How to Integrate PQC into Existing ZK-SNARK Trusted Setups

Zero-Knowledge Succinct Non-Interactive Arguments of Knowledge (ZK-SNARKs) rely on a trusted setup ceremony to generate a Common Reference String (CRS). The security of this CRS is currently based on classical cryptographic assumptions, such as the hardness of the Discrete Logarithm Problem (DLP) over elliptic curve groups. The advent of quantum computers poses a significant threat to these classical assumptions, potentially allowing an adversary to break the soundness of the proof system. Integrating Post-Quantum Cryptography (PQC) aims to create a hybrid or transitional setup that remains secure against both classical and quantum adversaries.

The core challenge is that PQC algorithms, like those based on lattices or hash functions, operate on fundamentally different mathematical structures than the elliptic curves used in SNARKs (e.g., BN254, BLS12-381). You cannot simply replace the elliptic curve pairing with a lattice-based operation. Instead, integration typically follows one of two paths: creating a hybrid cryptographic layer that combines classical and PQC security, or designing a post-quantum SNARK from the ground up and establishing a new, quantum-safe trusted setup for it. This guide focuses on the pragmatic approach of augmenting an existing setup.

A practical integration method involves using a PQC digital signature scheme, such as Dilithium (selected for standardization by NIST), to secure the transcript of the trusted setup ceremony. In a multi-party computation (MPC) ceremony, each participant's contribution is signed with their PQC private key before being aggregated. This creates a cryptographic record that is verifiable even if an attacker later gains quantum capabilities and attempts to forge a classical ECDSA signature. The ceremony's final output remains a classically secure CRS, but the process of creating it gains quantum-resistant accountability.

For developers, implementing this requires modifying the ceremony coordinator software. After a participant generates their contribution (a tau polynomial), they must also produce a PQC signature over the contribution's hash. The coordinator verifies both the classical proof (e.g., a Powers of Tau verification) and the PQC signature before accepting the contribution. Libraries like liboqs (Open Quantum Safe) provide bindings for languages like C, C++, and Python, enabling the integration of algorithms like Dilithium3 into existing ceremony tools.

Looking forward, full integration requires post-quantum secure zk-SNARK constructions like Ligero++ or Brakedown, which use hash-based or code-based assumptions. These systems would necessitate entirely new trusted setup protocols designed for their specific security requirements. The current transitional approach of hybrid signatures provides a crucial stopgap, allowing projects to future-proof their ceremony integrity while the ecosystem develops mature, quantum-native proving systems. This layered defense strategy is a recommended best practice for any project conducting a new trusted setup today.

Before attempting to integrate PQC algorithms, you must have a strong grasp of the underlying cryptographic primitives. This includes a working understanding of elliptic curve cryptography (ECC) used in current setups (e.g., the BLS12-381 curve in Groth16) and the fundamentals of lattice-based cryptography, which forms the basis for leading PQC candidates like CRYSTALS-Dilithium and CRYSTALS-Kyber. Familiarity with the Fiat-Shamir heuristic and the concept of a Common Reference String (CRS) is essential, as these are core components of most SNARK trusted setups.

You should be comfortable with the mechanics of a trusted setup ceremony, such as the Powers of Tau or Perpetual Powers of Tau. Understand the role of sequential contributions, the use of random beacons, and the security model that assumes at least one participant is honest. It's critical to know that the security of the final parameters relies on the computational hardness of the underlying problem (e.g., the Discrete Log Problem for ECC), which is what PQC aims to replace with quantum-resistant alternatives.

From a practical standpoint, experience with relevant libraries is necessary. For existing setups, this often means tools like snarkjs, libff, or arkworks. For PQC, you should explore implementations from the NIST Post-Quantum Cryptography Standardization project, such as the liboqs library or language-specific bindings. You'll need to understand how to generate and serialize cryptographic parameters and keys in these new formats.

Finally, recognize the core challenge: PQC integration is not a simple swap. Lattice-based operations are fundamentally different from elliptic curve operations. They often involve larger key and signature sizes, different algebraic structures, and new performance characteristics. Your goal is to map the abstract phases of a trusted setup—parameter generation, contribution, and verification—onto these new mathematical foundations while preserving the protocol's security guarantees.

The first step is a thorough audit of your current trusted setup. Identify the specific ZK-SNARK proving system you are using, such as Groth16, Plonk, or Marlin. For each, document the exact structured reference string (SRS) or common reference string (CRS) it relies on. This includes the SRS size (e.g., the number of powers of tau), the elliptic curve (e.g., BN254, BLS12-381), and the ceremony parameters (e.g., participant count, contribution mechanism). Tools like snarkjs can be used to inspect existing .ptau files to extract this metadata.

