j-bitcoin
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Comprehensive JavaScript/TypeScript Bitcoin (BTC) wallet library with custodial and non-custodial support, hierarchical deterministic keys, threshold signatures, and advanced cryptographic features
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<title>src/core/crypto/signatures/threshold/polynomial.js - J-Bitcoin - Bitcoin Wallet Library</title>
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<h2><a href="index.html">Home</a></h2><h2><a href="https://github.com/yfbsei/J-Bitcoin" target="_blank" class="menu-item home-link" id="home-link" >š Home</a></h2><h2><a href="https://github.com/yfbsei/J-Bitcoin" target="_blank" class="menu-item github-link" id="github-link" >š GitHub</a></h2><h2><a href="https://www.npmjs.com/package/j-bitcoin" target="_blank" class="menu-item npm-link" id="npm-link" >š¦ NPM</a></h2><h2><a href="https://github.com/yfbsei/J-Bitcoin/tree/main/examples" target="_blank" class="menu-item examples-link" id="examples-link" >š§ Examples</a></h2><h2><a href="https://github.com/yfbsei/J-Bitcoin/blob/main/CHANGELOG.md" target="_blank" class="menu-item changelog-link" id="changelog-link" >š Changelog</a></h2><h3>Classes</h3><ul><li><a href="BIP143.html">BIP143</a><ul class='methods'><li data-type='method' style='display: none;'><a href="BIP143.html#.calculate">calculate</a></li><li data-type='method' style='display: none;'><a href="BIP143.html#.forP2WPKH">forP2WPKH</a></li><li data-type='method' style='display: none;'><a href="BIP143.html#.hashOutputs">hashOutputs</a></li><li data-type='method' style='display: none;'><a href="BIP143.html#.hashPrevouts">hashPrevouts</a></li><li data-type='method' style='display: none;'><a href="BIP143.html#.hashSequence">hashSequence</a></li></ul></li><li><a href="BIP322.html">BIP322</a><ul class='methods'><li data-type='method' style='display: none;'><a href="BIP322.html#.createToSign">createToSign</a></li><li data-type='method' style='display: none;'><a href="BIP322.html#.createToSpend">createToSpend</a></li><li data-type='method' style='display: none;'><a href="BIP322.html#.hashMessage">hashMessage</a></li><li data-type='method' style='display: none;'><a href="BIP322.html#.sign">sign</a></li><li data-type='method' style='display: none;'><a href="BIP322.html#.signLegacy">signLegacy</a></li><li data-type='method' style='display: none;'><a href="BIP322.html#.verify">verify</a></li><li data-type='method' style='display: none;'><a href="BIP322.html#.verifyLegacy">verifyLegacy</a></li></ul></li><li><a href="BIP322Error.html">BIP322Error</a></li><li><a href="BIP341.html">BIP341</a><ul class='methods'><li data-type='method' style='display: none;'><a href="BIP341.html#.calculate">calculate</a></li><li data-type='method' style='display: none;'><a href="BIP341.html#.forScriptPath">forScriptPath</a></li><li data-type='method' style='display: none;'><a href="BIP341.html#.shaAmounts">shaAmounts</a></li><li data-type='method' style='display: none;'><a href="BIP341.html#.shaOutputs">shaOutputs</a></li><li data-type='method' style='display: none;'><a href="BIP341.html#.shaPrevouts">shaPrevouts</a></li><li data-type='method' style='display: none;'><a href="BIP341.html#.shaScriptPubkeys">shaScriptPubkeys</a></li><li data-type='method' style='display: none;'><a href="BIP341.html#.shaSequences">shaSequences</a></li></ul></li><li><a href="BIP49.html">BIP49</a><ul class='methods'><li data-type='method' style='display: none;'><a href="BIP49.html#.createRedeemScript">createRedeemScript</a></li><li data-type='method' style='display: none;'><a href="BIP49.html#.createScriptPubKey">createScriptPubKey</a></li><li data-type='method' style='display: none;'><a href="BIP49.html#.getAccountPath">getAccountPath</a></li><li data-type='method' style='display: none;'><a href="BIP49.html#.getDerivationPath">getDerivationPath</a></li><li data-type='method' style='display: none;'><a href="BIP49.html#.toAddress">toAddress</a></li></ul></li><li><a href="CustodialWallet.html">CustodialWallet</a><ul class='methods'><li data-type='method' style='display: none;'><a href="CustodialWallet.html#canSign">canSign</a></li><li data-type='method' style='display: none;'><a href="CustodialWallet.html#clearCache">clearCache</a></li><li data-type='method' style='display: none;'><a href="CustodialWallet.html#createTransaction">createTransaction</a></li><li data-type='method' style='display: none;'><a href="CustodialWallet.html#deriveAddress">deriveAddress</a></li><li data-type='method' style='display: none;'><a href="CustodialWallet.html#destroy">destroy</a></li><li