# Coded State Machine -- Scaling State Machine Execution under Byzantine Faults

## TL;DR

This paper introduces Coded State Machine (CSM), an information-theoretic framework that enables secure, efficient, and scalable execution of multiple state machines on untrusted Byzantine network nodes, improving over traditional replication methods.

## Contribution

The paper presents CSM, which achieves linear scaling in storage, throughput, and security, along with a novel delegation algorithm INTERMIX for verifiable distributed computation.

## Key findings

- CSM achieves optimal linear scaling in storage, throughput, and security.
- INTERMIX enables secure delegation of coding operations with near-linear scalability.
- The framework maintains security against Byzantine faults while improving efficiency.

## Abstract

We introduce an information-theoretic framework, named Coded State Machine (CSM), to securely and efficiently execute multiple state machines on untrusted network nodes, some of which are Byzantine. The standard method of solving this problem is using State Machine Replication, which achieves high security at the cost of low efficiency. We propose CSM, which achieves the optimal linear scaling in storage efficiency, throughput, and security simultaneously with the size of the network. The storage efficiency is scaled via the design of Lagrange coded states and coded input commands that require the same storage size as their origins. The computational efficiency is scaled using a novel delegation algorithm, called INTERMIX, which is an information-theoretically verifiable matrix-vector multiplication algorithm of independent interest. Using INTERMIX, the network nodes securely delegate their coding operations to a single worker node, and a small group of randomly selected auditor nodes verify its correctness, so that computational efficiency can scale almost linearly with the network size, without compromising on security.