Next, catalog all cryptographic primitives your setup's security depends on. This is critical for understanding the quantum threat surface. For systems based on elliptic curve pairings (like Groth16), the security relies on the elliptic curve discrete logarithm problem (ECDLP). You must note the specific hardness assumptions, such as the q-SDH assumption used in Groth16. Document any hash functions (like SHA-256 in MiMC) used within the circuit. This inventory forms your migration target list for PQC replacement.

Finally, evaluate the trust model and ceremony integrity. Determine if your setup is a universal (updatable) or circuit-specific setup. For universal setups, assess the procedure for safely transitioning to a new SRS. You must also verify the ceremony transcript for your current setup. Ensure you have the final contribution hash and, if possible, the contribution proofs from participants. This establishes a verifiable baseline before any modification, which is essential for maintaining trust during the migration process. The goal is to enter the PQC integration phase with a complete, unambiguous specification of the legacy system.

The core of a hybrid PQC/SNARK system is the selection of two cryptographic primitives: a post-quantum digital signature and a post-quantum key encapsulation mechanism (KEM). The signature secures the ceremony's transcript and participant authentication, while the KEM protects the communication channels used to distribute secret shares. For signatures, consider standardized finalists from the NIST PQC project like Dilithium (for general use) or SPHINCS+ (for conservative, hash-based security). For KEMs, Kyber (now ML-KEM) is the primary NIST standard, though Classic McEliece offers a stronger security reduction at the cost of larger key sizes.

With primitives chosen, you must select a construction—the architectural blueprint for how these algorithms integrate with the existing trusted setup. A common approach is the hybrid mode defined in NIST SP 800-56C Rev. 2, which combines a classical algorithm (like ECDSA or ECDH) with a PQC counterpart. This ensures cryptographic agility and backward compatibility. For a Groth16 or Plonk setup, this means participants would generate two signature keys (one classical, one PQC) and perform two KEM operations for each share transmission, creating a system that is secure against both classical and quantum adversaries.

The construction must also define the trust model for the PQC components. Will the ceremony require a majority of PQC signatures to approve the final transcript, or will a single valid PQC signature suffice alongside the classical one? This decision impacts the ceremony's resilience. Furthermore, the construction must specify how to handle the potentially larger key and signature sizes of PQC algorithms in the ceremony's communication protocol, ensuring network overhead does not compromise practicality.

Implementation requires careful protocol design. For example, when a participant contributes their secret to the Powers of Tau ceremony, they would sign their contribution with both an ECDSA and a Dilithium signature. The coordinator would then verify both before accepting the update. Similarly, the coordinator would encrypt the updated transcript for the next participant using both an ECDH-Kyber hybrid KEM. Libraries like liboqs (Open Quantum Safe) provide tested implementations for these algorithms, which can be integrated into existing setup software like the snarkjs or arkworks ecosystems.

Finally, document your primitive and construction choices explicitly in the ceremony specification. This includes the exact algorithm variants (e.g., Dilithium3, Kyber768), the hybrid construction standard (e.g., NIST SP 800-56C), and the trust model. This transparency allows for independent security analysis and sets a clear standard for all participants, ensuring the upgrade enhances the setup's security without introducing ambiguity or implementation inconsistencies.

The core challenge is to construct a new Structured Reference String (SRS) that is secure against both classical and quantum adversaries. This requires replacing the original elliptic curve operations, typically over BN254 or BLS12-381, with a post-quantum secure cryptographic primitive. The most promising candidate for this is lattice-based cryptography, specifically schemes built on the Learning With Errors (LWE) or Module-LWE problems. The new ceremony must generate public parameters (the PQC-SRS) that can be used to commit to polynomials and verify proofs, mirroring the functionality of the original setup but with quantum resistance.

Designing the ceremony involves defining new algorithms for the Powers of Tau phase. Instead of operating in an elliptic curve group where the discrete log is hard, participants will perform computations in a lattice-based commitment scheme, such as one based on Kate-Zaverucha-Goldberg (KZG) commitments instantiated with Module-LWE. Each participant i receives the previous SRS, applies a secret random scalar s_i to it (through specific lattice operations), and outputs a transformed SRS and a proof of correct computation. The final output is a structured string of lattice elements that can be used to commit to a polynomial f(x) as Com(f) = f(τ) * G, where G is now a public lattice basis and operations are performed modulo a lattice-defined modulus q.

A critical technical requirement is backward compatibility or a clear migration path. If the goal is to upgrade an existing application (e.g., a rollup), you must decide whether the new PQC-SRS will run in parallel, requiring a bridging verifier that understands both proof systems, or if it will completely replace the old one after a hard fork. The ceremony software itself must be adapted; for example, a tool like the Power of Tau Coordinator would need its cryptographic backend swapped out to use libraries like OpenFHE or Microsoft SEAL for lattice operations.

Security considerations are paramount. The ceremony must maintain the trusted setup security model: if at least one participant is honest and destroys their toxic waste (s_i), the final SRS is secure. This property must be proven for the new lattice construction. Furthermore, the design must guard against quantum-specific attacks on the multi-party computation protocol itself. The final ceremony design document should specify the exact lattice parameters (dimension n, modulus q, error distribution), the participant onboarding process, and the verification software for auditors.

