FlexProofs Introduces Vector Commitment Scheme with Linear-Time Proof Generation

Global: FlexProofs Introduces Vector Commitment Scheme with Linear-Time Proof Generation

Researchers Jing Liu and Liang Feng Zhang announced a new vector commitment (VC) scheme called FlexProofs in a paper submitted to arXiv on January 6, 2026 and revised on January 9, 2026. The scheme enables a prover to generate all individual opening proofs for a vector of size N in optimal O(N) time while offering a flexible batch size parameter that can further reduce computation time. FlexProofs is also designed to be directly compatible with a family of zkSNARKs that encode inputs as multi‑linear polynomials.

Background

Vector commitments are cryptographic primitives that allow a prover to commit to an entire vector while later opening individual entries efficiently. Existing solutions, such as HydraProofs, already achieve O(N) proof generation but lack flexibility in batching, limiting performance gains in large‑scale deployments.

Key Innovations

FlexProofs introduces two principal advances. First, it incorporates a batch size parameter b that can be increased to accelerate proof generation beyond the baseline O(N) time. Second, the authors present the first functional commitment (FC) scheme capable of handling multi‑exponentiations with batch opening, a critical building block for the overall construction.

Performance Evaluation

Experimental results reported in the paper show that for a vector of size N = 2^16 and a batch parameter b = log^2 N, FlexProofs achieves a six‑fold speedup compared with HydraProofs. The authors attribute this improvement to the flexible batching mechanism and the efficient functional commitment design.

Potential Applications

When combined with suitable zkSNARKs, FlexProofs can support practical cryptographic protocols such as verifiable secret sharing and verifiable robust aggregation. These applications benefit from the ability to generate all necessary proofs quickly and to integrate seamlessly with existing zero‑knowledge proof systems.

Implications and Future Work

The introduction of a flexible batch parameter opens avenues for further optimization in environments where proof generation latency is critical. The authors suggest that future research may explore adaptive selection of the batch size based on workload characteristics and integration with other emerging proof systems.

This report is based on information from arXiv, licensed under Academic Preprint / Open Access. Based on the abstract of the research paper. Full text available via ArXiv.