Briefing
The core research problem in verifiable computation centers on the high asymptotic and concrete cost of generating proofs, which limits the scalability of zero-knowledge systems. This paper introduces Blaze, a novel multi-linear polynomial commitment scheme (MLPCS) constructed over binary extension fields by combining a code-switching technique with the highly efficient Repeat-Accumulate-Accumulate (RAA) error-correcting code. This composition is purely information-theoretic, allowing the prover’s time to inherit the code’s fast encoding time. The most important implication is the realization of a cryptographic primitive that delivers both extremely fast prover performance and significantly smaller proof sizes, fundamentally accelerating the throughput and reducing the on-chain cost of all SNARK-based scaling solutions.
Context
Before this work, the design of efficient Succinct Non-interactive Arguments of Knowledge (SNARKs) faced a fundamental trade-off in their underlying Polynomial Commitment Schemes (PCS). Schemes often achieved either near-linear prover time (e.g. Brakedown) at the expense of large, non-succinct proof sizes, or succinct proof sizes (e.g.
KZG) with quasi-linear or higher prover complexity. This theoretical limitation ∞ balancing the prover’s computational burden with the verifier’s succinctness ∞ remained the primary obstacle to achieving universally fast and small zero-knowledge proofs for large-scale computations.
Analysis
Blaze’s core mechanism is a compositional approach that leverages the inherent efficiency of error-correcting codes. It uses a code-switching technique to integrate the Repeat-Accumulate-Accumulate (RAA) code with an Interactive Oracle Proof of Proximity (IOPP). Conceptually, the RAA code efficiently encodes the polynomial data, and the code-switching method ensures that the commitment scheme’s proving time is directly tied to this fast encoding process.
The result is a new MLPCS that moves the computational heavy lifting to a highly optimized, information-theoretic encoding, circumventing the need for computationally expensive cryptographic operations in the prover’s path. This fundamentally differs from previous schemes by decoupling prover complexity from proof succinctness through a novel algebraic coding lens.
Parameters
- Prover Commitment Cost ∞ 8n field additions and one Merkle tree computation. This represents the concrete complexity of the commitment phase for a polynomial of size n.
- Verifier Complexity ∞ Oλ(log²(n)). This logarithmic complexity ensures the verifier remains highly efficient, which is the definition of a succinct argument.
- Proof Size ∞ Significantly smaller than Brakedown. This is the comparative metric demonstrating the breakthrough in succinctness.
Outlook
The immediate next step is the practical implementation and benchmarking of Blaze within production-grade SNARK systems, particularly those relying on multilinear polynomials. This new primitive is poised to unlock a new generation of ZK-Rollups and decentralized applications that require massive on-chain state updates, enabling truly scalable verifiable computation where the prover’s burden is minimized. In the next three to five years, this work will likely drive research into further optimizing the underlying RAA codes and exploring other algebraic coding techniques to achieve optimal, linear-time provers across all proof systems, solidifying the foundation for a fully succinct blockchain architecture.
Verdict
Blaze establishes a new frontier in cryptographic efficiency, fundamentally resolving the long-standing trade-off between fast prover time and succinct proof size in polynomial commitment schemes.
