Zero-Knowledge Proofs in Rust & Circom: SnarkJS Verification & Production Guide

Table of Contents(14 sections)
Zero-Knowledge Proofs (ZKPs) enable one party (the prover) to convince another party (the verifier) that a statement is true, without revealing any information beyond the validity of the statement itself. This guide details the practical implementation of ZKPs using Circom for circuit definition, Rust with arkworks for proof generation, and SnarkJS for verification, including integration with Solidity.
High-Performance Systems & Modern Databases
ZKP Fundamentals & Architecture
At its core, a ZKP system involves:
- Statement Definition: A mathematical statement to be proven.
- Circuit Design: Translating the statement into an arithmetic circuit.
- Witness Generation: Computing private inputs (witnesses) that satisfy the circuit.
- Proof Generation: Creating a cryptographic proof based on the circuit and witness.
- Proof Verification: Checking the validity of the proof against public inputs.
We will focus on zk-SNARKs (Zero-Knowledge Succinct Non-Interactive Argument of Knowledge), specifically Groth16, due to its efficiency and widespread adoption.
Architecture Overview
Our production architecture involves:
- Circom: Domain-specific language for defining arithmetic circuits. Compiles to R1CS (Rank-1 Constraint System) and WASM for witness generation.
- Rust (
arkworks): High-performance library for cryptographic primitives, used for Groth16 proof generation. This can run in a dedicated microservice. - SnarkJS: JavaScript library for witness generation (using WASM output from Circom) and proof verification (both off-chain and on-chain via Solidity verifier contracts).
- Solidity: Smart contract language for on-chain proof verification.
Circuit Design with Circom
Circom is a DSL for defining arithmetic circuits. It compiles to an R1CS representation, which is a set of quadratic equations over a finite field.
Example: Identity Proof Circuit (identity.circom)
This circuit proves knowledge of a secret input x satisfying the constraint that it equals public input identity_hash. This is a simplified identity proof.
pragma circom 2.1.5;
template IdentityProof() {
signal input x; // Private input
signal input identity_hash; // Public input
// Constraint: x must equal identity_hash
x === identity_hash;
}
component main = IdentityProof();
Example: Range Proof Circuit (range.circom)
This circuit proves that a secret input x lies within a specific range [min, max] without revealing x. We'll use a bit decomposition approach.
pragma circom 2.1.5;
// Helper component to check if a number is within a range [0, N-1]
// by decomposing it into bits.
template Num2Bits(n) {
signal input in;
signal output out[n];
var sum = 0;
for (var i = 0; i < n; i++) {
out[i] <-- (in >> i) & 1; // Extract i-th bit
out[i] * (1 - out[i]) === 0; // Constraint: bit must be 0 or 1
sum += out[i] * (1 << i);
}
sum === in; // Constraint: sum of bits must equal input
}
template RangeProof(n_bits, min_val, max_val) {
signal input x; // Private input
signal input public_min; // Public input (for flexibility, can be hardcoded)
signal input public_max; // Public input (for flexibility, can be hardcoded)
// Ensure x is non-negative (if range starts from 0)
// For simplicity, we assume x >= 0. If negative numbers are possible,
// a more complex range check is needed.
// Check x >= public_min
signal diff_min;
diff_min <== x - public_min;
component bits_diff_min = Num2Bits(n_bits); // n_bits should be sufficient for max_val - min_val
bits_diff_min.in <== diff_min;
// Check x <= public_max
signal diff_max;
diff_max <== public_max - x;
component bits_diff_max = Num2Bits(n_bits); // n_bits should be sufficient for max_val - min_val
bits_diff_max.in <== diff_max;
// Public inputs must match the hardcoded range for this specific proof instance
public_min === min_val;
public_max === max_val;
}
// Example: Prove x is in range [10, 100] using 8 bits (max value 2^8 - 1 = 255)
component main = RangeProof(8, 10, 100);
Compiling Circom Circuits
To compile these circuits, you need circom installed.
# Install circom if not already installed
# npm install -g circom_tester # or yarn global add circom_tester
# Compile IdentityProof
circom identity.circom --r1cs --wasm --sym --json
# Compile RangeProof
circom range.circom --r1cs --wasm --sym --json
This generates:
.r1cs: The R1CS constraint system._js/: Directory containingwitness_calculator.jsand*.wasmfor witness generation..sym: Debugging symbols..json: Circuit information.
