr", "typeString": "uint256[3] memory" } }, "id": 4055, "indexExpression": { "hexValue": "32", "id": 4054, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "2167:1:8", "typeDescriptions": { "typeIdentifier": "t_rational_2_by_1", "typeString": "int_const 2" }, "value": "2" }, "isConstant": false, "isLValue": true, "isPure": false, "lValueRequested": false, "nodeType": "IndexAccess", "src": "2165:4:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 4056, "name": "p", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3903, "src": "2171:1:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { 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"functionCall", "lValueRequested": false, "names": [], "nodeType": "FunctionCall", "src": "6771:18:8", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "6766:23:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 4764, "nodeType": "ExpressionStatement", "src": "6766:23:8" }, { "expression": { "id": 4771, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 4765, "name": "t", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4659, "src": "6799:1:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "arguments": [ { "id": 4767, "name": "t", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4659, "src": "6810:1:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 4768, "name": "u0", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4631, "src": "6813:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 4769, "name": "p", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3903, "src": "6817:1:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 4766, "name": "mulmod", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": -16, "src": "6803:6:8", "typeDescriptions": { "typeIdentifier": "t_function_mulmod_pure$_t_uint256_$_t_uint256_$_t_uint256_$returns$_t_uint256_$", "typeString": "function (uint256,uint256,uint256) pure returns (uint256)" } }, "id": 4770, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "names": [], "nodeType": "FunctionCall", "src": "6803:16:8", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "6799:20:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 4772, "nodeType": "ExpressionStatement", "src": "6799:20:8" }, { "expression": { "id": 4779, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 4773, "name": "t0", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4637, "src": "6829:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "arguments": [ { "id": 4775, "name": "t0", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4637, "src": "6841:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 4776, "name": "u3", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4653, "src": "6845:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 4777, "name": "p", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3903, "src": "6849:1:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 4774, "name": "mulmod", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": -16, "src": "6834:6:8", "typeDescriptions": { "typeIdentifier": "t_function_mulmod_pure$_t_uint256_$_t_uint256_$_t_uint256_$returns$_t_uint256_$", "typeString": "function (uint256,uint256,uint256) pure returns (uint256)" } }, "id": 4778, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "names": [], "nodeType": "FunctionCall", "src": "6834:17:8", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "6829:22:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 4780, "nodeType": "ExpressionStatement", "src": "6829:22:8" }, { "expression": { "id": 4789, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 4781, "name": "y2", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4642, "src": "6862:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "arguments": [ { "id": 4783, "name": "t", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4659, "src": "6874:1:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 4786, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 4784, "name": "p", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3903, "src": "6877:1:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "-", "rightExpression": { "id": 4785, "name": "t0", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4637, "src": "6879:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "6877:4:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 4787, "name": "p", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3903, "src": "6883:1:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 4782, "name": "addmod", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": -2, "src": "6867:6:8", "typeDescriptions": { "typeIdentifier": "t_function_addmod_pure$_t_uint256_$_t_uint256_$_t_uint256_$returns$_t_uint256_$", "typeString": "function (uint256,uint256,uint256) pure returns (uint256)" } }, "id": 4788, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "names": [], "nodeType": "FunctionCall", "src": "6867:18:8", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "6862:23:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 4790, "nodeType": "ExpressionStatement", "src": "6862:23:8" }, { "expression": { "id": 4797, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 4791, "name": "z2", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4644, "src": "6896:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "arguments": [ { "id": 