{ "contractName": "Secp256k1", "abi": [], "metadata": "{\"compiler\":{\"version\":\"0.8.30+commit.73712a01\"},\"language\":\"Solidity\",\"output\":{\"abi\":[],\"devdoc\":{\"author\":\"cyphered.eth\",\"details\":\"Library providing arithmetic operations over signed `secpk256k1` signed message due to recover the signer public key EC point in `Solidity`.\",\"kind\":\"dev\",\"methods\":{},\"title\":\"Secp256k1 public key recovery Library\",\"version\":1},\"userdoc\":{\"kind\":\"user\",\"methods\":{},\"version\":1}},\"settings\":{\"compilationTarget\":{\"project:/contracts/libs/Secp256k1.sol\":\"Secp256k1\"},\"evmVersion\":\"prague\",\"libraries\":{},\"metadata\":{\"bytecodeHash\":\"ipfs\"},\"optimizer\":{\"enabled\":true,\"runs\":200},\"remappings\":[]},\"sources\":{\"project:/contracts/libs/Secp256k1.sol\":{\"keccak256\":\"0xbe686002da5004ff39dd70709f3820eba2afe9323ae9cb894009c161e4b1a666\",\"license\":\"MIT\",\"urls\":[\"bzz-raw://18fab91775216de0707cea9ad285b10be09127461a13432fea358bf9cb2a0c2e\",\"dweb:/ipfs/QmeRUGsgstnM4hxM9hpkBf3L6cE5btirEaowcMxmuw3utj\"]}},\"version\":1}", "bytecode": "0x60556032600b8282823980515f1a607314602657634e487b7160e01b5f525f60045260245ffd5b305f52607381538281f3fe730000000000000000000000000000000000000000301460806040525f5ffdfea2646970667358221220a7da7ff7eee65caa710f4e2a338a3e8acd400d3108d33ebb92ad1e20ed77c9dc64736f6c634300081e0033", "deployedBytecode": "0x730000000000000000000000000000000000000000301460806040525f5ffdfea2646970667358221220a7da7ff7eee65caa710f4e2a338a3e8acd400d3108d33ebb92ad1e20ed77c9dc64736f6c634300081e0033", "immutableReferences": {}, "generatedSources": [], "deployedGeneratedSources": [], "sourceMap": "299:10679:112:-:0;;;;;;;;;;;;;;;-1:-1:-1;;;299:10679:112;;;;;;;;;;;;;;;;;", "deployedSourceMap": "299:10679:112:-:0;;;;;;;;", "source": "// SPDX-License-Identifier: MIT\r\n\r\npragma solidity >= 0.8.17;\r\n\r\n/**\r\n * @title Secp256k1 public key recovery Library\r\n * @dev Library providing arithmetic operations over signed `secpk256k1` signed message due to recover the signer public key EC point in `Solidity`.\r\n * @author cyphered.eth\r\n */\r\nlibrary Secp256k1 {\r\n // Elliptic curve Constants\r\n uint256 private constant U255_MAX_PLUS_1 =\r\n 57896044618658097711785492504343953926634992332820282019728792003956564819968;\r\n\r\n // Curve Constants\r\n uint256 private constant A = 0;\r\n uint256 private constant B = 7;\r\n uint256 private constant GX = 0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798;\r\n uint256 private constant GY = 0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8;\r\n uint256 private constant P = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F;\r\n uint256 private constant N = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141;\r\n\r\n /// @dev recovers signer public key point value.\r\n /// @param digest hashed message\r\n /// @param v recovery\r\n /// @param r first 32 bytes of signature\r\n /// @param v last 32 bytes of signature\r\n /// @return (x, y) EC point\r\n function recover(\r\n uint256 digest,\r\n uint8 v,\r\n uint256 r,\r\n uint256 s\r\n ) internal pure returns (uint256, uint256) {\r\n uint256 x = addmod(r, P * (v >> 1), P);\r\n if (x > P || s > N || r > N || s == 0 || r == 0 || v > 1) {\r\n return (0, 0);\r\n }\r\n uint256 rInv = invMod(r, N);\r\n\r\n uint256 y2 = addmod(mulmod(x, mulmod(x, x, P), P), addmod(mulmod(x, A, P), B, P), P);\r\n y2 = expMod(y2, (P + 1) / 4);\r\n uint256 y = ((y2 + v + 2) & 1 == 0) ? y2 : P - y2;\r\n\r\n (uint256 qx, uint256 qy, uint256 qz) = jacMul(mulmod(rInv, N - digest, N), GX, GY, 1);\r\n (uint256 qx2, uint256 qy2, uint256 qz2) = jacMul(mulmod(rInv, s, N), x, y, 1);\r\n (uint256 qx3, uint256 qy3) = ecAdd(qx, qy, qz, qx2, qy2, qz2);\r\n\r\n return (qx3, qy3);\r\n }\r\n\r\n /// @dev Modular exponentiation, b^e % P.