Trusted Setup
Groth16 requires a trusted setup. For production, use a multi-party computation (MPC) ceremony. For development, snarkjs can generate a phase 1 setup.
# Generate a new trusted setup (powers of tau)
snarkjs powersoftau new bn128 12 pot12_0000.ptau -v
# Contribute to the setup (simulated for dev)
snarkjs powersoftau contribute pot12_0000.ptau pot12_0001.ptau --name="First contribution" -v
# Apply the circuit-specific phase 2 setup for IdentityProof
snarkjs groth16 setup identity.r1cs pot12_0001.ptau identity_0000.zkey
# Contribute to the phase 2 setup (simulated for dev)
snarkjs zkey contribute identity_0000.zkey identity_final.zkey --name="Second contribution" -v
# Export verification key
snarkjs zkey export verificationkey identity_final.zkey verification_key_identity.json
# Repeat for RangeProof
snarkjs groth16 setup range.r1cs pot12_0001.ptau range_0000.zkey
snarkjs zkey contribute range_0000.zkey range_final.zkey --name="Range contribution" -v
snarkjs zkey export verificationkey range_final.zkey verification_key_range.json
The identity_final.zkey and range_final.zkey files contain the proving key, and verification_key_identity.json / verification_key_range.json contain the verification key.
Witness Generation with SnarkJS
Witness generation is typically done on the client-side or in a dedicated service. snarkjs provides a JavaScript API for this.
// witness_generator.ts
import { WitnessCalculator } from 'circom_runtime';
import * as fs from 'fs';
import * as path from 'path';
async function generateWitness(circuitName: string, inputs: Record<string, any>): Promise<any> {
const wasmPath = path.join(__dirname, `${circuitName}_js`, `${circuitName}.wasm`);
const witnessCalculator = await WitnessCalculator(fs.readFileSync(wasmPath));
const fullWitness = await witnessCalculator.calculateWitness(inputs, true);
// The first element is the signal `1`, subsequent elements are public inputs, then private inputs.
// We usually only need the full witness for proof generation.
return fullWitness;
}
// Example usage for IdentityProof
async function generateIdentityWitness() {
const privateX = 12345;
const publicIdentityHash = 12345; // Must match privateX for a valid proof
const inputs = {
x: privateX,
identity_hash: publicIdentityHash,
};
console.log(`Generating witness for IdentityProof with inputs: ${JSON.stringify(inputs)}`);
const witness = await generateWitness('identity', inputs);
console.log('IdentityProof Witness generated.');
// In a real scenario, you might serialize this witness or pass it directly.
// For arkworks, we need the public inputs and the full witness.
// The arkworks prover expects a specific format, typically a vector of field elements.
// The witness array from snarkjs is already field elements.
return { witness, publicInputs: [publicIdentityHash] };
}
// Example usage for RangeProof
async function generateRangeWitness() {
const privateX = 50;
const publicMin = 10;
const publicMax = 100;
const inputs = {
x: privateX,
public_min: publicMin,
public_max: publicMax,
};
console.log(`Generating witness for RangeProof with inputs: ${JSON.stringify(inputs)}`);
const witness = await generateWitness('range', inputs);
console.log('RangeProof Witness generated.');
return { witness, publicInputs: [publicMin, publicMax] };
}
// To run:
// ts-node witness_generator.ts
// (Ensure circom_runtime is installed: npm install circom_runtime)
Proof Generation with Rust (arkworks)
Rust with arkworks provides a robust and performant environment for ZKP operations. We'll use ark-circom to load the R1CS and ark-groth16 for proof generation.
First, set up your Rust project:
cargo new --bin zkp_prover
cd zkp_prover
Add dependencies to Cargo.toml:
[package]
name = "zkp_prover"
version = "0.1.0"
edition = "2021"
[dependencies]
ark-bn254 = { version = "0.4.0", features = ["curve"] }
ark-circom = "0.4.0"
ark-ff = "0.4.0"
ark-groth16 = "0.4.0"
ark-relations = "0.4.0"
ark-std = { version = "0.4.0", features = ["print-trace"] }
serde = { version = "1.0", features = ["derive"] }
serde_json = "1.0"
hex = "0.4"
Now, the Rust code for proof generation. This example assumes the identity_final.zkey and identity.r1cs files are accessible.
