Information-Theoretic Distributed Point Functions with Shorter Keys
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914510465400832 |
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| author | Deng, Hang Zhang, Liang Feng |
| author_facet | Deng, Hang Zhang, Liang Feng |
| contents | A t-private n-server Information-Theoretic Distributed Point Function ((t,n)-ITDPF) allows one to convert any point function f_{alpha,beta}(x): [N] -> G into n shares (secret keys), such that each server can compute an additive share of f_{alpha,beta}(x) with a key while any <= t servers learn absolutely no information about the function. This paper constructs a novel share conversion based on the private information retrieval (PIR) of Ghasemi, Kopparty, and Sudan (STOC 2025) and proposes a perfectly secure 1-private ITDPF with output group G = Z_p, where p can be any prime. Compared with the existing perfectly secure ITDPFs for the same output group, the proposed ITDPF is more efficient with asymptotically shorter secret keys. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24385 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Information-Theoretic Distributed Point Functions with Shorter Keys Deng, Hang Zhang, Liang Feng Cryptography and Security E.3 A t-private n-server Information-Theoretic Distributed Point Function ((t,n)-ITDPF) allows one to convert any point function f_{alpha,beta}(x): [N] -> G into n shares (secret keys), such that each server can compute an additive share of f_{alpha,beta}(x) with a key while any <= t servers learn absolutely no information about the function. This paper constructs a novel share conversion based on the private information retrieval (PIR) of Ghasemi, Kopparty, and Sudan (STOC 2025) and proposes a perfectly secure 1-private ITDPF with output group G = Z_p, where p can be any prime. Compared with the existing perfectly secure ITDPFs for the same output group, the proposed ITDPF is more efficient with asymptotically shorter secret keys. |
| title | Information-Theoretic Distributed Point Functions with Shorter Keys |
| topic | Cryptography and Security E.3 |
| url | https://arxiv.org/abs/2604.24385 |