.
diff --git a/packages/groth16/README.md b/packages/groth16/README.md
new file mode 100644
index 000000000..9ee19e40b
--- /dev/null
+++ b/packages/groth16/README.md
@@ -0,0 +1,125 @@
+
+
+ SnarkJS Groth16
+
+ A snippet of SnarkJS code for verifying and generating Groth16 proofs only.
+
+
+
+
+ 
+
+
+ 
+
+
+ 
+
+
+ 
+
+
+ 
+
+
+ 
+
+
+ 
+
+
+
+
+
+| This package contains [SnarkJS](https://github.com/iden3/snarkjs) functions for generating and verifying zero knowledge proofs with Groth16 specifically. In addition to the original code it also uses the cached `bn128` curve if it already exists, making verification and generation of consecutive proofs faster. |
+| ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
+
+Some advantages of using this package instead of `snarkjs` directly are:
+* It only includes code to verify and generate Groth16 proofs, making your final bundle lighter.
+* It doesn't call the [ffjavascript](https://github.com/iden3/ffjavascript) `buildBn128` function if a `bn128` cached curve already exists, making verification and generation of consecutive proofs much faster (e.g. verification seems to be ~9 times faster after the first one).
+* It includes TS types.
+* It provides an ESM bundle that is compatible with browsers. So there is no need to add any polyfill or additional configuration.
+
+## 🛠 Install
+
+### npm or yarn
+
+Install the `@zk-kit/groth16` package and its peer dependencies with npm:
+
+```bash
+npm i @zk-kit/groth16
+```
+
+or yarn:
+
+```bash
+yarn add @zk-kit/groth16
+```
+
+## 📜 Usage
+
+\# **prove**(input: _CircuitSignals_, wasmFile: _ZKArtifact_, zkeyFile: _ZKArtifact_): Promise\<_{
+proof: Groth16Proof
+publicSignals: PublicSignals
+}_>
+
+```typescript
+import { prove } from "@zk-kit/groth16"
+
+const input = {
+ message: 12,
+ scope: 122
+}
+
+const proof = await prove(input, "./circuit.zkey", "./circuit.wasm")
+
+console.log(proof)
+/*
+{
+ proof: {
+ pi_a: [
+ '8259885706934172848141475422209230656096448508815982888010519325096632035723',
+ '3142099172052192611205205328157407975469005554072266974009053708782134081166',
+ '1'
+ ],
+ pi_b: [ [Array], [Array], [Array] ],
+ pi_c: [
+ '13863804425308906943736719856399634046638544298517159271373916818387594277305',
+ '21340646707244019956779928177502771923632450548108204371058275686712196195969',
+ '1'
+ ],
+ protocol: 'groth16',
+ curve: 'bn128'
+ },
+ publicSignals: [
+ '527758365153958423212195330785598453331596731388181860789801455413116800554',
+ '19104626566001952573667666924569656871967113105870778077087237826253896482830',
+ '122'
+ ]
+}
+*/
+```
+
+\# **verify**(verificationKey: _any_, proof: _{
+proof: Groth16Proof
+publicSignals: PublicSignals
+}_): Promise\<_boolean_>
+
+```typescript
+import { verify } from "@zk-kit/groth16"
+import verificationKey from "./circuit.json"
+
+const response = await verify(verificationKey, proof)
+
+console.log(response) // true
+```
diff --git a/packages/groth16/build.tsconfig.json b/packages/groth16/build.tsconfig.json
new file mode 100644
index 000000000..2d4a1d6da
--- /dev/null
+++ b/packages/groth16/build.tsconfig.json
@@ -0,0 +1,8 @@
+{
+ "extends": "../../tsconfig.json",
+ "compilerOptions": {
+ "baseUrl": ".",
+ "declarationDir": "dist/types"
+ },
+ "include": ["src"]
+}
diff --git a/packages/groth16/package.json b/packages/groth16/package.json
new file mode 100644
index 000000000..22ecb348d
--- /dev/null
+++ b/packages/groth16/package.json
@@ -0,0 +1,52 @@
+{
+ "name": "@zk-kit/groth16",
+ "version": "0.2.0",
+ "description": "A snippet of SnarkJS code for verifying and generating Groth16 proofs only.",
+ "license": "MIT",
+ "main": "dist/index.node.js",
+ "exports": {
+ "node": {
+ "import": "./dist/index.node.mjs",
+ "require": "./dist/index.node.js"
+ },
+ "browser": "./dist/index.browser.mjs",
+ "default": "./dist/index.browser.mjs"
+ },
+ "types": "dist/types/index.d.ts",
+ "files": [
+ "dist/",
+ "src/",
+ "LICENSE",
+ "README.md"
+ ],
+ "repository": "https://github.com/privacy-scaling-explorations/zk-kit",
+ "homepage": "https://github.com/privacy-scaling-explorations/zk-kit/tree/main/packages/groth16",
+ "bugs": {
+ "url": "https://github.com/privacy-scaling-explorations/zk-kit.git/issues"
+ },
+ "scripts": {
+ "build:watch": "rollup -c rollup.config.ts -w --configPlugin typescript",
+ "build": "rimraf dist && yarn build:browser && yarn build:node",
+ "build:browser": "rollup -c rollup.browser.config.ts --configPlugin typescript",
+ "build:node": "rollup -c rollup.node.config.ts --configPlugin typescript",
+ "prepublishOnly": "yarn build"
+ },
+ "publishConfig": {
+ "access": "public"
+ },
+ "devDependencies": {
+ "@iden3/binfileutils": "0.0.11",
+ "@rollup/plugin-commonjs": "^24.1.0",
+ "@rollup/plugin-node-resolve": "^15.0.2",
+ "@rollup/plugin-virtual": "^3.0.2",
+ "fastfile": "0.0.20",
+ "rimraf": "^5.0.5",
+ "rollup": "^4.0.2",
+ "rollup-plugin-cleanup": "^3.2.1",
+ "rollup-plugin-typescript2": "^0.31.2"
+ },
+ "dependencies": {
+ "circom_runtime": "0.1.24",
+ "ffjavascript": "0.2.60"
+ }
+}
diff --git a/packages/groth16/rollup.browser.config.ts b/packages/groth16/rollup.browser.config.ts
new file mode 100644
index 000000000..058143451
--- /dev/null
+++ b/packages/groth16/rollup.browser.config.ts
@@ -0,0 +1,56 @@
+import commonjs from "@rollup/plugin-commonjs"
+import { nodeResolve } from "@rollup/plugin-node-resolve"
+import virtual from "@rollup/plugin-virtual"
+import * as fs from "fs"
+import cleanup from "rollup-plugin-cleanup"
+import typescript from "rollup-plugin-typescript2"
+
+// Needed by fastfile.