// src/main.rs
use ark_bn254::{Bn254, Fr};
use ark_circom::{CircomBuilder, CircomCircuit, R1CS};
use ark_ff::{BigInt, PrimeField};
use ark_groth16::{
create_random_proof, generate_random_parameters, prepare_verifying_key, verify_proof, Proof,
};
use ark_std::{rand::thread_rng, UniformRand};
use serde::{Deserialize, Serialize};
use std::{collections::HashMap, fs::File, io::BufReader, path::PathBuf};
// Structure to hold the proof data for serialization
#[derive(Serialize, Deserialize, Debug)]
pub struct Groth16Proof {
pub a: Vec<String>, // G1 point (x, y)
pub b: Vec<Vec<String>>, // G2 point (x[0], x[1], y[0], y[1])
pub c: Vec<String>, // G1 point (x, y)
}
impl From<Proof<Bn254>> for Groth16Proof {
fn from(proof: Proof<Bn254>) -> Self {
Self {
a: vec![
format!("{:?}", proof.a.x),
format!("{:?}", proof.a.y),
],
b: vec![
vec![
format!("{:?}", proof.b.x.c0),
format!("{:?}", proof.b.x.c1),
],
vec![
format!("{:?}", proof.b.y.c0),
format!("{:?}", proof.b.y.c1),
],
],
c: vec![
format!("{:?}", proof.c.x),
format!("{:?}", proof.c.y),
],
}
}
}
// Helper to convert field elements to BigInt for CircomBuilder
fn field_to_bigint<F: PrimeField>(f: F) -> BigInt<4> {
f.into_bigint()
}
async fn generate_identity_proof(
r1cs_path: PathBuf,
zkey_path: PathBuf,
private_x: u64,
public_identity_hash: u64,
) -> Result<(Groth16Proof, Vec<Fr>), Box<dyn std::error::Error>> {
let mut rng = thread_rng();
// 1. Load R1CS
let r1cs = R1CS::from_file(r1cs_path)?;
// 2. Create CircomBuilder and assign inputs
let mut builder = CircomBuilder::new(r1cs);
builder.push_input("x", private_x);
builder.push_input("identity_hash", public_identity_hash);
// 3. Build the circuit and generate the witness
let circuit = builder.setup();
let full_assignments = circuit.generate_witness()?;
// Extract public inputs from the full witness
// The first element is always 1, then public inputs, then private inputs.
// For IdentityProof, public_identity_hash is the only public input.
let public_inputs = vec![full_assignments[1]]; // Assuming identity_hash is the first public signal after 1
// 4. Load proving key from zkey file
// In a real scenario, you'd load the proving key directly, not generate it.
// For simplicity, we'll generate parameters here using the R1CS.
// For production, the `zkey_path` would contain the pre-computed proving key.
// ark-circom's `CircomBuilder` can directly load the proving key from a zkey.
// However, `ark-groth16` expects `ProvingKey`.
// A more direct way to load from zkey is complex due to `ark-circom`'s current API.
// For this example, we'll generate parameters from R1CS, which is NOT production-ready.
// Production: Load PK from `zkey_path` (e.g., using `snarkjs zkey export json` and parsing).
let params = generate_random_parameters::<Bn254, _, _>(circuit.clone(), &mut rng)?;
// 5. Create the proof
let proof = create_random_proof(circuit, params, &mut rng)?;
Ok((proof.into(), public_inputs))
}
#[tokio::main]
async fn main() -> Result<(), Box<dyn std::error::Error>> {
// Paths to your compiled Circom artifacts and zkey
let r1cs_path = PathBuf::from("./identity.r1cs");
let zkey_path = PathBuf::from("./identity_final.zkey"); // This is the proving key
let private_x = 12345;
let public_identity_hash = 12345;
println!("Generating IdentityProof...");
let (proof, public_inputs) = generate_identity_proof(
r1cs_path,
zkey_path,
private_x,
public_identity_hash,
).await?;
println!("Proof generated: {:?}", proof);
println!("Public inputs: {:?}", public_inputs);
// For verification, you would typically send `proof` and `public_inputs` to a verifier.
// Here, we'll demonstrate local verification using ark-groth16.
// In production, the verification key would be loaded from `verification_key_identity.json`.
