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"type": "uint256" }, { "name": "z0", "type": "uint256" } ], "name": "twiceProj", "outputs": [ { "name": "x1", "type": "uint256" }, { "name": "y1", "type": "uint256" }, { "name": "z1", "type": "uint256" } ], "payable": false, "stateMutability": "pure", "type": "function" }, { "constant": true, "inputs": [ { "name": "x0", "type": "uint256" }, { "name": "y0", "type": "uint256" }, { "name": "z0", "type": "uint256" }, { "name": "x1", "type": "uint256" }, { "name": "y1", "type": "uint256" }, { "name": "z1", "type": "uint256" } ], "name": "addProj", "outputs": [ { "name": "x2", "type": "uint256" }, { "name": "y2", "type": "uint256" }, { "name": "z2", "type": "uint256" } ], "payable": false, "stateMutability": "pure", "type": "function" }, { "constant": true, "inputs": [ { "name": "x0", "type": "uint256" }, { "name": "y0", "type": "uint256" }, { "name": "x1", "type": "uint256" }, { "name": "y1", "type": "uint256" } ], "name": "add", "outputs": [ { "name": "", "type": "uint256" }, { "name": "", 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"source": "pragma solidity ^0.5.0;\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 * @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": "/Users/tilmandrerup/Desktop/airtime/github/elliptic-curve-solidity/contracts/curves/EllipticCurve.sol", "ast": { "absolutePath": "/Users/tilmandrerup/Desktop/airtime/github/elliptic-curve-solidity/contracts/curves/EllipticCurve.sol", "exportedSymbols": { "EllipticCurve": [ 1383 ] }, "id": 1384, "nodeType": "SourceUnit", "nodes": [ { "id": 50, "literals": [ "solidity", "^", "0.5", ".0" ], "nodeType": "PragmaDirective", "src": "0:23:1" }, { "baseContracts": [], "contractDependencies": [], "contractKind": "contract", "documentation": "@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 (https://github.com/orbs-network/elliptic-curve-solidity)\n * @dev NOTE: To disambiguate 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"typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 930, "name": "addmod", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 1442, "src": "6793:6:1", "typeDescriptions": { "typeIdentifier": "t_function_addmod_pure$_t_uint256_$_t_uint256_$_t_uint256_$returns$_t_uint256_$", "typeString": "function (uint256,uint256,uint256) pure returns (uint256)" } }, "id": 936, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "names": [], "nodeType": "FunctionCall", "src": "6793:18:1", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "6788:23:1", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "id": 938, "nodeType": "ExpressionStatement", "src": "6788:23:1" }, { "expression": { "argumentTypes": null, "id": 945, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "argumentTypes": null, "id": 939, "name": "z2", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 792, "src": "6822:2:1", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "Assignment", "operator": "=", "rightHandSide": { "argumentTypes": null, "arguments": [ { "argumentTypes": null, "id": 941, "name": "u3", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 801, "src": "6834:2:1", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "argumentTypes": null, "id": 942, "name": "v", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 777, "src": "6838:1:1", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "argumentTypes": null, "id": 943, "name": "p", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 65, "src": "6841:1:1", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "expression": { "argumentTypes": [ { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" }, { "typeIdentifier": "t_uint256", "typeString": "uint256" } ], "id": 940, "name": "mulmod", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 1455, "src": "6827:6:1", "typeDescriptions": { "typeIdentifier": "t_function_mulmod_pure$_t_uint256_$_t_uint256_$_t_uint256_$returns$_t_uint256_$", "typeString": "function (uint256,uint256,uint256) pure returns (uint256)" } }, "id": 944, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "names": [], "nodeType": "FunctionCall", "src": "6827:16:1", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "src": "6822:21:1", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": 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"typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 787, "name": "uint", "nodeType": "ElementaryTypeName", "src": "6222:4:1", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "value": null, "visibility": "internal" }, { "constant": false, "id": 790, "name": "y2", "nodeType": "VariableDeclaration", "scope": 948, "src": "6231:7:1", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 789, "name": "uint", "nodeType": "ElementaryTypeName", "src": "6231:4:1", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "value": null, "visibility": "internal" }, { "constant": false, "id": 792, "name": "z2", "nodeType": "VariableDeclaration", "scope": 948, "src": "6240:7:1", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": 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"nodeType": "VariableDeclarationStatement", "src": "7041:7:1" }, { "expression": { "argumentTypes": null, "id": 978, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftHandSide": { "argumentTypes": null, "components": [ { "argumentTypes": null, "id": 966, "name": "x0", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 950, "src": "7060:2:1", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "argumentTypes": null, "id": 967, "name": "y0", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 952, "src": "7064:2:1", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, { "argumentTypes": null, "id": 968, "name": "z0", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 964, "src": "7068:2:1", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } } ], "id": 969, "isConstant": 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} ], "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": 970, "name": "addProj", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 775, "src": "7074:7:1", "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": 977, "isConstant": false, "isLValue": false, "isPure": false, "kind": "functionCall", "lValueRequested": false, "names": [], 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"addAndReturnProjectivePoint(uint256,uint256,uint256,uint256)": { "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" }, "userdoc": { "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)" } }