Why Groth16's Optimization for Pairings Is an Architectural Mistake

Groth16's per-circuit trusted setup is a systemic vulnerability. Each new application requires a fresh, expensive, and risky ceremony, creating a permanent point of failure and operational overhead.

• Ceremony Cost: ~$100k+ per circuit, plus ongoing audit burden.
• Single Point of Failure: Compromise of a single toxic waste parameter invalidates all proofs.
• Operational Friction: Prevents agile development and deployment of new logic.

Optimization for a single pairing operation creates a hardware monoculture. It forces all provers onto a narrow, expensive path (high-end CPUs/GPUs) and is hostile to future acceleration (e.g., FPGAs, custom ASICs).

• Prover Diversity: Zero. All implementations target the same compute profile.
• Innovation Ceiling: Architectural rigidity prevents leveraging new hardware breakthroughs like parallel-friendly STARKs or PlonKish arithmetization.

Groth16 proofs are not recursion-friendly. Verifying a Groth16 proof inside another circuit is prohibitively expensive, blocking native proof aggregation and seamless L2→L1 bridging. This forces complex, trust-minimized bridging protocols like LayerZero and Across to rely on slower, heavier attestation schemes.

• Aggregation Cost: ~1M+ constraints per proof verification, making recursive SNARKs impractical.
• Systemic Latency: Prevents instant, cryptographic finality across chains.

Universal setups (PLONK) and recursion-native constructions (Halo2) solve Groth16's core flaws. They enable agile development and proof aggregation, forming the backbone of next-gen L2s like zkSync Era, Scroll, and Polygon zkEVM.

• Universal Trust: One-time setup for unlimited circuits.
• Recursion Native: Enables proof aggregation (e.g., Nova) for constant-time verification.
• Prover Flexibility: Supports a wider range of optimization and hardware strategies.

Every Groth16 circuit requires a one-time, multi-party trusted setup. While ceremonies like Zcash's Powers of Tau are impressive, they create a permanent security assumption. A single compromised participant can forge proofs. This is an architectural anachronism in an era of transparent (STARKs) or universal/updatable (Plonk) setups.

• Ceremony Size: Zcash's Sapling used ~90 participants.
• Attack Vector: A single malicious party with the final toxic waste can mint infinite coins.
• Maintenance Burden: Requires re-running for every new circuit.

Groth16 generates a proving key and verification key pair for each unique circuit. Changing a single logic gate invalidates the keys, requiring a new trusted setup. This makes iterative development, bug fixes, and protocol upgrades prohibitively expensive, locking teams into frozen logic.

• Dev Cost: Days/weeks of delay for minor circuit tweaks.
• Protocol Risk: Inability to patch vulnerabilities without a full ceremony.
• Contrast: Plonk's universal setup allows instant circuit updates.

Groth16's optimization is for a single pairing check, making verification extremely cheap on-chain. However, the prover workload is dominated by massive, non-parallelizable multiexponentiations within specific elliptic curve groups (BN254). This creates a hardware arms race, favoring expensive, specialized setups and pushing proof generation towards centralized services.

• Prover Cost: ~5-10x more expensive than Plonk for complex circuits.
• Hardware Lock-in: Optimized for few, high-end GPUs/ASICs.
• Ecosystem Risk: Centralizes prover infrastructure, undermining decentralization.

Groth16's efficiency is married to the BN254 elliptic curve, which lacks modern cryptographic agility. It is not quantum-safe and has known weaknesses (the "curse of small characteristic"). Migrating to newer, safer curves (e.g., BLS12-381) requires a full protocol overhaul. This creates technical debt that newer systems (using STARKs over finite fields) avoid.

• Quantum Vulnerability: Susceptible to Shor's algorithm.
• Ecosystem Fragmentation: Incompatible with modern curves used by Eth2, Filecoin.
• Future-Proofing: Zero. Requires a full rewrite to upgrade.

Groth16's per-circuit trusted setup is a permanent, non-upgradable liability. Every logic change demands a new, high-stakes ceremony, creating operational bottlenecks and governance risk.\n- Ceremony fatigue for developers and users\n- Single point of failure for the entire proof system\n- Contrasts with universal setups (e.g., Perpetual Powers of Tau) used by PLONK, Halo2

The proof system is hard-coded to a single arithmetic circuit. This is antithetical to modern, iterative protocol development seen in DeFi (Uniswap, Aave) and L2 rollups.\n- Zero runtime adaptability; cannot add new opcodes or constraints\n- Forks require full re-audit and re-trusting\n- Contrasts with SNARK VM approaches (RISC Zero, SP1) which separate proof logic from core verification.

Optimizing for a single EVM pairing precompile (ECADD, ECMUL) creates vendor lock-in and long-term cost risk. It's a bet on Ethereum's core opcode pricing never changing.\n- Binds cost model to a single L1's fee market\n- Inefficient for other VMs or future Ethereum upgrades (EIP-7702, Verkle Trees)\n- Contrasts with STARKs and newer SNARKs (Plonky2) using hash-based proofs, agnostic to VM cryptography.

Groth16 proofs are not inherently recursive. Building L2 validity rollups or proof aggregation layers requires complex, inefficient wrapping, negating its supposed efficiency.\n- Forces extra proof layers (e.g., Nova, Cycle of Curves) for aggregation\n- Increases finality latency and developer complexity\n- Contrasts with Plonky2 or Circom with Spartan, designed for native recursion.