// Load verification key (for local verification demonstration)
let vk_file = File::open("./verification_key_identity.json")?;
let vk_json: serde_json::Value = serde_json::from_reader(BufReader::new(vk_file))?;
// Parse the verification key from JSON into ark-groth16's `VerifyingKey` struct.
// This parsing is non-trivial and requires careful mapping of JSON fields to struct fields.
// For simplicity, we'll re-generate VK from params for local verification.
// Production: Parse `verification_key_identity.json` into `ark_groth16::VerifyingKey<Bn254>`.
// This is a complex step due to the structure of `ark-groth16`'s `VerifyingKey` and `snarkjs`'s JSON output.
// A common approach is to use `snarkjs zkey export solidityverifier` and then use the generated Solidity contract.
// Or, write a custom parser for the `verification_key_identity.json` into `ark_groth16::VerifyingKey`.
// For this example, we'll use the `params` generated earlier to get the VK.
// This means the local verification uses the same setup as proof generation, which is not how production works.
// In production, the VK is fixed after trusted setup.
let r1cs_for_vk = R1CS::from_file(PathBuf::from("./identity.r1cs"))?;
let circuit_for_vk = CircomBuilder::new(r1cs_for_vk).setup();
let params_for_vk = generate_random_parameters::<Bn254, _, _>(circuit_for_vk, &mut rng)?;
let pvk = prepare_verifying_key(¶ms_for_vk.vk);
// Convert the generated proof back to ark-groth16's Proof struct for local verification
let ark_proof = Proof {
a: ark_bn254::G1Affine::new(
Fr::from_str_radix(&proof.a[0].trim_start_matches("0x"), 16)?,
Fr::from_str_radix(&proof.a[1].trim_start_matches("0x"), 16)?,
),
b: ark_bn254::G2Affine::new(
ark_bn254::Fq2::new(
Fr::from_str_radix(&proof.b[0][0].trim_start_matches("0x"), 16)?,
Fr::from_str_radix(&proof.b[0][1].trim_start_matches("0x"), 16)?,
),
ark_bn254::Fq2::new(
Fr::from_str_radix(&proof.b[1][0].trim_start_matches("0x"), 16)?,
Fr::from_str_radix(&proof.b[1][1].trim_start_matches("0x"), 16)?,
),
),
c: ark_bn254::G1Affine::new(
Fr::from_str_radix(&proof.c[0].trim_start_matches("0x"), 16)?,
Fr::from_str_radix(&proof.c[1].trim_start_matches("0x"), 16)?,
),
};
let is_valid = verify_proof(&pvk, &ark_proof, &public_inputs)?;
println!("Local verification result: {}", is_valid);
Ok(())
}
Important Note on Rust Prover: The generate_random_parameters call in the Rust example is for demonstration and local testing. In a production environment, the proving key (PK) would be loaded from the zkey_path generated during the trusted setup, not re-generated. Loading a ProvingKey from a snarkjs .zkey file directly into ark-groth16 is non-trivial due to format differences. A common workaround is to use snarkjs zkey export json and then parse that JSON into ark-groth16's ProvingKey structure, or to use ark-circom's CircomProver which handles zkey loading. The provided Groth16Proof struct is for serializing the ark-groth16 proof into a format compatible with SnarkJS/Solidity.
Proof Verification with SnarkJS
SnarkJS can verify proofs off-chain using the verification_key.json and the generated proof.
// verifier.ts
import * as snarkjs from 'snarkjs';
import * as fs from 'fs';
import * as path from 'path';
async function verifyProof(
circuitName: string,
publicInputs: any[],
proof: any
): Promise<boolean> {
const vKeyPath = path.join(__dirname, `verification_key_${circuitName}.json`);
const vKey = JSON.parse(fs.readFileSync(vKeyPath, 'utf-8'));
const res = await snarkjs.groth16.verify(vKey, publicInputs, proof);
return res;
}
// Example usage (assuming you have a proof and public inputs from the Rust prover)
async function runVerification() {
// These would typically come from the Rust prover service
const identityProof = {
pi_a: ["0x...", "0x...", "0x..."], // G1 point
pi_b: [["0x...", "0x..."], ["0x...", "0x..."]], // G2 point
pi_c: ["0x...", "0x...", "0x..."] // G1 point
};
const identityPublicInputs = ["12345"];
console.log('Verifying IdentityProof...');
const isValidIdentity = await verifyProof('identity', identityPublicInputs, identityProof);
console.log(`IdentityProof verification result: ${isValidIdentity}`);
// Example for RangeProof
const rangeProof = { /* ... */ };
const rangePublicInputs = ["10", "100"];
console.log('Verifying RangeProof...');
const isValidRange = await verifyProof('range', rangePublicInputs, rangeProof);
console.log(`RangeProof verification result: ${isValidRange}`);
}
// To run:
// ts-node verifier.ts
// (Ensure snarkjs is installed: npm install snarkjs)
The Groth16Proof struct in Rust is designed to serialize into a format that snarkjs.groth16.verify expects. The pi_a, pi_b, pi_c fields in SnarkJS correspond to a, b, c in ark-groth16.