+import { O_CREAT, O_EXCL, O_RDONLY, O_RDWR, O_TRUNC } from "constants"
+
+const constants = `
+export const O_TRUNC = ${O_TRUNC};
+export const O_CREAT = ${O_CREAT};
+export const O_RDWR = ${O_RDWR};
+export const O_EXCL = ${O_EXCL};
+export const O_RDONLY = ${O_RDONLY}
+`
+
+const empty = "export default {}"
+
+const pkg = JSON.parse(fs.readFileSync("./package.json", "utf-8"))
+const banner = `/**
+ * @module ${pkg.name}
+ * @version ${pkg.version}
+ * @file ${pkg.description}
+ * @copyright Ethereum Foundation 2023
+ * @license ${pkg.license}
+ * @see [Github]{@link ${pkg.homepage}}
+*/`
+
+export default {
+ input: "src/index.ts",
+ output: [
+ {
+ file: pkg.exports.browser,
+ format: "es",
+ banner
+ }
+ ],
+ external: Object.keys(pkg.dependencies),
+ plugins: [
+ typescript({
+ tsconfig: "./build.tsconfig.json",
+ useTsconfigDeclarationDir: true
+ }),
+ virtual({
+ fs: empty,
+ constants
+ }),
+ nodeResolve(),
+ commonjs({
+ esmExternals: true
+ }),
+ cleanup({ comments: "jsdoc" })
+ ]
+}
diff --git a/packages/groth16/rollup.node.config.ts b/packages/groth16/rollup.node.config.ts
new file mode 100644
index 000000000..66f4a02cb
--- /dev/null
+++ b/packages/groth16/rollup.node.config.ts
@@ -0,0 +1,44 @@
+import commonjs from "@rollup/plugin-commonjs"
+import { nodeResolve } from "@rollup/plugin-node-resolve"
+import * as fs from "fs"
+import cleanup from "rollup-plugin-cleanup"
+import typescript from "rollup-plugin-typescript2"
+
+const pkg = JSON.parse(fs.readFileSync("./package.json", "utf-8"))
+const banner = `/**
+ * @module ${pkg.name}
+ * @version ${pkg.version}
+ * @file ${pkg.description}
+ * @copyright Ethereum Foundation 2023
+ * @license ${pkg.license}
+ * @see [Github]{@link ${pkg.homepage}}
+*/`
+
+export default {
+ input: "src/index.ts",
+ output: [
+ {
+ file: pkg.exports.node.require,
+ format: "cjs",
+ banner,
+ exports: "auto"
+ },
+ {
+ file: pkg.exports.node.import,
+ format: "es",
+ banner
+ }
+ ],
+ external: Object.keys(pkg.dependencies),
+ plugins: [
+ typescript({
+ tsconfig: "./build.tsconfig.json",
+ useTsconfigDeclarationDir: true
+ }),
+ nodeResolve(),
+ commonjs({
+ esmExternals: true
+ }),
+ cleanup({ comments: "jsdoc" })
+ ]
+}
diff --git a/packages/groth16/snark-artifacts/index.json b/packages/groth16/snark-artifacts/index.json
new file mode 100644
index 000000000..874031cd3
--- /dev/null
+++ b/packages/groth16/snark-artifacts/index.json
@@ -0,0 +1,95 @@
+{
+ "protocol": "groth16",
+ "curve": "bn128",
+ "nPublic": 3,
+ "vk_alpha_1": [
+ "20491192805390485299153009773594534940189261866228447918068658471970481763042",
+ "9383485363053290200918347156157836566562967994039712273449902621266178545958",
+ "1"
+ ],
+ "vk_beta_2": [
+ [
+ "6375614351688725206403948262868962793625744043794305715222011528459656738731",
+ "4252822878758300859123897981450591353533073413197771768651442665752259397132"
+ ],
+ [
+ "10505242626370262277552901082094356697409835680220590971873171140371331206856",
+ "21847035105528745403288232691147584728191162732299865338377159692350059136679"
+ ],
+ ["1", "0"]
+ ],
+ "vk_gamma_2": [
+ [
+ "10857046999023057135944570762232829481370756359578518086990519993285655852781",
+ "11559732032986387107991004021392285783925812861821192530917403151452391805634"
+ ],
+ [
+ "8495653923123431417604973247489272438418190587263600148770280649306958101930",
+ "4082367875863433681332203403145435568316851327593401208105741076214120093531"
+ ],
+ ["1", "0"]
+ ],
+ "vk_delta_2": [
+ [
+ "17546152771742044890128665170773308307706885904145171368861289731338407120726",
+ "21635289475723704811498602453116541869848271742675656134593605133653559871988"
+ ],
+ [
+ "12208424286857750236404959484429248934995357114248145547240410687755355066198",
+ "19321625097082563598592975631421044551870980615218660051914871088320678365555"
+ ],
+ ["1", "0"]
+ ],
+ "vk_alphabeta_12": [
+ [
+ [
+ "2029413683389138792403550203267699914886160938906632433982220835551125967885",
+ "21072700047562757817161031222997517981543347628379360635925549008442030252106"
+ ],
+ [
+ "5940354580057074848093997050200682056184807770593307860589430076672439820312",
+ "12156638873931618554171829126792193045421052652279363021382169897324752428276"
+ ],
+ [
+ "7898200236362823042373859371574133993780991612861777490112507062703164551277",
+ "7074218545237549455313236346927434013100842096812539264420499035217050630853"
+ ]
+ ],
+ [
+ [
+ "7077479683546002997211712695946002074877511277312570035766170199895071832130",
+ "10093483419865920389913245021038182291233451549023025229112148274109565435465"
+ ],
+ [
+ "4595479056700221319381530156280926371456704509942304414423590385166031118820",
+ "19831328484489333784475432780421641293929726139240675179672856274388269393268"
+ ],
+ [
+ "11934129596455521040620786944827826205713621633706285934057045369193958244500",
+ "8037395052364110730298837004334506829870972346962140206007064471173334027475"
+ ]
+ ]
+ ],
+ "IC": [
+ [
+ "10540353245037691655240058832465935071147222378795512774896416883563614389198",
