FlexProofs: A Vector Commitment with Flexible Linear Time for Computing All Proofs
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908754572738560 |
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| author | Liu, Jing Zhang, Liang Feng |
| author_facet | Liu, Jing Zhang, Liang Feng |
| contents | In this paper, we introduce FlexProofs, a new vector commitment (VC) scheme that achieves two key properties: (1) the prover can generate all individual opening proofs for a vector of size $N$ in optimal time ${\cal O}(N)$, and there is a flexible batch size parameter $b$ that can be increased to further reduce the time to generate all proofs; and (2) the scheme is directly compatible with a family of zkSNARKs that encode their input as a multi-linear polynomial. As a critical building block, we propose the first functional commitment (FC) scheme for multi-exponentiations with batch opening. Compared with HydraProofs, the only existing VC scheme that computes all proofs in optimal time ${\cal O}(N)$ and is directly compatible with zkSNARKs, FlexProofs may speed up the process of generating all proofs, if the parameter $b$ is properly chosen. Our experiments show that for $N=2^{16}$ and $b=\log^2 N$, FlexProofs can be $6\times$ faster than HydraProofs. Moreover, when combined with suitable zkSNARKs, FlexProofs enable practical applications such as verifiable secret sharing and verifiable robust aggregation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03031 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | FlexProofs: A Vector Commitment with Flexible Linear Time for Computing All Proofs Liu, Jing Zhang, Liang Feng Cryptography and Security Logic in Computer Science In this paper, we introduce FlexProofs, a new vector commitment (VC) scheme that achieves two key properties: (1) the prover can generate all individual opening proofs for a vector of size $N$ in optimal time ${\cal O}(N)$, and there is a flexible batch size parameter $b$ that can be increased to further reduce the time to generate all proofs; and (2) the scheme is directly compatible with a family of zkSNARKs that encode their input as a multi-linear polynomial. As a critical building block, we propose the first functional commitment (FC) scheme for multi-exponentiations with batch opening. Compared with HydraProofs, the only existing VC scheme that computes all proofs in optimal time ${\cal O}(N)$ and is directly compatible with zkSNARKs, FlexProofs may speed up the process of generating all proofs, if the parameter $b$ is properly chosen. Our experiments show that for $N=2^{16}$ and $b=\log^2 N$, FlexProofs can be $6\times$ faster than HydraProofs. Moreover, when combined with suitable zkSNARKs, FlexProofs enable practical applications such as verifiable secret sharing and verifiable robust aggregation. |
| title | FlexProofs: A Vector Commitment with Flexible Linear Time for Computing All Proofs |
| topic | Cryptography and Security Logic in Computer Science |
| url | https://arxiv.org/abs/2601.03031 |