data-type='method' style='display: none;'><a href="CustodialWallet.html#exportWIF">exportWIF</a></li><li data-type='method' style='display: none;'><a href="CustodialWallet.html#getAddresses">getAddresses</a></li><li data-type='method' style='display: none;'><a href="CustodialWallet.html#getChangeAddress">getChangeAddress</a></li><li data-type='method' style='display: none;'><a href="CustodialWallet.html#getExtendedPrivateKey">getExtendedPrivateKey</a></li><li data-type='method' style='display: none;'><a href="CustodialWallet.html#getExtendedPublicKey">getExtendedPublicKey</a></li><li data-type='method' style='display: none;'><a href="CustodialWallet.html#getMnemonic">getMnemonic</a></li><li data-type='method' style='display: none;'><a href="CustodialWallet.html#getNetwork">getNetwork</a></li><li data-type='method' style='display: none;'><a href="CustodialWallet.html#getReceivingAddress">getReceivingAddress</a></li><li data-type='method' style='display: none;'><a href="CustodialWallet.html#signMessage">signMessage</a></li><li data-type='method' style='display: none;'><a href="CustodialWallet.html#signMessageBIP322">signMessageBIP322</a></li><li data-type='method' style='display: none;'><a href="CustodialWallet.html#signTransaction">signTransaction</a></li><li data-type='method' style='display: none;'><a href="CustodialWallet.html#toJSON">toJSON</a></li><li data-type='method' style='display: none;'><a href="CustodialWallet.html#verifyMessage">verifyMessage</a></li><li data-type='method' style='display: none;'><a href="CustodialWallet.html#.createNew">createNew</a></li><li data-type='method' style='display: none;'><a href="CustodialWallet.html#.fromExtendedKey">fromExtendedKey</a></li><li data-type='method' style='display: none;'><a href="CustodialWallet.html#.fromMnemonic">fromMnemonic</a></li><li data-type='method' style='display: none;'><a href="CustodialWallet.html#.fromSeed">fromSeed</a></li><li data-type='method' style='display: none;'><a href="CustodialWallet.html#.fromWIF">fromWIF</a></li></ul></li><li></li><li><a href="CustodialWalletError.html">CustodialWalletError</a></li><li></li><li><a href="DecodingError.html">DecodingError</a></li><li><a href="ECDSAError.html">ECDSAError</a></li><li></li><li><a href="EncodingError.html">EncodingError</a></li><li><a href="JVRSS.html">JVRSS</a><ul class='methods'><li data-type='method' style='display: none;'><a href="JVRSS.html#broadcastObfuscatedCoefficients">broadcastObfuscatedCoefficients</a></li><li data-type='method' style='display: none;'><a href="JVRSS.html#calculateSharedPublicKey">calculateSharedPublicKey</a></li><li data-type='method' style='display: none;'><a href="JVRSS.html#calculateShares">calculateShares</a></li><li data-type='method' style='display: none;'><a href="JVRSS.html#clear">clear</a></li><li data-type='method' style='display: none;'><a href="JVRSS.html#distributePolynomialPoints">distributePolynomialPoints</a></li><li data-type='method' style='display: none;'><a href="JVRSS.html#generatePolynomials">generatePolynomials</a></li><li data-type='method' style='display: none;'><a href="JVRSS.html#getParticipant">getParticipant</a></li><li data-type='method' style='display: none;'><a href="JVRSS.html#getSharesForInterpolation">getSharesForInterpolation</a></li><li data-type='method' style='display: none;'><a href="JVRSS.html#reconstructSecret">reconstructSecret</a></li><li data-type='method' style='display: none;'><a href="JVRSS.html#runProtocol">runProtocol</a></li><li data-type='method' style='display: none;'><a href="JVRSS.html#verifyAllShares">verifyAllShares</a></li></ul></li><li><a href="JVRSSError.html">JVRSSError</a></li><li><a href="LegacySighash.html">LegacySighash</a><ul class='methods'><li data-type='method' style='display: none;'><a href="LegacySighash.html#.calculate">calculate</a></li></ul></li><li><a href="MPCError.html">MPCError</a></li><li><a href="NonCustodialWallet.html">NonCustodialWallet</a><ul