# R15: Efficient Pseudorandom Correlation Generators over Z/p^k Z

Galois-ring constructions extend pseudorandom correlation generation to integer rings, including multiplication-related correlations. PLLM status: tracked.

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Document ID: `pllm.docs.research.papers.r15-ring-pcg`  
Release: `0.1.0`

**Status:** `tracked`
**Year:** 2025
**Authors:** Zhe Li, Chaoping Xing, Yizhou Yao, Chen Yuan
**External source:** [Efficient Pseudorandom Correlation Generators over Z/p^k Z](https://link.springer.com/chapter/10.1007/978-3-032-01884-7_7)

## Source contribution

Galois-ring constructions extend pseudorandom correlation generation to integer rings, including multiplication-related correlations.

## PLLM perspective

Implement reviewed parameter sets and the actual requested correlation schema. Expose seed setup, expansion time, memory and transcript requirements; do not substitute ordinary PRG seeds.

Earlier Galois-ring checks were algebra only, not a PCG implementation.

This paper remains tracked. Named modules below are implementation targets, not finished PLLM components; no reproduction, integration, assurance, or matched benchmark is claimed.

The source's boundary remains binding: PCGs do not automatically compress arbitrary garbled tables or spectral coefficients. Small toy parameters are not deployment security parameters.

## PLLM modules and documentation

Target module identifiers: `prepare.ring_pcg`, `correlation.ole`, `correlation.authenticated_triple`. These identifiers describe scoped work unless this page explicitly links an implementation source. Dependencies: None.

- [Research backlog](/research/backlog/)
- [Reimplementation backlog](/research/backlog/)
- [Clean-room workflow](/research/clean-room/)

## Backlog

This source is assigned to reimplementation priority 7, **Preparation, compression, and acceleration**. Its source-registry order is 15. Follow current gates and unfinished work in the [research backlog](/research/backlog/).