dorsal/arxiv
View SchemaConverse Bounds for Sun-Jafar-type Weak Private Information Retrieval
| Authors | Chandan Anand, Jayesh Seshadri, Prasad Krishnan, Gowtham R. Kurri |
|---|---|
| Categories | |
| ArXiv ID | 2601.10643vv1 |
| URL | https://arxiv.org/abs/2601.10643 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
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.
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"abstract": "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.",
"arxiv_id": "2601.10643",
"authors": [
"Chandan Anand",
"Jayesh Seshadri",
"Prasad Krishnan",
"Gowtham R. Kurri"
],
"categories": [
"cs.IT",
"cs.CR",
"math.IT"
],
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Converse Bounds for Sun-Jafar-type Weak Private Information Retrieval",
"url": "https://arxiv.org/abs/2601.10643",
"version": "v1"
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