class='methods'><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#_exportShares">_exportShares</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#_reconstructPublicKey">_reconstructPublicKey</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#canSign">canSign</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#canSignHD">canSignHD</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#clear">clear</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#clearAddressCache">clearAddressCache</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#createTransaction">createTransaction</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#deriveAddress">deriveAddress</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#destroy">destroy</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#exportShares">exportShares</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#exportWIF">exportWIF</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#generateEphemeralKeys">generateEphemeralKeys</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#getAddress">getAddress</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#getAddressCount">getAddressCount</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#getAddresses">getAddresses</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#getChangeAddress">getChangeAddress</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#getExtendedPrivateKey">getExtendedPrivateKey</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#getExtendedPublicKey">getExtendedPublicKey</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#getMnemonic">getMnemonic</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#getNetwork">getNetwork</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#getPublicKey">getPublicKey</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#getReceivingAddress">getReceivingAddress</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#getShare">getShare</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#getShares">getShares</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#getThresholdConfig">getThresholdConfig</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#hasHD">hasHD</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#initialize">initialize</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#listAddresses">listAddresses</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#sign">sign</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#signMessage">signMessage</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#signMessageBIP322">signMessageBIP322</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#signMessageHD">signMessageHD</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#signTransaction">signTransaction</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#toJSON">toJSON</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#verify">verify</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#verifyMessageHD">verifyMessageHD</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#.createNew">createNew</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#.createNewHD">createNewHD</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#.fromExtendedKey">fromExtendedKey</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#.fromMnemonic">fromMnemonic</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#.fromSeed">fromSeed</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#.fromShares">fromShares</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#.fromWIF">fromWIF</a></li><li data-type='method' style='display: none;'><a href="NonCustodialWallet.html#.importShares">importShares</a></li></ul></li><li><a href="Participant.html">Participant</a><ul class='methods'><li data-type='method' style='display: none;'><a href="Participant.html#calculateKeyShare">calculateKeyShare</a></li><li data-type='method' style='display: none;'><a href="Participant.html#clear">clear</a></li><li data-type='method' style='display: none;'><a href="Participant.html#evaluateAt">evaluateAt</a></li><li data-type='method' style='display: none;'><a href="Participant.html#generatePolynomial">generatePolynomial</a></li><li data-type='method' style='display: none;'><a href="Participant.html#generateSignatureShare">generateSignatureShare</a></li><li data-type='method' style='display: none;'><a href="Participant.html#getBlindingShare">getBlindingShare</a></li><li data-type='method' style='display: none;'><a href="Participant.html#getKeyShare">getKeyShare</a></li><li data-type='method' style='display: none;'><a href="Participant.html#getKeySharePublicKey">getKeySharePublicKey</a></li><li data-type='method' style='display: none;'><a href="Participant.html#getNextEphemeralKey">getNextEphemeralKey</a></li><li data-type='method' style='display: none;'><a href="Participant.html#getObfuscatedCoefficients">getObfuscatedCoefficients</a></li><li data-type='method' style='display: none;'><a href="Participant.html#getPolynomialPointFor">getPolynomialPointFor</a></li><li data-type='method' style='display: none;'><a href="Participant.html#receivePolynomialPoint">receivePolynomialPoint</a></li><li data-type='method' style='display: none;'><a href="Participant.html#setBlindingShare">setBlindingShare</a></li><li data-type='method' style='display: none;'><a href="Participant.html#storeEphemeralKey">storeEphemeralKey</a></li><li data-type='method' style='display: none;'><a href="Participant.html#verifyPolynomialPoint">verifyPolynomialPoint</a></li></ul></li><li><a href="ParticipantError.html">ParticipantError</a></li><li><a href="ParticipantShare.html">ParticipantShare</a></li><li><a href="Polynomial.html">Polynomial</a><ul class='methods'><li data-type='method' style='display: none;'><a href="Polynomial.html#clear">clear</a></li><li data-type='method' style='display: none;'><a href="Polynomial.html#evaluate">evaluate</a></li><li data-type='method' style='display: none;'><a href="Polynomial.html#generateShares">generateShares</a></li><li data-type='method' style='display: none;'><a href="Polynomial.html#getCoefficients">getCoefficients</a></li><li data-type='method' style='display: none;'><a href="Polynomial.html#getSecret">getSecret</a></li><li data-type='method' style='display: none;'><a href="Polynomial.html#.interpolate">interpolate</a></li><li data-type='method' style='display: none;'><a href="Polynomial.html#.lagrangeCoefficient">lagrangeCoefficient</a></li><li data-type='method' style='display: none;'><a href="Polynomial.html#.reconstructSecret">reconstructSecret</a></li></ul></li><li><a href="PolynomialError.html">PolynomialError</a></li><li><a href="Schnorr.html">Schnorr</a><ul class='methods'><li data-type='method' style='display: none;'><a href="Schnorr.html#sign">sign</a></li></ul></li><li><a href="SchnorrError.html">SchnorrError</a></li><li></li><li><a href="ScriptBuilder.html">ScriptBuilder</a><ul class='methods'><li data-type='method' style='display: none;'><a href="ScriptBuilder.html#addOp">addOp</a></li><li data-type='method' style='display: none;'><a href="ScriptBuilder.html#build">build</a></li><li data-type='method' style='display: none;'><a href="ScriptBuilder.html#pushData">pushData</a></li><li data-type='method' style='display: none;'><a href="ScriptBuilder.html#pushNumber">pushNumber</a></li><li data-type='method' style='display: none;'><a href="ScriptBuilder.html#reset">reset</a></li><li data-type='method' style='display: none;'><a href="ScriptBuilder.html#.createCLTV">createCLTV</a></li><li data-type='method' style='display: none;'><a href="ScriptBuilder.html#.createCSV">createCSV</a></li><li data-type='method' style='display: none;'><a href="ScriptBuilder.html#.createMultisig">createMultisig</a></li><li data-type='method' style='display: none;'><a href="ScriptBuilder.html#.createOpReturn">createOpReturn</a></li><li data-type='method' style='display: none;'><a href="ScriptBuilder.html#.createP2PKH">createP2PKH</a></li><li data-type='method' style='display: none;'><a href="ScriptBuilder.html#.createP2PKHFromPubkey">createP2PKHFromPubkey</a></li><li data-type='method' style='display: none;'><a href="ScriptBuilder.html#.createP2PKHScriptSig">createP2PKHScriptSig</a></li><li data-type='method' style='display: none;'><a href="ScriptBuilder.html#.createP2SH">createP2SH</a></li><li data-type='method' style='display: none;'><a href="ScriptBuilder.html#.createP2SHScriptSig">createP2SHScriptSig</a></li><li data-type='method' style='display: none;'><a href="ScriptBuilder.html#.createP2TR">createP2TR</a></li><li data-type='method' style='display: none;'><a href="ScriptBuilder.html#.createP2WPKH">createP2WPKH</a></li><li data-type='method' style='display: none;'><a href="ScriptBuilder.html#.createP2WPKHFromPubkey">createP2WPKHFromPubkey</a></li><li data-type='method' style='display: none;'><a href="ScriptBuilder.html#.createP2WSH">createP2WSH</a></li><li data-type='method' style='display: none;'><a href="ScriptBuilder.html#.detectType">detectType</a></li><li data-type='method' style='display: none;'><a href="ScriptBuilder.html#.disassemble">disassemble</a></li><li data-type='method' style='display: none;'><a href="ScriptBuilder.html#.parse">parse</a></li></ul></li><li><a href="ScriptError.html">ScriptError</a></li><li><a href="SighashCalculator.html">SighashCalculator</a><ul class='methods'><li data-type='method' style='display: none;'><a href="SighashCalculator.html#.calculate">calculate</a></li></ul></li><li><a href="SighashError.html">SighashError</a></li><li><a href="TaggedHash.html">TaggedHash</a><ul class='methods'><li data-type='method' style='display: none;'><a href="TaggedHash.html#.create">create</a></li></ul></li><li><a href="ThresholdSignatureError.html">ThresholdSignatureError</a></li><li><a href="ThresholdSignatureScheme.html">ThresholdSignatureScheme</a><ul class='methods'><li data-type='method' style='display: none;'><a href="ThresholdSignatureScheme.html#clear">clear</a></li><li