+ "20042286059857913285646233979306226083538103143380748863555356103197961213823",
+ "1"
+ ],
+ [
+ "12178048393484805922448151297512780036777540315506565788645040495931277621130",
+ "9697539656531822741576184528195082340044862873578980581504958946888585254425",
+ "1"
+ ],
+ [
+ "20991907493060125430185038723439696392069163847357524165903787100018954817952",
+ "12348708907766483529401318577288191297476103087328423321867414316726183562292",
+ "1"
+ ],
+ [
+ "6823739927950557742246913693052072220213742766782370219666937126411380340633",
+ "19878777316727584245579797737044924949420447706770682437221414501064053790692",
+ "1"
+ ]
+ ]
+}
diff --git a/packages/groth16/snark-artifacts/index.wasm b/packages/groth16/snark-artifacts/index.wasm
new file mode 100644
index 000000000..7a67220dc
Binary files /dev/null and b/packages/groth16/snark-artifacts/index.wasm differ
diff --git a/packages/groth16/snark-artifacts/index.zkey b/packages/groth16/snark-artifacts/index.zkey
new file mode 100644
index 000000000..3d37f26c1
Binary files /dev/null and b/packages/groth16/snark-artifacts/index.zkey differ
diff --git a/packages/groth16/src/index.ts b/packages/groth16/src/index.ts
new file mode 100644
index 000000000..d2ac9dc31
--- /dev/null
+++ b/packages/groth16/src/index.ts
@@ -0,0 +1,5 @@
+import prove from "./prove"
+import verify from "./verify"
+
+export { prove, verify }
+export * from "./types"
diff --git a/packages/groth16/src/prove.ts b/packages/groth16/src/prove.ts
new file mode 100644
index 000000000..285c8ba7c
--- /dev/null
+++ b/packages/groth16/src/prove.ts
@@ -0,0 +1,235 @@
+/* eslint-disable no-plusplus */
+/* eslint-disable eqeqeq */
+/* eslint-disable @typescript-eslint/naming-convention */
+/* istanbul ignore file */
+
+// @ts-ignore
+import * as binFileUtils from "@iden3/binfileutils"
+import { BigBuffer, Scalar, utils } from "ffjavascript"
+import { log2 } from "./utils"
+import * as zkeyUtils from "./zkey-utils"
+import * as wtnsUtils from "./wtns-utils"
+import wtnsCalculate from "./wtns-calculate"
+import { CircuitSignals, Groth16Proof, PublicSignals, ZKArtifact } from "./types"
+
+const { stringifyBigInts, unstringifyBigInts } = utils
+
+async function buildABC1(curve: any, zkey: any, witness: any, coeffs: any) {
+ const { n8 } = curve.Fr
+ const sCoef = 4 * 3 + zkey.n8r
+ const nCoef = (coeffs.byteLength - 4) / sCoef
+
+ const outBuffA = new BigBuffer(zkey.domainSize * n8)
+ const outBuffB = new BigBuffer(zkey.domainSize * n8)
+ const outBuffC = new BigBuffer(zkey.domainSize * n8)
+
+ const outBuf = [outBuffA, outBuffB]
+ for (let i = 0; i < nCoef; i++) {
+ const buffCoef = coeffs.slice(4 + i * sCoef, 4 + i * sCoef + sCoef)
+ const buffCoefV = new DataView(buffCoef.buffer)
+ const m = buffCoefV.getUint32(0, true)
+ const c = buffCoefV.getUint32(4, true)
+ const s = buffCoefV.getUint32(8, true)
+ const coef = buffCoef.slice(12, 12 + n8)
+ outBuf[m].set(
+ curve.Fr.add(outBuf[m].slice(c * n8, c * n8 + n8), curve.Fr.mul(coef, witness.slice(s * n8, s * n8 + n8))),
+ c * n8
+ )
+ }
+
+ for (let i = 0; i < zkey.domainSize; i++) {
+ outBuffC.set(curve.Fr.mul(outBuffA.slice(i * n8, i * n8 + n8), outBuffB.slice(i * n8, i * n8 + n8)), i * n8)
+ }
+
+ return [outBuffA, outBuffB, outBuffC]
+}
+
+async function joinABC(curve: any, _zkey: any, a: any, b: any, c: any) {
+ const MAX_CHUNK_SIZE = 1 << 22
+
+ const { n8 } = curve.Fr
+ const nElements = Math.floor(a.byteLength / curve.Fr.n8)
+
+ const promises = []
+
+ for (let i = 0; i < nElements; i += MAX_CHUNK_SIZE) {
+ const n = Math.min(nElements - i, MAX_CHUNK_SIZE)
+
+ const task = []
+
+ const aChunk = a.slice(i * n8, (i + n) * n8)
+ const bChunk = b.slice(i * n8, (i + n) * n8)
+ const cChunk = c.slice(i * n8, (i + n) * n8)
+
+ task.push({ cmd: "ALLOCSET", var: 0, buff: aChunk })
+ task.push({ cmd: "ALLOCSET", var: 1, buff: bChunk })
+ task.push({ cmd: "ALLOCSET", var: 2, buff: cChunk })
+ task.push({ cmd: "ALLOC", var: 3, len: n * n8 })
+ task.push({
+ cmd: "CALL",
+ fnName: "qap_joinABC",
+ params: [{ var: 0 }, { var: 1 }, { var: 2 }, { val: n }, { var: 3 }]
+ })
+ task.push({ cmd: "CALL", fnName: "frm_batchFromMontgomery", params: [{ var: 3 }, { val: n }, { var: 3 }] })
+ task.push({ cmd: "GET", out: 0, var: 3, len: n * n8 })
+ promises.push(curve.tm.queueAction(task))
+ }
+
+ const result = await Promise.all(promises)
+
+ let outBuff
+ if (a instanceof BigBuffer) {
+ // @ts-ignore
+ outBuff = new BigBuffer(a.byteLength)
+ } else {
+ outBuff = new Uint8Array(a.byteLength)
+ }
+
+ let p = 0
+ for (let i = 0; i < result.length; i++) {
+ outBuff.set(result[i][0], p)
+ p += result[i][0].byteLength
+ }
+
+ return outBuff
+}
+
+/**
+ * Creates a Groth16 proof composed of public signals and zero-knowledge parameters.
+ * @param input Input signals of the circuit.
+ * @param wasmFile WASM file of the circuit.
+ * @param zkeyFile ZKey file of the circuit.
+ * @returns A proof containing public signals and zero-knowledge parameters.
