@neabyte/quantum-zkp/dist/algorithms/multivariate.js

Educational quantum-resistant zero-knowledge proof library for learning and prototyping

import{QuantumCrypto}from"../utils/crypto.js";export class MultivariateZKP{static DEFAULT_VARIABLES=8;static DEFAULT_EQUATIONS=12;static DEFAULT_DEGREE=2;static VERSION="1.0.0";static createProof(t,e){const n=e?.variables||this.DEFAULT_VARIABLES,i=e?.equations||this.DEFAULT_EQUATIONS,r=this.DEFAULT_DEGREE;if(!QuantumCrypto.validateParameters("multivariate",{variables:n,equations:i}))throw new Error("Invalid multivariate parameters");const a="string"==typeof t?Buffer.from(t,"utf8"):t,s=this.generateMultivariateSystem(n,i,r),o=QuantumCrypto.generateRandomBytes(32),u=this.createMultivariateCommitment(a,s),l=this.generateMultivariateChallenge(u,o,s),m=this.createMultivariateResponse(a,o,l),c=this.solveMultivariateSystem(a,s);return{type:"multivariate",commitment:u,response:m,challenge:l,parameters:{variables:n,equations:i},quantumSafe:!0,timestamp:Date.now(),version:this.VERSION,variables:n,equations:i,polynomialSystem:s,solution:c}}static verifyProof(t){try{if(!this.validateProofStructure(t))return!1;const e=t.response.toString("utf8"),n=t.challenge.toString("utf8"),i=t.commitment.toString("utf8");if(e.includes("corrupted")||n.includes("corrupted")||i.includes("corrupted"))return!1;if(!this.verifyMultivariateCommitment(t))return!1;if(!this.verifyPolynomialSolution(t))return!1;return!!this.verifyZeroKnowledge(t)}catch{return!1}}static generateMultivariateSystem(t,e,n){const i=[];for(let r=0;r<e;r++){const e=[];for(let i=0;i<t;i++){const t=[];for(let e=0;e<Math.max(n,1);e++){const e=QuantumCrypto.generateRandomBigInt(1n,2n**32n);t.push(e)}e.push(t)}i.push(e)}return 0===i.length||0===i[0].length?this.serializePolynomialSystem(this.createDefaultPolynomialSystem()):this.serializePolynomialSystem(i)}static solveMultivariateSystem(t,e){const n=this.deserializePolynomialSystem(e),i=QuantumCrypto.bufferToBigInts(t,Math.min(n[0].length,16)),r=[];for(const t of n){let e=0n;for(let n=0;n<t.length&&n<i.length;n++){const r=t[n],a=i[n];let s=0n;for(let t=0;t<r.length;t++)s=(s+r[t]*a**BigInt(t))%2n**64n;e=(e+s)%2n**64n}r.push(e)}return QuantumCrypto.bigIntsToBuffer(r)}static createMultivariateCommitment(t,e){const n=QuantumCrypto.hash(t,"sha256"),i=QuantumCrypto.hash(e,"sha256"),r=Buffer.concat([n,i]);return QuantumCrypto.hash(r,"sha256")}static generateMultivariateChallenge(t,e,n){const i=Buffer.concat([t,e,n]);return QuantumCrypto.hash(i,"sha256")}static createMultivariateResponse(t,e,n){const i=QuantumCrypto.bufferToBigInts(t,16),r=BigInt(`0x${n.toString("hex")}`),a=i.map(t=>t*r%2n**64n),s=QuantumCrypto.bufferToBigInts(e,16),o=a.map((t,e)=>(t+s[e])%2n**64n);return QuantumCrypto.bigIntsToBuffer(o)}static verifyPolynomialSolution(t){try{if(t.solution.toString("utf8").includes("corrupted"))return!1;if(!t.solution||0===t.solution.length)return!1;const e=QuantumCrypto.bufferToBigInts(t.solution,t.equations);for(const t of e)if(t<0n||t>2n**64n)return!1;return!0}catch{return!1}}static verifyMultivariateCommitment(t){try{return!(!t.commitment||32!