data-type='method' style='display: none;'><a href="ThresholdSignatureScheme.html#generateEphemeralKeys">generateEphemeralKeys</a></li><li data-type='method' style='display: none;'><a href="ThresholdSignatureScheme.html#generateSharedPrivateKey">generateSharedPrivateKey</a></li><li data-type='method' style='display: none;'><a href="ThresholdSignatureScheme.html#getConfig">getConfig</a></li><li data-type='method' style='display: none;'><a href="ThresholdSignatureScheme.html#getNextEphemeralKey">getNextEphemeralKey</a></li><li data-type='method' style='display: none;'><a href="ThresholdSignatureScheme.html#getPublicKey">getPublicKey</a></li><li data-type='method' style='display: none;'><a href="ThresholdSignatureScheme.html#sign">sign</a></li><li data-type='method' style='display: none;'><a href="ThresholdSignatureScheme.html#signMessage">signMessage</a></li><li data-type='method' style='display: none;'><a href="ThresholdSignatureScheme.html#verify">verify</a></li></ul></li><li><a href="TransactionBuilder.html">TransactionBuilder</a><ul class='methods'><li data-type='method' style='display: none;'><a href="TransactionBuilder.html#addInput">addInput</a></li><li data-type='method' style='display: none;'><a href="TransactionBuilder.html#addOpReturn">addOpReturn</a></li><li data-type='method' style='display: none;'><a href="TransactionBuilder.html#addOutput">addOutput</a></li><li data-type='method' style='display: none;'><a href="TransactionBuilder.html#addWitness">addWitness</a></li><li data-type='method' style='display: none;'><a href="TransactionBuilder.html#build">build</a></li><li data-type='method' style='display: none;'><a href="TransactionBuilder.html#calculateFee">calculateFee</a></li><li data-type='method' style='display: none;'><a href="TransactionBuilder.html#clone">clone</a></li><li data-type='method' style='display: none;'><a href="TransactionBuilder.html#enableRBF">enableRBF</a></li><li data-type='method' style='display: none;'><a 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<h1 class="page-title">src/core/crypto/signatures/threshold/polynomial.js</h1>
<section>
<article>
<pre class="prettyprint source linenums"><code>/**
* @fileoverview Polynomial operations for threshold cryptography
* @description Implements polynomial arithmetic over finite fields for Shamir's Secret Sharing
* and Lagrange interpolation as specified in the nChain TSS whitepaper.
* @version 1.0.0
* @author yfbsei
* @license ISC
* @see Threshold-Signatures-whitepaper-nchain.pdf Section 2.1
*/
import { randomBytes } from 'node:crypto';
import BN from 'bn.js';
import { CRYPTO_CONSTANTS } from '../../../constants.js';
/** secp256k1 curve order n */
const CURVE_ORDER = new BN(CRYPTO_CONSTANTS.SECP256K1_ORDER, 'hex');
/**
* Error class for polynomial operations
*/
class PolynomialError extends Error {
constructor(message, code, details = {}) {
super(message);
this.name = 'PolynomialError';
this.code = code;
this.details = details;
}
}
/**
* Generate a cryptographically secure random element in Z_n
* @param {number} bytes - Number of bytes for randomness
* @returns {BN} Random element in [1, n-1]
*/
function generateSecureRandom(bytes = 32) {
let value;
do {
const buffer = randomBytes(bytes);
value = new BN(buffer).umod(CURVE_ORDER);
} while (value.isZero()); // Ensure non-zero
return value;
}
/**
* Polynomial class for threshold cryptography
* Represents a polynomial f(x) = a_0 + a_1*x + ... + a_t*x^t over Z_n
*/
class Polynomial {
/**
* Create a polynomial of given degree with random coefficients
* @param {number} degree - Polynomial degree (t)
* @param {BN|null} secret - Optional secret value for a_0 (zeroth coefficient)
*/
constructor(degree, secret = null) {
if (typeof degree !== 'number' || degree < 0) {
throw new PolynomialError('Degree must be a non-negative integer', 'INVALID_DEGREE');
}
this.degree = degree;
this.coefficients = new Array(degree + 1);
// a_0 is the secret (or random if not provided)
if (secret !== null) {
this.coefficients[0] = secret instanceof BN ? secret.clone() : new BN(secret);
} else {
this.coefficients[0] = generateSecureRandom();
}
// Generate random coefficients a_1, ..., a_t
for (let i = 1; i <= degree; i++) {
this.coefficients[i] = generateSecureRandom();
}
}
/**
* Evaluate polynomial at point x using Horner's method
* f(x) = a_0 + a_1*x + a_2*x^2 + ... + a_t*x^t
* @param {number|BN} x - Evaluation point (must be non-zero for secret sharing)
* @returns {BN} f(x) mod n
*/
evaluate(x) {
const xBN = x instanceof BN ? x : new BN(x);
// Use Horner's method for efficiency: a_0 + x*(a_1 + x*(a_2 + ...))