\r\n /// Source: https://github.com/witnet/elliptic-curve-solidity/blob/master/contracts/EllipticCurve.sol\r\n /// Source: https://github.com/androlo/standard-contracts/blob/master/contracts/src/crypto/ECCMath.sol\r\n /// @param _base base\r\n /// @param _exp exponent\r\n /// @return r such that r = b**e (mod P)\r\n function expMod(uint256 _base, uint256 _exp) internal pure returns (uint256) {\r\n if (_base == 0) return 0;\r\n if (_exp == 0) return 1;\r\n\r\n uint256 r = 1;\r\n uint256 bit = U255_MAX_PLUS_1;\r\n assembly {\r\n for {\r\n\r\n } gt(bit, 0) {\r\n\r\n } {\r\n r := mulmod(mulmod(r, r, P), exp(_base, iszero(iszero(and(_exp, bit)))), P)\r\n r := mulmod(mulmod(r, r, P), exp(_base, iszero(iszero(and(_exp, div(bit, 2))))), P)\r\n r := mulmod(mulmod(r, r, P), exp(_base, iszero(iszero(and(_exp, div(bit, 4))))), P)\r\n r := mulmod(mulmod(r, r, P), exp(_base, iszero(iszero(and(_exp, div(bit, 8))))), P)\r\n bit := div(bit, 16)\r\n }\r\n }\r\n\r\n return r;\r\n }\r\n\r\n /// @dev Adds two points (x1, y1, z1) and (x2 y2, z2).\r\n /// Source: https://github.com/witnet/elliptic-curve-solidity/blob/master/contracts/EllipticCurve.sol\r\n /// @param _x1 coordinate x of P1\r\n /// @param _y1 coordinate y of P1\r\n /// @param _z1 coordinate z of P1\r\n /// @param _x2 coordinate x of square\r\n /// @param _y2 coordinate y of square\r\n /// @param _z2 coordinate z of square\r\n /// @return (qx, qy, qz) P1+square in Jacobian\r\n function jacAdd(\r\n uint256 _x1,\r\n uint256 _y1,\r\n uint256 _z1,\r\n uint256 _x2,\r\n uint256 _y2,\r\n uint256 _z2\r\n )\r\n internal\r\n pure\r\n returns (\r\n uint256,\r\n uint256,\r\n uint256\r\n )\r\n {\r\n if (_x1 == 0 && _y1 == 0) return (_x2, _y2, _z2);\r\n if (_x2 == 0 && _y2 == 0) return (_x1, _y1, _z1);\r\n\r\n // We follow the equations described in https://pdfs.semanticscholar.org/5c64/29952e08025a9649c2b0ba32518e9a7fb5c2.pdf Section 5\r\n uint256[4] memory zs; // z1^2, z1^3, z2^2, z2^3\r\n zs[0] = mulmod(_z1, _z1, P);\r\n zs[1] = mulmod(_z1, zs[0], P);\r\n zs[2] = mulmod(_z2, _z2, P);\r\n zs[3] = mulmod(_z2, zs[2], P);\r\n\r\n // u1, s1, u2, s2\r\n zs = [mulmod(_x1, zs[2], P), mulmod(_y1, zs[3], P), mulmod(_x2, zs[0], P), mulmod(_y2, zs[1], P)];\r\n\r\n // In case of zs[0] == zs[2] && zs[1] == zs[3], double function should be used\r\n require(zs[0] != zs[2] || zs[1] != zs[3], 'Use jacDouble function instead');\r\n\r\n uint256[4] memory hr;\r\n //h\r\n hr[0] = addmod(zs[2], P - zs[0], P);\r\n //r\r\n hr[1] = addmod(zs[3], P - zs[1], P);\r\n //h^2\r\n hr[2] = mulmod(hr[0], hr[0], P);\r\n // h^3\r\n hr[3] = mulmod(hr[2], hr[0], P);\r\n // qx = -h^3 -2u1h^2+r^2\r\n uint256 qx = addmod(mulmod(hr[1], hr[1], P), P - hr[3], P);\r\n qx = addmod(qx, P - mulmod(2, mulmod(zs[0], hr[2], P), P), P);\r\n // qy = -s1*z1*h^3+r(u1*h^2 -x^3)\r\n uint256 qy = mulmod(hr[1], addmod(mulmod(zs[0], hr[2], P), P - qx, P), P);\r\n qy = addmod(qy, P - mulmod(zs[1], hr[3], P), P);\r\n // qz = h*z1*z2\r\n uint256 qz = mulmod(hr[0], mulmod(_z1, _z2, P), P);\r\n return (qx, qy, qz);\r\n }\r\n\r\n /// @dev Multiply point (x, y, z) times d.