+ */
+export default async function prove(
+ input: CircuitSignals,
+ wasmFile: ZKArtifact,
+ zkeyFile: ZKArtifact
+): Promise<{
+ proof: Groth16Proof
+ publicSignals: PublicSignals
+}> {
+ input = unstringifyBigInts(input)
+
+ const witnessFileName = {
+ type: "mem"
+ }
+
+ await wtnsCalculate(input, wasmFile, witnessFileName)
+
+ const { fd: fdWtns, sections: sectionsWtns } = await binFileUtils.readBinFile(
+ witnessFileName,
+ "wtns",
+ 2,
+ 1 << 25,
+ 1 << 23
+ )
+
+ const wtns = await wtnsUtils.readHeader(fdWtns, sectionsWtns)
+
+ const { fd: fdZKey, sections: sectionsZKey } = await binFileUtils.readBinFile(zkeyFile, "zkey", 2, 1 << 25, 1 << 23)
+
+ const zkey = await zkeyUtils.readHeader(fdZKey, sectionsZKey, undefined)
+
+ if (zkey.protocol !== "groth16") {
+ throw new Error("zkey file is not groth16")
+ }
+
+ if (!Scalar.eq(zkey.r, wtns.q)) {
+ throw new Error("Curve of the witness does not match the curve of the proving key")
+ }
+
+ if (wtns.nWitness !== zkey.nVars) {
+ throw new Error(`Invalid witness length. Circuit: ${zkey.nVars}, witness: ${wtns.nWitness}`)
+ }
+
+ const { curve } = zkey
+ const { Fr } = curve
+ const { G1 } = curve
+ const { G2 } = curve
+
+ const power = log2(zkey.domainSize)
+
+ const buffWitness = await binFileUtils.readSection(fdWtns, sectionsWtns, 2)
+ const buffCoeffs = await binFileUtils.readSection(fdZKey, sectionsZKey, 4)
+
+ const [buffA_T, buffB_T, buffC_T] = await buildABC1(curve, zkey, buffWitness, buffCoeffs)
+
+ const inc = power == Fr.s ? curve.Fr.shift : curve.Fr.w[power + 1]
+
+ const buffA = await Fr.ifft(buffA_T, "", "", undefined, "IFFT_A")
+ const buffAodd = await Fr.batchApplyKey(buffA, Fr.e(1), inc)
+ const buffAodd_T = await Fr.fft(buffAodd, "", "", undefined, "FFT_A")
+
+ const buffB = await Fr.ifft(buffB_T, "", "", undefined, "IFFT_B")
+ const buffBodd = await Fr.batchApplyKey(buffB, Fr.e(1), inc)
+ const buffBodd_T = await Fr.fft(buffBodd, "", "", undefined, "FFT_B")
+
+ const buffC = await Fr.ifft(buffC_T, "", "", undefined, "IFFT_C")
+ const buffCodd = await Fr.batchApplyKey(buffC, Fr.e(1), inc)
+ const buffCodd_T = await Fr.fft(buffCodd, "", "", undefined, "FFT_C")
+
+ const buffPodd_T = await joinABC(curve, zkey, buffAodd_T, buffBodd_T, buffCodd_T)
+
+ let proof: any = {}
+
+ const buffBasesA = await binFileUtils.readSection(fdZKey, sectionsZKey, 5)
+ proof.pi_a = await curve.G1.multiExpAffine(buffBasesA, buffWitness, undefined, "multiexp A")
+
+ const buffBasesB1 = await binFileUtils.readSection(fdZKey, sectionsZKey, 6)
+ let pib1 = await curve.G1.multiExpAffine(buffBasesB1, buffWitness, undefined, "multiexp B1")
+
+ const buffBasesB2 = await binFileUtils.readSection(fdZKey, sectionsZKey, 7)
+ proof.pi_b = await curve.G2.multiExpAffine(buffBasesB2, buffWitness, undefined, "multiexp B2")
+
+ const buffBasesC = await binFileUtils.readSection(fdZKey, sectionsZKey, 8)
+ proof.pi_c = await curve.G1.multiExpAffine(
+ buffBasesC,
+ buffWitness.slice((zkey.nPublic + 1) * curve.Fr.n8),
+ undefined,
+ "multiexp C"
+ )
+
+ const buffBasesH = await binFileUtils.readSection(fdZKey, sectionsZKey, 9)
+ const resH = await curve.G1.multiExpAffine(buffBasesH, buffPodd_T, undefined, "multiexp H")
+
+ const r = curve.Fr.random()
+ const s = curve.Fr.random()
+
+ proof.pi_a = G1.add(proof.pi_a, zkey.vk_alpha_1)
+ proof.pi_a = G1.add(proof.pi_a, G1.timesFr(zkey.vk_delta_1, r))
+
+ proof.pi_b = G2.add(proof.pi_b, zkey.vk_beta_2)
+ proof.pi_b = G2.add(proof.pi_b, G2.timesFr(zkey.vk_delta_2, s))
+
+ pib1 = G1.add(pib1, zkey.vk_beta_1)
+ pib1 = G1.add(pib1, G1.timesFr(zkey.vk_delta_1, s))
+
+ proof.pi_c = G1.add(proof.pi_c, resH)
+
+ proof.pi_c = G1.add(proof.pi_c, G1.timesFr(proof.pi_a, s))
+ proof.pi_c = G1.add(proof.pi_c, G1.timesFr(pib1, r))
+ proof.pi_c = G1.add(proof.pi_c, G1.timesFr(zkey.vk_delta_1, Fr.neg(Fr.mul(r, s))))
+
+ let publicSignals = []
+
+ for (let i = 1; i <= zkey.nPublic; i++) {
+ const b = buffWitness.slice(i * Fr.n8, i * Fr.n8 + Fr.n8)
+ publicSignals.push(Scalar.fromRprLE(b, undefined, undefined))
+ }
+
+ proof.pi_a = G1.toObject(G1.toAffine(proof.pi_a))
+ proof.pi_b = G2.toObject(G2.toAffine(proof.pi_b))
+ proof.pi_c = G1.toObject(G1.toAffine(proof.pi_c))
+
+ proof.protocol = "groth16"
+ proof.curve = curve.name
+
+ await fdZKey.close()
+ await fdWtns.close()
+
+ proof = stringifyBigInts(proof)
+ publicSignals = stringifyBigInts(publicSignals)
+
+ return { proof, publicSignals }
+}
diff --git a/packages/groth16/src/types/index.ts b/packages/groth16/src/types/index.ts
new file mode 100644
index 000000000..0583a0377
--- /dev/null
+++ b/packages/groth16/src/types/index.ts
@@ -0,0 +1,19 @@
+export type ZKArtifact = string | Uint8Array
+
+export type NumericString = `${number}` | string
+
+export type SignalValueType = NumericString | number | bigint | SignalValueType[]
+
+export interface CircuitSignals {
+ [signal: string]: SignalValueType
+}
+
+export interface Groth16Proof {
+ pi_a: NumericString[]
+ pi_b: NumericString[][]
+ pi_c: NumericString[]
+ protocol: string
+ curve: string
+}
+