4793, "name": "u3", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4653, "src": "6908:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 4794, "name": "v", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4629, "src": "6912:1:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 4795, "name": "p", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3903, "src": "6915:1:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 4792, "name": "mulmod", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": -16, "src": "6901:6:8", "typeDescriptions": { "typeIdentifier": "t_function_mulmod_pure$_t_uint256_$_t_uint256_$_t_uint256_$returns$_t_uint256_$", "typeString": "function (uint256,uint256,uint256) pure returns (uint256)" } }, "id": 4796, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "names": [], "nodeType": "FunctionCall", "src": "6901:16:8", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "6896:21:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 4798, "nodeType": "ExpressionStatement", "src": "6896:21:8" } ] }, "documentation": { "id": 4627, "nodeType": "StructuredDocumentation", "src": "6105:94:8", "text": " @dev Helper function that splits addProj to avoid too many local variables." }, "id": 4800, "implemented": true, "kind": "function", "modifiers": [], "name": "addProj2", "nodeType": "FunctionDefinition", "parameters": { "id": 4638, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 4629, "mutability": "mutable", "name": "v", "nodeType": "VariableDeclaration", "scope": 4800, "src": "6222:6:8", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 4628, "name": "uint", "nodeType": "ElementaryTypeName", "src": "6222:4:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 4631, "mutability": "mutable", "name": "u0", "nodeType": "VariableDeclaration", "scope": 4800, "src": "6230:7:8", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 4630, "name": "uint", "nodeType": "ElementaryTypeName", "src": "6230:4:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 4633, "mutability": "mutable", "name": "u1", "nodeType": "VariableDeclaration", "scope": 4800, "src": "6239:7:8", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 4632, "name": "uint", "nodeType": "ElementaryTypeName", "src": "6239:4:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 4635, "mutability": "mutable", "name": "t1", "nodeType": "VariableDeclaration", "scope": 4800, "src": "6248:7:8", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 4634, "name": "uint", "nodeType": "ElementaryTypeName", "src": "6248:4:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 4637, "mutability": "mutable", "name": "t0", "nodeType": "VariableDeclaration", "scope": 4800, "src": "6257:7:8", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 4636, "name": "uint", "nodeType": "ElementaryTypeName", "src": "6257:4:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "6221:44:8" }, "returnParameters": { "id": 4645, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 4640, "mutability": "mutable", "name": "x2", "nodeType": "VariableDeclaration", "scope": 4800, "src": "6296:7:8", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 4639, "name": "uint", "nodeType": "ElementaryTypeName", "src": "6296:4:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 4642, "mutability": "mutable", "name": "y2", "nodeType": "VariableDeclaration", "scope": 4800, "src": "6305:7:8", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 4641, "name": "uint", "nodeType": "ElementaryTypeName", "src": "6305:4:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 4644, "mutability": "mutable", "name": "z2", "nodeType": "VariableDeclaration", "scope": 4800, "src": "6314:7:8", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 4643, "name": "uint", "nodeType": "ElementaryTypeName", "src": "6314:4:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "6295:27:8" }, "scope": 5243, "src": "6204:720:8", "stateMutability": "pure", "virtual": false, "visibility": "private" }, { "body": { "id": 4839, "nodeType": "Block", "src": "7105:122:8", "statements": [ { "assignments": [ 4817 ], "declarations": [ { "constant": false, "id": 4817, "mutability": "mutable", "name": "z0", "nodeType": "VariableDeclaration", "scope": 4839, "src": "7115:7:8", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 4816, "name": "uint", "nodeType": "ElementaryTypeName", "src": "7115:4:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "id": 4818, "nodeType": "VariableDeclarationStatement", "src": "7115:7:8" }, { "expression": { "id": 4831, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "components": [ { "id": 4819, "name": "x0", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4803, "src": "7134:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 4820, "name": "y0", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4805, "src": "7138:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 4821, "name": "z0", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4817, "src": "7142:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "id": 4822, "isConstant": false, "isInlineArray": false, "isLValue": true, "isPure": false, "lValueRequested": true, "nodeType": "TupleExpression", "src": "7133:12:8", "typeDescriptions": { "typeIdentifier": "t_tuple$_t_uint256_$_t_uint256_$_t_uint256_$", "typeString": "tuple(uint256,uint256,uint256)" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "arguments": [ { "id": 4824, "name": "x0", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4803, "src": "7156:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 4825, "name": "y0", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4805, "src": "7160:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "hexValue": "31", "id": 4826, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7164:1:8", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, { "id": 4827, "name": "x1", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4807, "src": "7167:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 4828, "name": "y1", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4809, "src": "7171:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "hexValue": "31", "id": 4829, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "7175:1:8", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" } ], "id": 4823, "name": "addProj", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4626, "src": "7148:7:8", "typeDescriptions": { "typeIdentifier": "t_function_internal_pure$_t_uint256_$_t_uint256_$_t_uint256_$_t_uint256_$_t_uint256_$_t_uint256_$returns$_t_uint256_$_t_uint256_$_t_uint256_$", "typeString": "function (uint256,uint256,uint256,uint256,uint256,uint256) pure returns (uint256,uint256,uint256)" } }, "id": 4830, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "names": [], "nodeType": "FunctionCall", "src": "7148:29:8", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_tuple$_t_uint256_$_t_uint256_$_t_uint256_$", "typeString": "tuple(uint256,uint256,uint256)" } }, "src": "7133:44:8", "typeDescriptions": { "typeIdentifier": "t_tuple$__$", "typeString": "tuple()" } }, "id": 4832, "nodeType": "ExpressionStatement", "src": "7133:44:8" }, { "expression": { "arguments": [ { "id": 4834, "name": "x0", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4803, "src": "7209:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 4835, "name": "y0", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4805, "src": "7213:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 4836, "name": "z0", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4817, "src": "7217:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 4833, "name": "toAffinePoint", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4143, "src": "7195:13:8", "typeDescriptions": { "typeIdentifier": "t_function_internal_pure$_t_uint256_$_t_uint256_$_t_uint256_$returns$_t_uint256_$_t_uint256_$", "typeString": "function (uint256,uint256,uint256) pure returns (uint256,uint256)" } }, "id": 4837, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "names": [], "nodeType": "FunctionCall", "src": "7195:25:8", 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"typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 5047, "nodeType": "IfStatement", "src": "8724:109:8", "trueBody": { "id": 5046, "nodeType": "Block", "src": "8742:91:8", "statements": [ { "expression": { "id": 5044, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "components": [ { "id": 5032, "name": "x1", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4939, "src": "8761:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 5033, "name": "y1", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4941, "src": "8765:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 5034, "name": "z1", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4983, "src": "8769:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "id": 5035, "isConstant": false, "isInlineArray": false, "isLValue": true, "isPure": false, "lValueRequested": true, "nodeType": "TupleExpression", "src": "8760:12:8", "typeDescriptions": { "typeIdentifier": "t_tuple$_t_uint256_$_t_uint256_$_t_uint256_$", "typeString": "tuple(uint256,uint256,uint256)" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "arguments": [ { "id": 5037, "name": "base2X", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4971, "src": "8783:6:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 5038, "name": "base2Y", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4975, "src": "8791:6:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 5039, "name": "base2Z", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4979, "src": "8799:6:8", "typeDescriptions": 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"typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 5036, "name": "addProj", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4626, "src": "8775:7:8", "typeDescriptions": { "typeIdentifier": "t_function_internal_pure$_t_uint256_$_t_uint256_$_t_uint256_$_t_uint256_$_t_uint256_$_t_uint256_$returns$_t_uint256_$_t_uint256_$_t_uint256_$", "typeString": "function (uint256,uint256,uint256,uint256,uint256,uint256) pure returns (uint256,uint256,uint256)" } }, "id": 5043, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "names": [], "nodeType": "FunctionCall", "src": "8775:43:8", "tryCall": false, "typeDescriptions": { "typeIdentifier": "t_tuple$_t_uint256_$_t_uint256_$_t_uint256_$", "typeString": "tuple(uint256,uint256,uint256)" } }, "src": "8760:58:8", "typeDescriptions": { "typeIdentifier": "t_tuple$__$", "typeString": "tuple()" } }, "id": 5045, "nodeType": "ExpressionStatement", "src": "8760:58:8" } ] } }, { "expression": { "id": 5052, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "id": 