Converse Bounds for Sun-Jafar-type Weak Private Information Retrieval
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866917205742977024 |
|---|---|
| author | Anand, Chandan Seshadri, Jayesh Krishnan, Prasad Kurri, Gowtham R. |
| author_facet | Anand, Chandan Seshadri, Jayesh Krishnan, Prasad Kurri, Gowtham R. |
| contents | Building on the well-established capacity-achieving schemes of Sun-Jafar (for replicated storage) and the closely related scheme of Banawan-Ulukus (for MDS-coded setting), a recent work by Chandan et al. proposed new classes of weak private information retrieval (WPIR) schemes for the collusion-free (replication and MDS-coded) setting, as well as for the $T$-colluding scenario. In their work, Chandan et al. characterized the expressions for the rate-privacy trade-offs for these classes of WPIR schemes, under the mutual information leakage and maximal leakage metrics. Explicit achievable trade-offs for the same were also presented, which were shown to be competitive or better than prior WPIR schemes. However, the class-wise optimality of the reported trade-offs were unknown. In this work, we show that the explicit rate-privacy trade-offs reported for the Sun-Jafar-type schemes by Chandan et al. are optimal for the non-colluding and replicated setting. Furthermore, we prove the class-wise optimality for Banawan-Ulukus-type MDS-WPIR and Sun-Jafar-type $T$-colluding WPIR schemes, under threshold-constraints on the system parameters. When these threshold-constraints do not hold, we present counter-examples which show that even higher rates than those reported before can be achieved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10643 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Converse Bounds for Sun-Jafar-type Weak Private Information Retrieval Anand, Chandan Seshadri, Jayesh Krishnan, Prasad Kurri, Gowtham R. Information Theory Cryptography and Security Building on the well-established capacity-achieving schemes of Sun-Jafar (for replicated storage) and the closely related scheme of Banawan-Ulukus (for MDS-coded setting), a recent work by Chandan et al. proposed new classes of weak private information retrieval (WPIR) schemes for the collusion-free (replication and MDS-coded) setting, as well as for the $T$-colluding scenario. In their work, Chandan et al. characterized the expressions for the rate-privacy trade-offs for these classes of WPIR schemes, under the mutual information leakage and maximal leakage metrics. Explicit achievable trade-offs for the same were also presented, which were shown to be competitive or better than prior WPIR schemes. However, the class-wise optimality of the reported trade-offs were unknown. In this work, we show that the explicit rate-privacy trade-offs reported for the Sun-Jafar-type schemes by Chandan et al. are optimal for the non-colluding and replicated setting. Furthermore, we prove the class-wise optimality for Banawan-Ulukus-type MDS-WPIR and Sun-Jafar-type $T$-colluding WPIR schemes, under threshold-constraints on the system parameters. When these threshold-constraints do not hold, we present counter-examples which show that even higher rates than those reported before can be achieved. |
| title | Converse Bounds for Sun-Jafar-type Weak Private Information Retrieval |
| topic | Information Theory Cryptography and Security |
| url | https://arxiv.org/abs/2601.10643 |