+export type PublicSignals = NumericString[]
diff --git a/packages/groth16/src/utils.ts b/packages/groth16/src/utils.ts
new file mode 100644
index 000000000..198edd1d3
--- /dev/null
+++ b/packages/groth16/src/utils.ts
@@ -0,0 +1,14 @@
+/* eslint-disable import/prefer-default-export */
+/* eslint-disable no-return-assign */
+/* istanbul ignore file */
+
+export function log2(V: any) {
+ return (
+ ((V & 0xffff0000) !== 0 ? ((V &= 0xffff0000), 16) : 0) |
+ ((V & 0xff00ff00) !== 0 ? ((V &= 0xff00ff00), 8) : 0) |
+ ((V & 0xf0f0f0f0) !== 0 ? ((V &= 0xf0f0f0f0), 4) : 0) |
+ ((V & 0xcccccccc) !== 0 ? ((V &= 0xcccccccc), 2) : 0) |
+ // @ts-ignore
+ ((V & 0xaaaaaaaa) !== 0)
+ )
+}
diff --git a/packages/groth16/src/verify.ts b/packages/groth16/src/verify.ts
new file mode 100644
index 000000000..016ee202e
--- /dev/null
+++ b/packages/groth16/src/verify.ts
@@ -0,0 +1,90 @@
+/* eslint-disable no-plusplus */
+/* eslint-disable @typescript-eslint/naming-convention */
+/* istanbul ignore file */
+
+import { Scalar, utils, buildBn128 } from "ffjavascript"
+import { Groth16Proof, PublicSignals } from "./types"
+
+const { unstringifyBigInts } = utils
+
+function isWellConstructed(curve: any, proof: any) {
+ const { G1 } = curve
+ const { G2 } = curve
+
+ return G1.isValid(proof.pi_a) && G2.isValid(proof.pi_b) && G1.isValid(proof.pi_c)
+}
+
+function publicInputsAreValid(curve: any, publicInputs: any) {
+ for (let i = 0; i < publicInputs.length; i++) {
+ if (!Scalar.lt(publicInputs[i], curve.r)) {
+ return false
+ }
+ }
+ return true
+}
+
+/**
+ * Verifies if a Groth16 proof is valid or not.
+ * @param verificationKey The verification key used to verify the proof.
+ * @param proof The proof containing public signals and zero-knowledge parameters.
+ * @returns True if the proof is valid, and false otherwise.
+ */
+export default async function verify(
+ verificationKey: any,
+ {
+ proof,
+ publicSignals
+ }: {
+ proof: Groth16Proof
+ publicSignals: PublicSignals
+ }
+): Promise {
+ verificationKey = unstringifyBigInts(verificationKey)
+ proof = unstringifyBigInts(proof)
+ publicSignals = unstringifyBigInts(publicSignals)
+
+ // @ts-ignore
+ const curve = globalThis.curve_bn128 ?? (await buildBn128(undefined, undefined))
+
+ const IC0 = curve.G1.fromObject(verificationKey.IC[0])
+ const IC = new Uint8Array(curve.G1.F.n8 * 2 * publicSignals.length)
+ const w = new Uint8Array(curve.Fr.n8 * publicSignals.length)
+
+ if (!publicInputsAreValid(curve, publicSignals)) {
+ return false
+ }
+
+ for (let i = 0; i < publicSignals.length; i++) {
+ const buffP = curve.G1.fromObject(verificationKey.IC[i + 1])
+ IC.set(buffP, i * curve.G1.F.n8 * 2)
+ Scalar.toRprLE(w, curve.Fr.n8 * i, publicSignals[i], curve.Fr.n8)
+ }
+
+ let cpub = await curve.G1.multiExpAffine(IC, w)
+ cpub = curve.G1.add(cpub, IC0)
+
+ const pi_a = curve.G1.fromObject(proof.pi_a)
+ const pi_b = curve.G2.fromObject(proof.pi_b)
+ const pi_c = curve.G1.fromObject(proof.pi_c)
+
+ if (!isWellConstructed(curve, { pi_a, pi_b, pi_c })) {
+ return false
+ }
+
+ const vk_gamma_2 = curve.G2.fromObject(verificationKey.vk_gamma_2)
+ const vk_delta_2 = curve.G2.fromObject(verificationKey.vk_delta_2)
+ const vk_alpha_1 = curve.G1.fromObject(verificationKey.vk_alpha_1)
+ const vk_beta_2 = curve.G2.fromObject(verificationKey.vk_beta_2)
+
+ return curve.pairingEq(
+ curve.G1.neg(pi_a),
+ pi_b,
+ cpub,
+ vk_gamma_2,
+ pi_c,
+ vk_delta_2,
+
+ vk_alpha_1,
+ vk_beta_2
+ )
+}
diff --git a/packages/groth16/src/wtns-calculate.ts b/packages/groth16/src/wtns-calculate.ts
new file mode 100644
index 000000000..263f7e91e
--- /dev/null
+++ b/packages/groth16/src/wtns-calculate.ts
@@ -0,0 +1,39 @@
+/* eslint-disable eqeqeq */
+/* istanbul ignore file */
+
+// @ts-ignore
+import * as binFileUtils from "@iden3/binfileutils"
+// @ts-ignore
+import { WitnessCalculatorBuilder } from "circom_runtime"
+// @ts-ignore
+import * as fastFile from "fastfile"
+import { utils } from "ffjavascript"
+import * as wtnsUtils from "./wtns-utils"
+
+const { unstringifyBigInts } = utils
+
+export default async function wtnsCalculate(_input: any, wasmFileName: any, wtnsFileName: any) {
+ const input = unstringifyBigInts(_input)
+
+ const fdWasm = await fastFile.readExisting(wasmFileName)
+ const wasm = await fdWasm.read(fdWasm.totalSize)
+ await fdWasm.close()
+
+ const wc = await WitnessCalculatorBuilder(wasm)
+
+ if (wc.circom_version() == 1) {
+ const w = await wc.calculateBinWitness(input)
+
+ const fdWtns = await binFileUtils.createBinFile(wtnsFileName, "wtns", 2, 2)
+
+ await wtnsUtils.writeBin(fdWtns, w, wc.prime)
+ await fdWtns.close()
+ } else {
+ const fdWtns = await fastFile.createOverride(wtnsFileName)
+
+ const w = await wc.calculateWTNSBin(input)
+
+ await fdWtns.write(w)
+ await fdWtns.close()
+ }
+}
diff --git a/packages/groth16/src/wtns-utils.ts b/packages/groth16/src/wtns-utils.ts
new file mode 100644
index 000000000..cadca43b2
--- /dev/null
+++ b/packages/groth16/src/wtns-utils.ts
@@ -0,0 +1,32 @@
+/* eslint-disable eqeqeq */
+/* istanbul ignore file */
+
+// @ts-ignore