Integrating post-quantum cryptography (PQC) into an existing trusted setup begins with a critical assessment. You must first audit your current ceremony's cryptographic stack. Identify the specific elliptic curve (e.g., BN254, BLS12-381) and the underlying pairing-friendly group used for the Structured Reference String (SRS). This determines which PQC algorithms are compatible for replacement. The primary target is the discrete logarithm problem within the group, which is vulnerable to Shor's algorithm. The goal is to augment or replace this component with a post-quantum secure cryptographic assumption, such as those based on lattice problems (e.g., Module-LWE) or isogenies.

A hybrid or transitional approach is often the most practical migration path. Instead of a full, immediate replacement, you can implement a PQC wrapper around the existing classical setup. One method is to use a PQC-secure digital signature scheme (like Dilithium or Falcon) to attest to the integrity of each participant's contribution during the multi-party computation (MPC). This adds a layer of quantum-resistant authentication to the ceremony transcript, protecting against forgery in a post-quantum future while the core SRS generation remains classically secure for now.

For a full integration, you must select a post-quantum secure zk-SNARK construction. Promising candidates include Ligero++, Brakedown, or STARKs, which are based on hash functions (quantum-resistant) rather than discrete logarithms. Migration requires rebuilding your circuit compiler toolchain (e.g., Circom, arkworks) to target these new backends. This involves generating new proving and verification keys from a fresh, PQC-based trusted setup. Expect significant changes to proving time, proof size, and verification gas costs on-chain, which must be benchmarked against your application's requirements.

The technical implementation involves several concrete steps. First, choose a PQC library like Open Quantum Safe (liboqs) or a specialized zk-SNARK library such as Nova-Scotia. Next, modify your trusted setup ceremony software to integrate the new cryptographic primitives. For a Phase 2 Perpetual Powers of Tau setup, this means altering the contribution mechanism to work with the new algebra. You must also update all verifier contracts on-chain to use the new verification algorithm. Thoroughly test the new pipeline with a testnet ceremony before committing mainnet assets.

A successful migration mandates a clear rollout strategy. Plan for a dual-proof period where your system accepts both the old classical proofs and the new PQC-secure proofs, allowing users and applications to transition smoothly. Monitor the evolving NIST PQC standardization process, as final standards (FIPS 203, 204, 205) will inform long-term algorithm choices. Document the entire process and consider open-sourcing your ceremony tooling to enhance transparency and security for the broader community, reinforcing the trustlessness of the new setup.

Integrating PQC into your ZK-SNARK trusted setup is a multi-phase process. Start with a cryptographic audit of your current system, identifying all components that rely on classical hardness assumptions vulnerable to quantum attacks. This includes the underlying elliptic curve (like BN254 or BLS12-381), the hash function used in the commitment scheme, and any symmetric encryption. Tools like the NIST Post-Quantum Cryptography Standardization project provide the definitive list of approved algorithms, such as CRYSTALS-Dilithium for signatures and CRYSTALS-Kyber for key encapsulation.

The core technical challenge is replacing the elliptic curve pairing. Current ZK-SNARKs (e.g., Groth16) rely on pairings over specific curves. You must migrate to a post-quantum secure cryptographic group, such as one based on isogenies or lattice-based constructions. This is not a drop-in replacement; it requires modifying the underlying arithmetic circuits and the trusted setup ceremony protocol itself. Research from projects like ZPrize and academic papers on "SNARKs for all" provide essential guidance on constructing SNARKs over new cryptographic backbones.

For a practical migration, consider a hybrid approach. Implement a dual-signature scheme where the ceremony transcript is signed with both the classical ECDSA and a PQC algorithm like Dilithium. This creates a transitional layer of security. Furthermore, you can design your system to be algorithm-agile, allowing the underlying cryptographic primitives to be swapped via governance or upgradeable contracts as PQC standards mature. This is crucial given that NIST standards are still evolving and performance optimizations are ongoing.

Next, focus on performance and tooling. PQC algorithms often have larger key and signature sizes, impacting proof generation time and on-chain verification gas costs. Benchmark your modified prover and verifier using libraries like liboqs. You will likely need to optimize circuit constraints and explore recursive proof aggregation to manage increased computational load. Engaging with the open-source communities around zk-SNARK frameworks (e.g., Circom, Halo2, Noir) is critical to stay abreast of PQC integration efforts.

Finally, security and transparency remain paramount. Any new trusted setup ceremony for a PQC-enhanced system must be executed with the same rigorous, multi-party computation (MPC) procedures and public auditing as classical setups. Document the entire migration process, publish the new circuits and ceremony transcripts, and encourage third-party review. The goal is not just to adopt PQC, but to maintain and enhance the trustless guarantees that make ZK-SNARKs valuable for applications like private transactions and scalable rollups.