Monotone Erasure Codes

2026-05-21

AI Summary

This work addresses the limitations of existing erasure codes, which rely on threshold fault models and thus fail to accommodate the generalized trust requirements in blockchain systems defined by arbitrary monotone access structures. To bridge this gap, the paper introduces Linear Monotone Erasure Codes (LMEC), the first coding scheme that incorporates access structures specified by any monotone Boolean formula into erasure code design. Leveraging vector spaces over finite fields, the authors construct efficient encoding and decoding algorithms that support generalized fault assumptions while achieving minimal storage overhead under partitioned access structures. The proposed scheme is successfully integrated into a communication-efficient Asynchronous Verifiable Information Dispersal (AVID) protocol, significantly broadening the applicability of erasure coding in distributed trusted systems.

Abstract

Erasure codes are a critical component in reliable storage systems today, and many blockchain systems use consensus protocols that involve erasure codes to reduce their communication cost. Existing erasure codes rely on a threshold failure assumption, but recent blockchain systems have departed from this simple model and use generalized failure assumptions. This paper introduces monotone erasure codes that respect arbitrary trust assumptions on a set of nodes. The paper first describes a method for constructing a monotone erasure code from any access structure given by a monotone Boolean formula. Next, the relevant notion of a linear monotone erasure code is introduced, which works on vectors over a finite field and where the encoding is a linear operation. We then focus on constructing linear monotone erasure codes: We give an efficient algorithm to construct linear monotone erasure codes for any access structure, and we show how to efficiently construct linear monotone erasure codes for the special case of partitioned access structures with minimal storage overhead. Last but not least, this work also shows how to use monotone erasure codes to obtain a communication-efficient, generalized version of the well-known asynchronous verifiable information dispersal (AVID) primitive, which is a key building block for developing efficient reliable broadcast and consensus protocols.

Problem

• erasure codes
• trust assumptions
• blockchain
• access structure
• monotone Boolean formula

Innovation

• monotone erasure codes
• access structure
• linear coding
• asynchronous verifiable information dispersal
• generalized failure assumptions