+import * as binFileUtils from "@iden3/binfileutils"
+import { Scalar } from "ffjavascript"
+
+export async function writeBin(fd: any, witnessBin: any, prime: any) {
+ await binFileUtils.startWriteSection(fd, 1)
+ const n8 = (Math.floor((Scalar.bitLength(prime) - 1) / 64) + 1) * 8
+ await fd.writeULE32(n8)
+ await binFileUtils.writeBigInt(fd, prime, n8)
+ if (witnessBin.byteLength % n8 != 0) {
+ throw new Error("Invalid witness length")
+ }
+ await fd.writeULE32(witnessBin.byteLength / n8)
+ await binFileUtils.endWriteSection(fd)
+
+ await binFileUtils.startWriteSection(fd, 2)
+ await fd.write(witnessBin)
+ await binFileUtils.endWriteSection(fd)
+}
+
+export async function readHeader(fd: any, sections: any) {
+ await binFileUtils.startReadUniqueSection(fd, sections, 1)
+ const n8 = await fd.readULE32()
+ const q = await binFileUtils.readBigInt(fd, n8)
+ const nWitness = await fd.readULE32()
+ await binFileUtils.endReadSection(fd)
+
+ return { n8, q, nWitness }
+}
diff --git a/packages/groth16/src/zkey-utils.ts b/packages/groth16/src/zkey-utils.ts
new file mode 100644
index 000000000..c3b245a28
--- /dev/null
+++ b/packages/groth16/src/zkey-utils.ts
@@ -0,0 +1,63 @@
+/* eslint-disable import/prefer-default-export */
+/* istanbul ignore file */
+
+// @ts-ignore
+import * as binFileUtils from "@iden3/binfileutils"
+import { buildBn128 } from "ffjavascript"
+import { log2 } from "./utils"
+
+async function readG1(fd: any, curve: any, toObject: any) {
+ const buff = await fd.read(curve.G1.F.n8 * 2)
+ const res = curve.G1.fromRprLEM(buff, 0)
+ return toObject ? curve.G1.toObject(res) : res
+}
+
+async function readG2(fd: any, curve: any, toObject: any) {
+ const buff = await fd.read(curve.G2.F.n8 * 2)
+ const res = curve.G2.fromRprLEM(buff, 0)
+ return toObject ? curve.G2.toObject(res) : res
+}
+
+async function readHeaderGroth16(fd: any, sections: any, toObject: any) {
+ const zkey: any = {}
+
+ zkey.protocol = "groth16"
+
+ await binFileUtils.startReadUniqueSection(fd, sections, 2)
+ const n8q = await fd.readULE32()
+ zkey.n8q = n8q
+ zkey.q = await binFileUtils.readBigInt(fd, n8q)
+
+ const n8r = await fd.readULE32()
+ zkey.n8r = n8r
+ zkey.r = await binFileUtils.readBigInt(fd, n8r)
+
+ // @ts-ignore
+ zkey.curve = globalThis.curve_bn128 ?? (await buildBn128(undefined, undefined))
+
+ zkey.nVars = await fd.readULE32()
+ zkey.nPublic = await fd.readULE32()
+ zkey.domainSize = await fd.readULE32()
+ zkey.power = log2(zkey.domainSize)
+ zkey.vk_alpha_1 = await readG1(fd, zkey.curve, toObject)
+ zkey.vk_beta_1 = await readG1(fd, zkey.curve, toObject)
+ zkey.vk_beta_2 = await readG2(fd, zkey.curve, toObject)
+ zkey.vk_gamma_2 = await readG2(fd, zkey.curve, toObject)
+ zkey.vk_delta_1 = await readG1(fd, zkey.curve, toObject)
+ zkey.vk_delta_2 = await readG2(fd, zkey.curve, toObject)
+ await binFileUtils.endReadSection(fd)
+
+ return zkey
+}
+
+export async function readHeader(fd: any, sections: any, toObject: any) {
+ await binFileUtils.startReadUniqueSection(fd, sections, 1)
+ const protocolId = await fd.readULE32()
+ await binFileUtils.endReadSection(fd)
+
+ if (protocolId === 1) {
+ return readHeaderGroth16(fd, sections, toObject)
+ }
+
+ throw new Error("Protocol not supported: ")
+}
diff --git a/packages/groth16/tests/index.test.ts b/packages/groth16/tests/index.test.ts
new file mode 100644
index 000000000..c2f04e379
--- /dev/null
+++ b/packages/groth16/tests/index.test.ts
@@ -0,0 +1,46 @@
+import { getCurveFromName } from "ffjavascript"
+import { verify, prove } from "../src"
+import verificationKey from "../snark-artifacts/index.json"
+
+describe("Groth16", () => {
+ const wasmFilePath = "./packages/groth16/snark-artifacts/index.wasm"
+ const zkeyFilePath = "./packages/groth16/snark-artifacts/index.zkey"
+
+ let curve: any
+ let proof: any
+
+ beforeAll(async () => {
+ curve = await getCurveFromName("bn128")
+ })
+
+ afterAll(async () => {
+ await curve.terminate()
+ })
+
+ it("Should generate a proof", async () => {
+ proof = await prove(
+ {
+ message: 12,
+ scope: 122
+ },
+ wasmFilePath,
+ zkeyFilePath
+ )
+
+ expect(typeof proof).toBe("object")
+ }, 20000)
+
+ it("Should verify a valid proof", async () => {
+ const response = await verify(verificationKey, proof)
+
+ expect(response).toBe(true)
+ })
+
+ it("Should verify an invalid proof", async () => {
+ proof.publicSignals[0] = 0
+
+ const response = await verify(verificationKey, proof)
+
+ expect(response).toBe(false)
+ })
+})
diff --git a/packages/groth16/tsconfig.json b/packages/groth16/tsconfig.json
new file mode 100644
index 000000000..d90026c5a
--- /dev/null
+++ b/packages/groth16/tsconfig.json
@@ -0,0 +1,7 @@
+{
+ "extends": "../../tsconfig.json",
+ "compilerOptions": {
+ "resolveJsonModule": true
+ },
+ "include": ["src", "tests", "rollup.browser.config.ts", "rollup.node.config.ts"]
+}
diff --git a/packages/groth16/typedoc.json b/packages/groth16/typedoc.json
new file mode 100644
index 000000000..77a471c91
--- /dev/null
+++ b/packages/groth16/typedoc.json
@@ -0,0 +1,3 @@
+{
+ "entryPoints": ["src/index.ts"]
+}