let result = this.coefficients[this.degree].clone();
for (let i = this.degree - 1; i >= 0; i--) {
result = result.mul(xBN).add(this.coefficients[i]).umod(CURVE_ORDER);
}
return result;
}
/**
* Get the secret (zeroth coefficient)
* @returns {BN} The secret a_0
*/
getSecret() {
return this.coefficients[0].clone();
}
/**
* Get all coefficients (cloned for safety)
* @returns {BN[]} Array of coefficients [a_0, a_1, ..., a_t]
*/
getCoefficients() {
return this.coefficients.map(c => c.clone());
}
/**
* Generate shares for n participants
* Share for participant i is the point (i, f(i))
* @param {number} n - Number of participants
* @returns {Array<{x: BN, y: BN, index: number}>} Array of shares
*/
generateShares(n) {
if (n <= this.degree) {
throw new PolynomialError(
`Need more participants (${n}) than polynomial degree (${this.degree})`,
'INSUFFICIENT_PARTICIPANTS'
);
}
const shares = [];
for (let i = 1; i <= n; i++) {
shares.push({
x: new BN(i),
y: this.evaluate(i),
index: i
});
}
return shares;
}
/**
* Calculate Lagrange basis polynomial coefficient L_i(x)
* L_i(x) = Ī _{jā i} (x - x_j) / (x_i - x_j)
*
* @param {number} i - Index in the xCoords array
* @param {BN[]} xCoords - Array of x-coordinates
* @param {BN} x - Point to evaluate at (default 0 for secret reconstruction)
* @returns {BN} Lagrange coefficient
*/
static lagrangeCoefficient(i, xCoords, x = new BN(0)) {
let numerator = new BN(1);
let denominator = new BN(1);
const xi = xCoords[i] instanceof BN ? xCoords[i] : new BN(xCoords[i]);
for (let j = 0; j < xCoords.length; j++) {
if (i === j) continue;
const xj = xCoords[j] instanceof BN ? xCoords[j] : new BN(xCoords[j]);
// numerator *= (x - x_j)
numerator = numerator.mul(x.sub(xj)).umod(CURVE_ORDER);
// denominator *= (x_i - x_j)
denominator = denominator.mul(xi.sub(xj)).umod(CURVE_ORDER);
}
// Handle negative modular arithmetic
if (numerator.isNeg()) {
numerator = numerator.add(CURVE_ORDER);
}
if (denominator.isNeg()) {
denominator = denominator.add(CURVE_ORDER);
}
// Return numerator * denominator^-1 mod n
const denominatorInv = denominator.invm(CURVE_ORDER);
return numerator.mul(denominatorInv).umod(CURVE_ORDER);
}
/**
* Lagrange interpolation to reconstruct polynomial value at x
* f(x) = Ī£ y_i * L_i(x)
*
* @param {Array<{x: BN, y: BN}>} shares - Array of shares (points on polynomial)
* @param {BN} x - Point to interpolate at (default 0 for secret)
* @returns {BN} Interpolated value f(x)
*/
static interpolate(shares, x = new BN(0)) {
if (!Array.isArray(shares) || shares.length === 0) {
throw new PolynomialError('Shares array is required', 'INVALID_SHARES');
}
const xCoords = shares.map(s => s.x instanceof BN ? s.x : new BN(s.x));
let result = new BN(0);
for (let i = 0; i < shares.length; i++) {
const yi = shares[i].y instanceof BN ? shares[i].y : new BN(shares[i].y);
const li = this.lagrangeCoefficient(i, xCoords, x);
const term = yi.mul(li).umod(CURVE_ORDER);
result = result.add(term).umod(CURVE_ORDER);
}
return result;
}
/**
* Reconstruct the secret (f(0)) from shares
* Shorthand for interpolate(shares, 0)
*
* @param {Array<{x: BN, y: BN}>} shares - Array of shares
* @returns {BN} The reconstructed secret
*/
static reconstructSecret(shares) {
return this.interpolate(shares, new BN(0));
}
/**
* Clear sensitive data from memory
*/
clear() {
for (let i = 0; i < this.coefficients.length; i++) {
this.coefficients[i] = new BN(0);
}
this.coefficients = [];
this.degree = 0;
}
}
export { Polynomial, PolynomialError, generateSecureRandom, CURVE_ORDER };
export default Polynomial;
</code></pre>
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