5048, "name": "scalar", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4936, "src": "8847:6:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 5051, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 5049, "name": "scalar", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4936, "src": "8856:6:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">>", "rightExpression": { "hexValue": "31", "id": 5050, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "8866:1:8", "typeDescriptions": { "typeIdentifier": "t_rational_1_by_1", "typeString": "int_const 1" }, "value": "1" }, "src": "8856:11:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "8847:20:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 5053, "nodeType": "ExpressionStatement", "src": "8847:20:8" } ] }, "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 5015, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 5013, "name": "scalar", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4936, "src": "8623:6:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">", "rightExpression": { "hexValue": "30", "id": 5014, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "8632:1:8", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "8623:10:8", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 5055, "nodeType": "WhileStatement", "src": "8617:261:8" }, { "expression": { "arguments": [ { "id": 5057, "name": "x1", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4939, "src": "8909:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 5058, "name": "y1", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4941, "src": "8913:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 5059, "name": "z1", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4983, "src": "8917:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 5056, "name": "toAffinePoint", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 4143, "src": "8895:13:8", "typeDescriptions": { "typeIdentifier": "t_function_internal_pure$_t_uint256_$_t_uint256_$_t_uint256_$returns$_t_uint256_$_t_uint256_$", "typeString": "function (uint256,uint256,uint256) pure returns (uint256,uint256)" } }, "id": 5060, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "names": [], "nodeType": "FunctionCall", "src": "8895:25:8", "tryCall": false, "typeDescriptions": { "typeIdentifier": 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"uint256" } }, "visibility": "internal" }, { "constant": false, "id": 4934, "mutability": "mutable", "name": "y0", "nodeType": "VariableDeclaration", "scope": 5063, "src": "8089:7:8", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 4933, "name": "uint", "nodeType": "ElementaryTypeName", "src": "8089:4:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 4936, "mutability": "mutable", "name": "scalar", "nodeType": "VariableDeclaration", "scope": 5063, "src": "8098:11:8", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 4935, "name": "uint", "nodeType": "ElementaryTypeName", "src": "8098:4:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "8079:31:8" }, "returnParameters": { "id": 4942, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 4939, "mutability": "mutable", "name": "x1", "nodeType": "VariableDeclaration", "scope": 5063, "src": "8140:7:8", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 4938, "name": "uint", "nodeType": "ElementaryTypeName", "src": "8140:4:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 4941, "mutability": "mutable", "name": "y1", "nodeType": "VariableDeclaration", "scope": 5063, "src": "8149:7:8", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 4940, "name": "uint", "nodeType": "ElementaryTypeName", "src": "8149:4:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "8139:18:8" }, "scope": 5243, "src": "8056:871:8", "stateMutability": "pure", "virtual": false, "visibility": "public" }, { "body": { "id": 5079, "nodeType": "Block", "src": "9104:54:8", "statements": [ { "expression": { "arguments": [ { "id": 5074, "name": "gx", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3897, "src": "9136:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 5075, "name": "gy", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3900, "src": "9140:2:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "id": 5076, "name": "scalar", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 5066, "src": "9144:6:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": 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{ "id": 5064, "nodeType": "StructuredDocumentation", "src": "8933:73:8", "text": " @dev Multiply the curve's generator point by a scalar." }, "functionSelector": "0afb4ddc", "id": 5080, "implemented": true, "kind": "function", "modifiers": [], "name": "multipleGeneratorByScalar", "nodeType": "FunctionDefinition", "parameters": { "id": 5067, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 5066, "mutability": "mutable", "name": "scalar", "nodeType": "VariableDeclaration", "scope": 5080, "src": "9046:11:8", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 5065, "name": "uint", "nodeType": "ElementaryTypeName", "src": "9046:4:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "9045:13:8" }, "returnParameters": { "id": 5072, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 5069, "mutability": "mutable", "name": "", "nodeType": "VariableDeclaration", "scope": 5080, "src": "9088:4:8", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 