diff --git a/types/ffjavascript/index.d.ts b/types/ffjavascript/index.d.ts
new file mode 100644
index 000000000..f754ad716
--- /dev/null
+++ b/types/ffjavascript/index.d.ts
@@ -0,0 +1,509 @@
+/** Declaration file generated by dts-gen */
+
+declare module "ffjavascript" {
+ export class BigBuffer {
+ constructor(...args: any[])
+
+ set(...args: any[]): void
+
+ slice(...args: any[]): void
+ }
+
+ export class ChaCha {
+ constructor(...args: any[])
+
+ nextBool(...args: any[]): void
+
+ nextU32(...args: any[]): void
+
+ nextU64(...args: any[]): void
+
+ update(...args: any[]): void
+ }
+
+ export class EC {
+ constructor(...args: any[])
+
+ add(...args: any[]): void
+
+ affine(...args: any[]): void
+
+ double(...args: any[]): void
+
+ eq(...args: any[]): void
+
+ fromRng(...args: any[]): void
+
+ fromRprBE(...args: any[]): void
+
+ fromRprBEM(...args: any[]): void
+
+ fromRprCompressed(...args: any[]): void
+
+ fromRprLE(...args: any[]): void
+
+ fromRprLEJM(...args: any[]): void
+
+ fromRprLEM(...args: any[]): void
+
+ fromRprUncompressed(...args: any[]): void
+
+ isZero(...args: any[]): void
+
+ mulScalar(...args: any[]): void
+
+ multiAffine(...args: any[]): void
+
+ neg(...args: any[]): void
+
+ sub(...args: any[]): void
+
+ timesScalar(...args: any[]): void
+
+ toRprBE(...args: any[]): void
+
+ toRprBEM(...args: any[]): void
+
+ toRprCompressed(...args: any[]): void
+
+ toRprLE(...args: any[]): void
+
+ toRprLEJM(...args: any[]): void
+
+ toRprLEM(...args: any[]): void
+
+ toRprUncompressed(...args: any[]): void
+
+ toString(...args: any[]): void
+ }
+
+ export class F1Field {
+ constructor(...args: any[])
+
+ e(...args: any[]): any
+ add(...args: any[]): any
+ sub(...args: any[]): any
+ neg(...args: any[]): any
+ mul(...args: any[]): any
+ mulScalar(...args: any[]): any
+ square(...args: any[]): any
+ eq(...args: any[]): any
+ neq(...args: any[]): any
+ lt(...args: any[]): any
+ gt(...args: any[]): any
+ leq(...args: any[]): any
+ geq(...args: any[]): any
+ div(...args: any[]): any
+ idiv(...args: any[]): any
+ inv(...args: any[]): any
+ mod(...args: any[]): any
+ pow(...args: any[]): any
+ exp(...args: any[]): any
+ band(...args: any[]): any
+ bor(...args: any[]): any
+ bxor(...args: any[]): any
+ bnot(...args: any[]): any
+ shl(...args: any[]): any
+ shr(...args: any[]): any
+ land(...args: any[]): any
+ lor(...args: any[]): any
+ lnot(...args: any[]): any
+ sqrt_old(...args: any[]): any
+ normalize(...args: any[]): any
+ random(...args: any[]): any
+ toString(...args: any[]): any
+ isZero(...args: any[]): any
+ fromRng(...args: any[]): any
+
+ fromRprBE(...args: any[]): void
+
+ fromRprBEM(...args: any[]): void
+
+ fromRprLE(...args: any[]): void
+
+ fromRprLEM(...args: any[]): void
+
+ toRprBE(...args: any[]): void
+
+ toRprBEM(...args: any[]): void
+
+ toRprLE(...args: any[]): void
+
+ toRprLEM(...args: any[]): void
+ }
+
+ export class F2Field {
+ constructor(...args: any[])
+
+ add(...args: any[]): void
+
+ conjugate(...args: any[]): void
+
+ copy(...args: any[]): void
+
+ div(...args: any[]): void
+
+ double(...args: any[]): void
+
+ eq(...args: any[]): void
+
+ exp(...args: any[]): void
+
+ fromRng(...args: any[]): void
+
+ fromRprBE(...args: any[]): void
+
+ fromRprBEM(...args: any[]): void
+
+ fromRprLE(...args: any[]): void
+
+ fromRprLEM(...args: any[]): void
+
+ geq(...args: any[]): void
+
+ gt(...args: any[]): void
+
+ inv(...args: any[]): void
+
+ isZero(...args: any[]): void
+
+ leq(...args: any[]): void
+
+ lt(...args: any[]): void
+
+ mul(...args: any[]): void
+
+ mulScalar(...args: any[]): void
+
+ neg(...args: any[]): void
+
+ neq(...args: any[]): void
+
+ pow(...args: any[]): void
+
+ random(...args: any[]): void
+
+ square(...args: any[]): void
+
+ sub(...args: any[]): void
+
+ toRprBE(...args: any[]): void
+
+ toRprBEM(...args: any[]): void
+
+ toRprLE(...args: any[]): void
+
+ toRprLEM(...args: any[]): void
+
+ toString(...args: any[]): void
+ }
+
+ export class F3Field {
+ constructor(...args: any[])
+
+ add(...args: any[]): void
+
+ affine(...args: any[]): void
+
+ copy(...args: any[]): void
+
+ div(...args: any[]): void
+
+ double(...args: any[]): void
+
+ eq(...args: any[]): void
+
+ exp(...args: any[]): void
+
+ fromRng(...args: any[]): void
+
+ fromRprBE(...args: any[]): void
+
+ fromRprBEM(...args: any[]): void
+
+ fromRprLE(...args: any[]): void
+
+ fromRprLEM(...args: any[]): void
+
+ geq(...args: any[]): void
+
+ gt(...args: any[]): void
+
+ inv(...args: any[]): void
+
+ isZero(...args: any[]): void
+
+ leq(...args: any[]): void
+
+ lt(...args: any[]): void
+
+ mul(...args: any[]): void
+
+ mulScalar(...args: any[]): void
+
+ neg(...args: any[]): void
+
+ neq(...args: any[]): void
+
+ pow(...args: any[]): void
+
+ random(...args: any[]): void
+
+ square(...args: any[]): void
+
+ sub(...args: any[]): void
+
+ toRprBE(...args: any[]): void
+
+ toRprBEM(...args: any[]): void
+
+ toRprLE(...args: any[]): void
+
+ toRprLEM(...args: any[]): void
+
+ toString(...args: any[]): void
+ }
+
+ export class PolField {
+ constructor(...args: any[])
+
+ add(...args: any[]): void