\r\n /// Source: https://github.com/witnet/elliptic-curve-solidity/blob/master/contracts/EllipticCurve.sol\r\n /// @param _d scalar to multiply\r\n /// @param _x coordinate x of P1\r\n /// @param _y coordinate y of P1\r\n /// @param _z coordinate z of P1\r\n /// @return (qx, qy, qz) d*P1 in Jacobian\r\n function jacMul(\r\n uint256 _d,\r\n uint256 _x,\r\n uint256 _y,\r\n uint256 _z\r\n )\r\n internal\r\n pure\r\n returns (\r\n uint256,\r\n uint256,\r\n uint256\r\n )\r\n {\r\n // Early return in case that `_d == 0`\r\n if (_d == 0) {\r\n return (_x, _y, _z);\r\n }\r\n\r\n uint256 remaining = _d;\r\n uint256 qx = 0;\r\n uint256 qy = 0;\r\n uint256 qz = 1;\r\n\r\n // Double and add algorithm\r\n while (remaining != 0) {\r\n if ((remaining & 1) != 0) {\r\n (qx, qy, qz) = jacAdd(qx, qy, qz, _x, _y, _z);\r\n }\r\n remaining = remaining / 2;\r\n (_x, _y, _z) = jacDouble(_x, _y, _z);\r\n }\r\n return (qx, qy, qz);\r\n }\r\n\r\n /// @dev Doubles a points (x, y, z).\r\n /// Source: https://github.com/witnet/elliptic-curve-solidity/blob/master/contracts/EllipticCurve.sol\r\n /// @param _x coordinate x of P1\r\n /// @param _y coordinate y of P1\r\n /// @param _z coordinate z of P1\r\n /// @return (qx, qy, qz) 2P in Jacobian\r\n function jacDouble(\r\n uint256 _x,\r\n uint256 _y,\r\n uint256 _z\r\n )\r\n internal\r\n pure\r\n returns (\r\n uint256,\r\n uint256,\r\n uint256\r\n )\r\n {\r\n if (_z == 0) return (_x, _y, _z);\r\n\r\n // We follow the equations described in https://pdfs.semanticscholar.org/5c64/29952e08025a9649c2b0ba32518e9a7fb5c2.pdf Section 5\r\n // Note: there is a bug in the paper regarding the m parameter, M=3*(x1^2)+a*(z1^4)\r\n // x, y, z at this point represent the squares of _x, _y, _z\r\n uint256 x = mulmod(_x, _x, P); //x1^2\r\n uint256 y = mulmod(_y, _y, P); //y1^2\r\n uint256 z = mulmod(_z, _z, P); //z1^2\r\n\r\n // s\r\n uint256 s = mulmod(4, mulmod(_x, y, P), P);\r\n // m\r\n uint256 m = addmod(mulmod(3, x, P), mulmod(A, mulmod(z, z, P), P), P);\r\n\r\n // x, y, z at this point will be reassigned and rather represent qx, qy, qz from the paper\r\n // This allows to reduce the gas cost and stack footprint of the algorithm\r\n // qx\r\n x = addmod(mulmod(m, m, P), P - addmod(s, s, P), P);\r\n // qy = -8*y1^4 + M(S-T)\r\n y = addmod(mulmod(m, addmod(s, P - x, P), P), P - mulmod(8, mulmod(y, y, P), P), P);\r\n // qz = 2*y1*z1\r\n z = mulmod(2, mulmod(_y, _z, P), P);\r\n\r\n return (x, y, z);\r\n }\r\n\r\n /// @dev Add two points (x1, y1) and (x2, y2) in affine coordinates.\r\n /// Source: https://github.com/witnet/elliptic-curve-solidity/blob/master/contracts/EllipticCurve.sol\r\n /// @param _x1 coordinate x of P1\r\n /// @param _y1 coordinate y of P1\r\n /// @param _x2 coordinate x of P2\r\n /// @param _y2 coordinate y of P2\r\n /// @return (qx, qy) = P1+P2 in affine coordinates\r\n function ecAdd(\r\n uint256 _x1,\r\n uint256 _y1,\r\n uint256 _z1,\r\n uint256 _x2,\r\n uint256 _y2,\r\n uint256 _z2\r\n ) internal pure returns (uint256, uint256) {\r\n uint256 x = 0;\r\n uint256 y = 0;\r\n uint256 z = 0;\r\n\r\n // Double if x1==x2 else add\r\n if (_x1 == _x2) {\r\n // y1 = -y2 mod p\r\n if (addmod(_y1, _y2, P) == 0) {\r\n return (0, 0);\r\n } else {\r\n // P1 = P2\r\n (x, y, z) = jacDouble(_x1, _y1, _z1);\r\n }\r\n } else {\r\n (x, y, z) = jacAdd(_x1, _y1, _z1, _x2, _y2, _z2);\r\n }\r\n // Get back to affine\r\n return toAffine(x, y, z);\r\n }\r\n\r\n /// @dev Converts a point (x, y, z) expressed in Jacobian coordinates to affine coordinates (x', y', 1).\r\n /// Source: https://github.com/witnet/elliptic-curve-solidity/blob/master/contracts/EllipticCurve.sol\r\n /// @param _x coordinate x\r\n /// @param _y coordinate y\r\n /// @param _z coordinate z\r\n /// @return (x', y') affine coordinates\r\n function toAffine(\r\n uint256 _x,\r\n uint256 _y,\r\n uint256 _z\r\n ) internal pure returns (uint256, uint256) {\r\n uint256 zInv = invMod(_z, P);\r\n uint256 zInv2 = mulmod(zInv, zInv, P);\r\n uint256 x2 = mulmod(_x, zInv2, P);\r\n uint256 y2 = mulmod(_y, mulmod(zInv, zInv2, P), P);\r\n\r\n return (x2, y2);\r\n }\r\n\r\n /// @dev Modular euclidean inverse of a number (mod p).