# R16: Practical Secure Delegated Linear Algebra with Trapdoored Matrices

This work uses trapdoored pseudorandom matrices for efficient delegated linear algebra under an LPN-based approach. PLLM status: tracked.

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Document ID: `pllm.docs.research.papers.r16-trapdoored-matrices`  
Release: `0.1.0`

**Status:** `tracked`
**Year:** 2025
**Authors:** Mark Braverman, Stephen Newman
**External source:** [Practical Secure Delegated Linear Algebra with Trapdoored Matrices](https://arxiv.org/html/2502.13060v3)

## Source contribution

This work uses trapdoored pseudorandom matrices for efficient delegated linear algebra under an LPN-based approach.

## PLLM perspective

Implement the paper-specific matrix/trapdoor generation and delegation protocol before attempting a setup adaptation. State who knows each operand and each trapdoor.

Identified as a lead previously; not executed in the supplied archives.

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: Public low-rank masks leak nullspace projections. This construction must not be approximated by an unproven structured mask.

## PLLM modules and documentation

Target module identifiers: `prepare.trapdoored_matrix`, `protocol.delegated_linear`. 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 1, **Delegated matrix-vector execution**. Its source-registry order is 16. Follow current gates and unfinished work in the [research backlog](/research/backlog/).