zkMaP: Zero-Knowledge Succinct Non-Interactive Matrix Multiplication Proofs
Bibliographic record
Abstract
We introduce zkMaP (Zero-Knowledge Succinct Non-Interactive Matrix Multiplication Proofs), a novel non-interactive zero-knowledge proof system for verifying matrix multiplication with significant improvements in efficiency and scalability. Our protocol leverages KZG polynomial commitments and an innovative inner-product reduction technique to reduce the verification of n x n matrix multiplication to a single pairing equation, thereby enabling constant-time verification independent of the matrix size. In particular, zkMaP requires only two pairing operations and produces proofs as small as 320 bytes, yielding a 96 percent reduction in proof size compared to prior schemes. Furthermore, the prover's computational complexity follows the state-of-the-art at O(n^2), with experimental results demonstrating that proofs for 1024 x 1024 matrices can be generated in approximately 12.21 seconds, offering a 16.14x speedup over previous methods. Our implementation also exhibits better memory efficiency, using only 24.58 MB of prover-side RAM for 1024 x 1024 matrices, and supports scalable batch processing, achieving per-proof generation times of 46.79 milliseconds for 1024 instances while maintaining a constant verification time of 3.6 ms.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.008 |
| Open science | 0.004 | 0.008 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.017 | 0.005 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".