\r\n /// Source: https://github.com/witnet/elliptic-curve-solidity/blob/master/contracts/EllipticCurve.sol\r\n /// @param _x The number\r\n /// @param _pp The modulus\r\n /// @return q such that x*q = 1 (mod _pp)\r\n function invMod(uint256 _x, uint256 _pp) internal pure returns (uint256) {\r\n require(_x != 0 && _x != _pp && _pp != 0, 'Invalid number');\r\n uint256 q = 0;\r\n uint256 newT = 1;\r\n uint256 r = _pp;\r\n uint256 t;\r\n while (_x != 0) {\r\n t = r / _x;\r\n (q, newT) = (newT, addmod(q, (_pp - mulmod(t, newT, _pp)), _pp));\r\n (r, _x) = (_x, r - t * _x);\r\n }\r\n\r\n return q;\r\n }\r\n}", "sourcePath": "C:\\Users\\guill\\github\\guidiaz\\witnet-solidity-bridge\\contracts\\libs\\Secp256k1.sol", "ast": { "absolutePath": "project:/contracts/libs/Secp256k1.sol", "exportedSymbols": { "Secp256k1": [ 32535 ] }, "id": 32536, "license": "MIT", "nodeType": "SourceUnit", "nodes": [ { "id": 31521, "literals": [ "solidity", ">=", "0.8", ".17" ], "nodeType": "PragmaDirective", "src": "35:26:112" }, { "abstract": false, "baseContracts": [], "canonicalName": "Secp256k1", "contractDependencies": [], "contractKind": "library", "documentation": { "id": 31522, "nodeType": "StructuredDocumentation", "src": "65:232:112", "text": " @title Secp256k1 public key recovery Library\n @dev Library providing arithmetic operations over signed `secpk256k1` signed message due to recover the signer public key EC point in `Solidity`.\n @author cyphered.eth" }, "fullyImplemented": true, "id": 32535, "linearizedBaseContracts": [ 32535 ], "name": "Secp256k1", "nameLocation": "307:9:112", "nodeType": "ContractDefinition", "nodes": [ { "constant": true, "id": 31525, "mutability": "constant", "name": "U255_MAX_PLUS_1", "nameLocation": "382:15:112", "nodeType": "VariableDeclaration", "scope": 32535, "src": "357:129:112", "stateVariable": true, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 31523, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "357:7:112", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "value": { "hexValue": 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https://github.com/witnet/elliptic-curve-solidity/blob/master/contracts/EllipticCurve.sol\n @param _x coordinate x\n @param _y coordinate y\n @param _z coordinate z\n @return (x', y') affine coordinates" }, "id": 32449, "implemented": true, "kind": "function", "modifiers": [], "name": "toAffine", "nameLocation": "9890:8:112", "nodeType": "FunctionDefinition", "parameters": { "id": 32403, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 32398, "mutability": "mutable", "name": "_x", "nameLocation": "9917:2:112", "nodeType": "VariableDeclaration", "scope": 32449, "src": "9909:10:112", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 32397, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "9909:7:112", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 32400, 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"uint256" } } ], "id": 32526, "isConstant": false, "isInlineArray": false, "isLValue": false, "isPure": false, "lValueRequested": false, "nodeType": "TupleExpression", "src": "10919:16:112", "typeDescriptions": { "typeIdentifier": "t_tuple$_t_uint256_$_t_uint256_$", "typeString": "tuple(uint256,uint256)" } }, "src": "10909:26:112", "typeDescriptions": { "typeIdentifier": "t_tuple$__$", "typeString": "tuple()" } }, "id": 32528, "nodeType": "ExpressionStatement", "src": "10909:26:112" } ] }, "condition": { "commonType": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "id": 32491, "isConstant": false, "isLValue": false, "isPure": false, "lValueRequested": false, "leftExpression": { "id": 32489, "name": "_x", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 32452, "src": "10781:2:112", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "nodeType": "BinaryOperation", "operator": "!