On-Chain Verification with Solidity
For on-chain verification, snarkjs can generate a Solidity verifier contract.
# Export Solidity verifier for IdentityProof
snarkjs zkey export solidityverifier identity_final.zkey verifier_identity.sol
# Export Solidity verifier for RangeProof
snarkjs zkey export solidityverifier range_final.zkey verifier_range.sol
The generated verifier_identity.sol will contain a verifyProof function.
// verifier_identity.sol (simplified)
pragma solidity ^0.8.0;
contract Verifier {
function verifyProof(
uint[2] memory _pA,
uint[2][2] memory _pB,
uint[2] memory _pC,
uint[1] memory _pubSignals
) public view returns (bool) {
// ... cryptographic verification logic ...
// This function will return true if the proof is valid for the given public signals.
}
}
To call this from a DApp, you'd pass the proof components (pi_a, pi_b, pi_c) and public signals from your frontend or backend service.
// web3_verifier.ts (example using ethers.js)
import { ethers } from 'ethers';
import * as fs from 'fs';
import * as path from 'path';
// Assuming you have a deployed Verifier contract
const VERIFIER_CONTRACT_ADDRESS = "0x..."; // Replace with your deployed contract address
const VERIFIER_ABI = JSON.parse(fs.readFileSync(path.join(__dirname, 'Verifier_abi.json'), 'utf-8'));
async function verifyOnChain(
provider: ethers.Provider,
proof: any, // SnarkJS proof format
publicInputs: string[]
): Promise<boolean> {
const verifier = new ethers.Contract(VERIFIER_CONTRACT_ADDRESS, VERIFIER_ABI, provider);
// Convert SnarkJS proof format to Solidity-compatible format
const pA: [string, string] = [proof.pi_a[0], proof.pi_a[1]];
const pB: [[string, string], [string, string]] = [
[proof.pi_b[0][0], proof.pi_b[0][1]],
[proof.pi_b[1][0], proof.pi_b[1][1]]
];
const pC: [string, string] = [proof.pi_c[0], proof.pi_c[1]];
// Public signals need to be `uint` in Solidity, so convert from string
const pubSignals = publicInputs.map(s => ethers.BigNumber.from(s));
try {
const isValid = await verifier.verifyProof(pA, pB, pC, pubSignals);
return isValid;
} catch (error) {
console.error("On-chain verification failed:", error);
return false;
}
}
// Example usage:
// const provider = new ethers.JsonRpcProvider("YOUR_RPC_URL");
// const proof = { /* ... from Rust prover ... */ };
// const publicInputs = ["12345"];
// const isValid = await verifyOnChain(provider, proof, publicInputs);
// console.log(`On-chain verification result: ${isValid}`);
Architecture & Tradeoffs Comparison
| Feature/Aspect | Circom + SnarkJS (JS Prover) | Circom + Rust (arkworks Prover) |
|---|---|---|
| Prover Language | JavaScript/TypeScript | Rust |
| Performance (Proving) | Slower, WASM-based | Faster, native Rust |
| Witness Generation | SnarkJS (WASM) | SnarkJS (WASM) or custom Rust |
| Proving Key Loading | Direct from .zkey | Requires custom parsing or ark-circom specific handling |
| Verification (Off-chain) | SnarkJS (JS) | ark-groth16 (Rust) |
| Verification (On-chain) | SnarkJS-generated Solidity | SnarkJS-generated Solidity |
| Ecosystem Maturity | High for Circom/SnarkJS | High for arkworks (general crypto), growing for ZKP |
| Developer Experience | Easier for web devs | Steeper learning curve for Rust/crypto |
| Use Case | Client-side proving, smaller proofs | Server-side proving, high-throughput, large proofs |
Production Gotchas & Troubleshooting
-
Field Element Mismatch: All computations in ZKPs are over a finite field (e.g.,
Frfor BN254). Ensure all inputs (private and public) are within this field's modulus. Large numbers must be handled carefully, often requiring bit decomposition in circuits.- Symptom:
Constraint doesn't matcherrors during witness generation orInvalid proofduring verification. - Fix: Double-check input values. If using
BigIntin JavaScript, ensure they are correctly converted to field elements. In Circom,Num2Bitsis crucial for range checks.
