Parameter Generation

Parameter Generation and Trusted Setup

This document describes the parameter generation process and trusted setup ceremony for the Roru Protocol's zero-knowledge proof system.

Overview

Purpose

Generate the proving and verifying keys needed for zero-knowledge proof generation and verification.

Setup Types

Trusted Setup: Requires trust in setup participants.

Verifiable Setup: Setup can be verified but still requires some trust.

No Setup: No setup required (if possible).

Groth16 Setup

Setup Process

Phase 1: Powers of Tau

1. Generate random tau

2. Compute powers: tau, tau^2, ..., tau^n

3. Publish powers (without revealing tau)

Phase 2: Circuit-Specific

1. Generate random alpha, beta

2. Compute circuit-specific parameters

3. Combine with powers of tau

Setup Output

Proving Key: Used to generate proofs Verifying Key: Used to verify proofs

Multi-Party Computation

MPC Setup

Process:

1. Multiple participants

2. Each contributes randomness

3. Combine contributions

4. Final parameters computed

Security: As long as one participant is honest, setup is secure.

Ceremony Structure

Ceremony Steps:

1. Participant registration

2. Contribution phase

3. Verification phase

4. Finalization

Parameter Format

Proving Key

Key Structure:

• Circuit-specific parameters

• Precomputed values

• Optimization data

Verifying Key

Key Structure:

• Public verification parameters

• Circuit structure

• Verification data

Security Considerations

Trust Requirements

Trust Model:

• Trust in setup participants

• Trust in ceremony execution

• Trust in parameter distribution

Mitigation Strategies

Strategies:

• Multi-party computation

• Public ceremony

• Verifiable contributions

• Transparency

Parameter Distribution

Distribution Method

Distribution:

• Public verification keys

• Secure proving keys

• Hash verification

• Signature verification

Verification

Verification Process:

1. Download parameters

2. Verify hash

3. Verify signature

4. Use for proofs

Conclusion

Parameter generation provides:

• Security: Cryptographic parameters

• Trust: Transparent process

• Verification: Verifiable setup

• Distribution: Secure distribution

• Confidence: Trusted process

Understanding setup is essential for security.