+
+ computeVanishingPolinomial(...args: any[]): void
+
+ div(...args: any[]): void
+
+ double(...args: any[]): void
+
+ eq(...args: any[]): void
+
+ eval(...args: any[]): void
+
+ eval2(...args: any[]): void
+
+ evaluateLagrangePolynomials(...args: any[]): void
+
+ extend(...args: any[]): void
+
+ fft(...args: any[]): void
+
+ fft2(...args: any[]): void
+
+ ifft(...args: any[]): void
+
+ ifft2(...args: any[]): void
+
+ lagrange(...args: any[]): void
+
+ log2(...args: any[]): void
+
+ mul(...args: any[]): void
+
+ mulFFT(...args: any[]): void
+
+ mulNormal(...args: any[]): void
+
+ mulScalar(...args: any[]): void
+
+ normalize(...args: any[]): void
+
+ oneRoot(...args: any[]): void
+
+ reduce(...args: any[]): void
+
+ ruffini(...args: any[]): void
+
+ scaleX(...args: any[]): void
+
+ square(...args: any[]): void
+
+ sub(...args: any[]): void
+
+ toString(...args: any[]): void
+ }
+
+ export class ZqField {
+ constructor(...args: any[])
+
+ e(...args: any[]): any
+ add(...args: any[]): any
+ sub(...args: any[]): any
+ neg(...args: any[]): any
+ mul(...args: any[]): any
+ mulScalar(...args: any[]): any
+ square(...args: any[]): any
+ eq(...args: any[]): any
+ neq(...args: any[]): any
+ lt(...args: any[]): any
+ gt(...args: any[]): any
+ leq(...args: any[]): any
+ geq(...args: any[]): any
+ div(...args: any[]): any
+ idiv(...args: any[]): any
+ inv(...args: any[]): any
+ mod(...args: any[]): any
+ pow(...args: any[]): any
+ exp(...args: any[]): any
+ band(...args: any[]): any
+ bor(...args: any[]): any
+ bxor(...args: any[]): any
+ bnot(...args: any[]): any
+ shl(...args: any[]): any
+ shr(...args: any[]): any
+ land(...args: any[]): any
+ lor(...args: any[]): any
+ lnot(...args: any[]): any
+ sqrt_old(...args: any[]): any
+ normalize(...args: any[]): any
+ random(...args: any[]): any
+ toString(...args: any[]): any
+ isZero(...args: any[]): any
+ fromRng(...args: any[]): any
+
+ fromRprBE(...args: any[]): void
+
+ fromRprBEM(...args: any[]): void
+
+ fromRprLE(...args: any[]): void
+
+ fromRprLEM(...args: any[]): void
+
+ toRprBE(...args: any[]): void
+
+ toRprBEM(...args: any[]): void
+
+ toRprLE(...args: any[]): void
+
+ toRprLEM(...args: any[]): void
+ }
+
+ export function buildBls12381(singleThread: any, plugins: any): any
+
+ export function buildBn128(singleThread: any, plugins: any): any
+
+ export function getCurveFromName(name: any, singleThread?: any, plugins?: any): any
+
+ export function getCurveFromQ(q: any, singleThread: any, plugins: any): any
+
+ export function getCurveFromR(r: any, singleThread: any, plugins: any): any
+
+ export namespace Scalar {
+ const one: any
+
+ const zero: any
+
+ function abs(a: any): any
+
+ function add(a: any, b: any): any
+
+ function band(a: any, b: any): any
+
+ function bitLength(a: any): any
+
+ function bits(n: any): any
+
+ function bor(a: any, b: any): any
+
+ function bxor(a: any, b: any): any
+
+ function div(a: any, b: any): any
+
+ function e(s: any, radix: any): any
+
+ function eq(a: any, b: any): any
+
+ function exp(a: any, b: any): any
+
+ function fromArray(a: any, radix: any): any
+
+ function fromRprBE(buff: any, o: any, n8: any): any
+
+ function fromRprLE(buff: any, o: any, n8: any): any
+
+ function fromString(s: any, radix: any): any
+
+ function geq(a: any, b: any): any
+
+ function gt(a: any, b: any): any
+
+ function isNegative(a: any): any
+
+ function isOdd(a: any): any
+
+ function isZero(a: any): any
+
+ function land(a: any, b: any): any
+
+ function leq(a: any, b: any): any
+
+ function lnot(a: any): any
+
+ function lor(a: any, b: any): any
+
+ function lt(a: any, b: any): any
+
+ function mod(a: any, b: any): any
+
+ function mul(a: any, b: any): any
+
+ function naf(n: any): any
+
+ function neg(a: any): any
+
+ function neq(a: any, b: any): any
+
+ function pow(a: any, b: any): any
+
+ function shiftLeft(a: any, n: any): any
+
+ function shiftRight(a: any, n: any): any
+
+ function shl(a: any, n: any): any
+
+ function shr(a: any, n: any): any
+
+ function square(a: any): any
+
+ function sub(a: any, b: any): any
+
+ function toArray(s: any, radix: any): any
+
+ function toLEBuff(a: any): any
+
+ function toNumber(s: any): any
+
+ function toRprBE(buff: any, o: any, e: any, n8: any): void
+
+ function toRprLE(buff: any, o: any, e: any, n8: any): void
+
+ function toString(a: any, radix: any): any
+ }
+
+ export namespace utils {
+ function array2buffer(arr: any, sG: any): any
+
+ function beBuff2int(buff: any): any
+
+ function beInt2Buff(n: any, len: any): any
+
+ function bitReverse(idx: any, bits: any): any
+
+ function buffReverseBits(buff: any, eSize: any): void
+
+ function buffer2array(buff: any, sG: any): any
+
+ function leBuff2int(buff: any): any
+
+ function leInt2Buff(n: any, len: any): any
+
+ function log2(V: any): any
+
+ function stringifyBigInts(o: any): any
+
+ function stringifyFElements(F: any, o: any): any
+
+ function unstringifyBigInts(o: any): any
+
+ function unstringifyFElements(F: any, o: any): any
+ }
+}
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