- Symptom:
-
Trusted Setup Mismatch: Using a proving key (
.zkey) generated with one R1CS and trying to prove against a different R1CS will fail. Similarly, the verification key (.jsonor Solidity contract) must correspond to the exact proving key used.- Symptom:
Error: Invalid prooforError: Could not verify proofduring verification. - Fix: Always ensure the
.zkey,.r1cs, andverification_key.json(or Solidity verifier) originate from the same trusted setup and circuit compilation. Version control your.zkeyandverification_key.jsonfiles.
- Symptom:
-
Input Ordering for Public Signals: The order of public inputs passed to the verifier (both SnarkJS and Solidity) must exactly match the order in which they are declared as public signals in the Circom circuit. The first public signal in Circom becomes the first element in the
_pubSignalsarray in Solidity.- Symptom: Proof verifies successfully but for incorrect public inputs, or fails unexpectedly.
- Fix: Carefully inspect the
circuit.jsonor.symfile generated by Circom to determine the exact order of public inputs.
-
arkworksProving Key Loading: Directly loading asnarkjs.zkeyintoark-groth16'sProvingKeystruct is not straightforward.ark-circomoffers some utilities, but often requires custom parsing or usingsnarkjsto export thezkeyas JSON and then mapping it.- Symptom:
ark-groth16ProvingKeydeserialization errors or complex type mismatches. - Fix: For production, consider using
ark-circom'sCircomProverwhich is designed to work with Circom artifacts, or implement a robust JSON parser for thezkeyexport. Alternatively, generate theProvingKeydirectly withinarkworksif you control the entire setup process.
- Symptom:
-
Gas Costs for On-Chain Verification: Groth16 verification on Ethereum is expensive. The gas cost scales with the number of public inputs.
- Symptom: Transactions run out of gas or are prohibitively expensive.
- Fix: Minimize public inputs. Batch proofs if possible (though this adds complexity). Consider layer 2 solutions or off-chain verification for most use cases, only using on-chain verification for critical state transitions.
Frequently Asked Questions
-
Why use Circom for circuit definition instead of directly in Rust? Circom provides a high-level, domain-specific language optimized for expressing arithmetic circuits. It simplifies the process of translating mathematical statements into R1CS constraints, which is error-prone and verbose in general-purpose languages like Rust. While
arkworkshas circuit building primitives, Circom's abstraction is often preferred for initial circuit design and rapid iteration. -
What is the role of the
.zkeyfile? The.zkeyfile contains the proving key (PK) and the verification key (VK) for a specific circuit after the trusted setup phase. The PK is used by the prover to generate proofs, and the VK is used by the verifier to check proofs. It's a critical artifact that must be secured and versioned. -
Can I use a different proving system like Plonk or Marlin? Yes,
arkworkssupports other proving systems. However, the tooling (Circom, SnarkJS) is primarily optimized for Groth16. Using other systems would require differentarkworkscrates (e.g.,ark-plonk) and potentially custom integration for witness generation and verification, assnarkjsdoes not directly support them for all operations. -
How do I handle large private inputs (e.g., a 256-bit hash) in Circom? Circom operates over a finite field, typically
Frof BN254 (254 bits). For inputs larger than this, or for operations that require bit-level manipulation, you must decompose the large number into its constituent bits or limbs using components likeNum2Bitsor custom multi-limb arithmetic circuits. This increases circuit size and proving time. -
Is the trusted setup truly "trusted"? What are the risks? The Groth16 trusted setup is a critical component. If any participant in the setup ceremony retains their secret share, they could potentially forge proofs. For this reason, multi-party computation (MPC) ceremonies are used, where many participants contribute, and it's assumed that at least one participant is honest and discards their secret. For high-security applications, using a well-established, publicly audited MPC ceremony is paramount.
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