5068, "name": "uint", "nodeType": "ElementaryTypeName", "src": "9088:4:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 5071, "mutability": "mutable", "name": "", "nodeType": "VariableDeclaration", "scope": 5080, "src": "9094:4:8", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 5070, "name": "uint", "nodeType": "ElementaryTypeName", "src": "9094:4:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "9087:12:8" }, "scope": 5243, "src": "9011:147:8", "stateMutability": "pure", "virtual": false, "visibility": "public" }, { "body": { "id": 5241, "nodeType": "Block", "src": "9372:787:8", "statements": [ { "condition": { "commonType": { "typeIdentifier": "t_bool", "typeString": "bool" }, "id": 5112, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_bool", "typeString": "bool" }, "id": 5106, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 5100, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "baseExpression": { "id": 5096, "name": "rs", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 5087, "src": "9466:2:8", "typeDescriptions": { "typeIdentifier": "t_array$_t_uint256_$2_memory_ptr", "typeString": "uint256[2] memory" } }, "id": 5098, "indexExpression": { "hexValue": "30", "id": 5097, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "9469:1:8", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "isConstant": false, "isLValue": true, "isPure": false, "lValueRequested": false, "nodeType": "IndexAccess", "src": "9466:5:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "==", "rightExpression": { "hexValue": "30", "id": 5099, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "9475:1:8", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "9466:10:8", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "nodeType": "BinaryOperation", "operator": "||", "rightExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 5105, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "baseExpression": { "id": 5101, "name": "rs", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 5087, "src": "9480:2:8", "typeDescriptions": { "typeIdentifier": "t_array$_t_uint256_$2_memory_ptr", "typeString": "uint256[2] memory" } }, "id": 5103, "indexExpression": { "hexValue": "30", "id": 5102, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "9483:1:8", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "isConstant": false, "isLValue": true, "isPure": false, "lValueRequested": false, "nodeType": "IndexAccess", "src": "9480:5:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": ">=", "rightExpression": { "id": 5104, "name": "n", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 3906, "src": "9489:1:8", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "9480:10:8", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "src": "9466:24:8", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "nodeType": "BinaryOperation", "operator": "||", "rightExpression": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 5111, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "baseExpression": { "id": 5107, "name": "rs", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 5087, "src": "9494:2:8", "typeDescriptions": { "typeIdentifier": "t_array$_t_uint256_$2_memory_ptr", 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"details": "Add two points in affine coordinates and return projective point." }, "addProj(uint256,uint256,uint256,uint256,uint256,uint256)": { "details": "Add two elliptic curve points in projective coordinates. See https://www.nayuki.io/page/elliptic-curve-point-addition-in-projective-coordinates" }, "isOnCurve(uint256,uint256)": { "details": "Check if a point in affine coordinates is on the curve." }, "isZeroCurve(uint256,uint256)": { "details": "Check if the curve is the zero curve." }, "multipleGeneratorByScalar(uint256)": { "details": "Multiply the curve's generator point by a scalar." }, "multiplyPowerBase2(uint256,uint256,uint256)": { "details": "Multiply an elliptic curve point by a 2 power base (i.e., (2^exp)*P))." }, "multiplyScalar(uint256,uint256,uint256)": { "details": "Multiply an elliptic curve point by a scalar." }, "toAffinePoint(uint256,uint256,uint256)": { "details": "Transform from projective to affine coordinates." }, "toProjectivePoint(uint256,uint256)": { "details": "Transform affine coordinates into projective coordinates." }, "twice(uint256,uint256)": { "details": "Double an elliptic curve point in affine coordinates." }, "twiceProj(uint256,uint256,uint256)": { "details": "Double an elliptic curve point in projective coordinates. See https://www.nayuki.io/page/elliptic-curve-point-addition-in-projective-coordinates" }, "validateSignature(bytes32,uint256[2],uint256[2])": { "details": "Validate combination of message, signature, and public key." }, "zeroAffine()": { "details": "Return the zero curve in affine coordinates." }, "zeroProj()": { "details": "Return the zero curve in projective coordinates." } }, "title": "EllipticCurve", "version": 1 }, "userdoc": { "kind": "user", "methods": {}, "notice": "Implements elliptic curve math; Parametrized for SECP256R1. Includes components of code by Andreas Olofsson, Alexander Vlasov (https://github.com/BANKEX/CurveArithmetics), and Avi Asayag (https://github.com/orbs-network/elliptic-curve-solidity) Source: https://github.com/tdrerup/elliptic-curve-solidity", "version": 1 } }