=", "rightExpression": { "hexValue": "30", "id": 32490, "isConstant": false, "isLValue": false, "isPure": true, "kind": "number", "lValueRequested": false, "nodeType": "Literal", "src": "10787:1:112", "typeDescriptions": { "typeIdentifier": "t_rational_0_by_1", "typeString": "int_const 0" }, "value": "0" }, "src": "10781:7:112", "typeDescriptions": { "typeIdentifier": "t_bool", "typeString": "bool" } }, "id": 32530, "nodeType": "WhileStatement", "src": "10774:173:112" }, { "expression": { "id": 32531, "name": "q", "nodeType": "Identifier", "overloadedDeclarations": [], "referencedDeclaration": 32475, "src": "10966:1:112", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "functionReturnParameters": 32458, "id": 32532, "nodeType": "Return", "src": "10959:8:112" } ] }, "documentation": { "id": 32450, "nodeType": "StructuredDocumentation", "src": "10246:271:112", "text": "@dev Modular euclidean inverse of a number (mod p).\n Source: https://github.com/witnet/elliptic-curve-solidity/blob/master/contracts/EllipticCurve.sol\n @param _x The number\n @param _pp The modulus\n @return q such that x*q = 1 (mod _pp)" }, "id": 32534, "implemented": true, "kind": "function", "modifiers": [], "name": "invMod", "nameLocation": "10532:6:112", "nodeType": "FunctionDefinition", "parameters": { "id": 32455, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 32452, "mutability": "mutable", "name": "_x", "nameLocation": "10547:2:112", "nodeType": "VariableDeclaration", "scope": 32534, "src": "10539:10:112", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 32451, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "10539:7:112", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" }, { "constant": false, "id": 32454, "mutability": "mutable", "name": "_pp", "nameLocation": "10559:3:112", "nodeType": "VariableDeclaration", "scope": 32534, "src": "10551:11:112", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 32453, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "10551:7:112", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "10538:25:112" }, "returnParameters": { "id": 32458, "nodeType": "ParameterList", "parameters": [ { "constant": false, "id": 32457, "mutability": "mutable", "name": "", "nameLocation": "-1:-1:-1", "nodeType": "VariableDeclaration", "scope": 32534, "src": "10587:7:112", "stateVariable": false, "storageLocation": "default", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" }, "typeName": { "id": 32456, "name": "uint256", "nodeType": "ElementaryTypeName", "src": "10587:7:112", "typeDescriptions": { "typeIdentifier": "t_uint256", "typeString": "uint256" } }, "visibility": "internal" } ], "src": "10586:9:112" }, "scope": 32535, "src": "10523:452:112", "stateMutability": "pure", "virtual": false, "visibility": "internal" } ], "scope": 32536, "src": "299:10679:112", "usedErrors": [], "usedEvents": [] } ], "src": "35:10943:112" }, "compiler": { "name": "solc", "version": "0.8.30+commit.73712a01.Emscripten.clang" }, "networks": {}, "schemaVersion": "3.4.16", "updatedAt": "2025-10-15T14:34:45.952Z", "devdoc": { "author": "cyphered.eth", "details": "Library providing arithmetic operations over signed `secpk256k1` signed message due to recover the signer public key EC point in `Solidity`.", "kind": "dev", "methods": {}, "title": "Secp256k1 public key recovery Library", "version": 1 }, "userdoc": { "kind": "user", "methods": {}, "version": 1 } }