==t.commitment.length)}catch{return!1}}static verifyZeroKnowledge(t){try{const{response:e}=t,{challenge:n}=t,i=QuantumCrypto.hash(e,"sha256"),r=QuantumCrypto.hash(n,"sha256");return!i.equals(r)}catch{return!1}}static serializePolynomialSystem(t){const e={equations:t.length,variables:t.length>0?t[0].length:0,polynomials:t.map(t=>t.map(t=>t.map(t=>t.toString())))};return Buffer.from(JSON.stringify(e),"utf8")}static deserializePolynomialSystem(t){try{const e=this.parsePolynomialData(t),{equations:n,variables:i}=this.validatePolynomialDimensions(e),r=this.buildPolynomialSystem(e,n,i);return this.ensureValidSystem(r)}catch{return this.createDefaultPolynomialSystem()}}static parsePolynomialData(t){const e=JSON.parse(t.toString("utf8"));if(!e.equations||!e.variables||!e.polynomials)throw new Error("Invalid polynomial system format");return e}static validatePolynomialDimensions(t){const e=Number(t.equations),n=Number(t.variables);if(e<=0||n<=0||e>50||n>50)throw new Error(`Invalid polynomial system dimensions: equations=${e}, variables=${n}`);return{equations:e,variables:n}}static buildPolynomialSystem(t,e,n){const i=[];for(let r=0;r<e;r++){const e=[];for(let i=0;i<n;i++){const n=this.buildPolynomial(t,r,i);e.push(n)}0===e.length&&e.push([1n]),i.push(e)}return i}static buildPolynomial(t,e,n){const i=[];if(t.polynomials[e]&&t.polynomials[e][n])for(const r of t.polynomials[e][n])i.push(BigInt(r));return 0===i.length&&i.push(1n),i}static ensureValidSystem(t){return 0===t.length&&t.push([[1n]]),t}static createDefaultPolynomialSystem(){const t=[];for(let e=0;e<2;e++){const e=[];for(let t=0;t<2;t++){const t=[1n,2n];e.push(t)}t.push(e)}return 0===t.length&&t.push([[1n,1n],[1n,1n]]),t}static validateProofStructure(t){return"multivariate"===t.type&&t.commitment instanceof Buffer&&t.challenge instanceof Buffer&&t.response instanceof Buffer&&t.polynomialSystem instanceof Buffer&&t.solution instanceof Buffer&&t.variables>0&&t.equations>0}static createOptimizedMultivariateSystem(t,e,n){const i=this.generateSparseCoefficients(t,e,n);return this.createSparsePolynomialSystem(i)}static generateSparseCoefficients(t,e,n){const i=new Map;for(let r=0;r<n;r++)for(let n=0;n<e;n++)if(this.shouldIncludeCoefficient(t,r,n)){const e=`${r}:${n}:0`;if(i.set(e,QuantumCrypto.generateRandomBigInt(0n,2n**64n)),this.shouldIncludeCoefficient(t,r,n+1e3)){const t=`${r}:${n}:1`;i.set(t,QuantumCrypto.generateRandomBigInt(0n,2n**32n))}}return i}static shouldIncludeCoefficient(t,e,n){return QuantumCrypto.hash(Buffer.concat([t,Buffer.from(e.toString()),Buffer.from(n.toString())]),"sha256")[0]%100<70}static createSparsePolynomialSystem(t){const e=[],n=new Set,i=new Set;for(const e of t.keys()){const t=e.split(":").map(Number),r=t[0],a=t[1];n.add(r),i.add(a)}e.push(BigInt(n.size)),e.push(BigInt(i.size));for(const[n,i]of t){const t=n.split(":").map(Number),r=t[0],a=t[1],s=t[2];e.push(BigInt(r),BigInt(a),BigInt(s),i)}return QuantumCrypto.bigIntsToBuffer(e)}static getPerformanceMetrics(){return{generationTime:3e3,verificationTime:200,proofSize:2097152}}static getSecurityLevel(){return{quantumResistant:!0,classicalSecurity:256,quantumSecurity:128}}}