Secure Network Function Computation for General Target and Security Functions

2026-04-01

AI Summary

This work addresses the fundamental challenge of securely computing a target function over a network in the presence of an eavesdropper, ensuring that the destination correctly computes the desired function while the eavesdropper gains no information about a specified secure function. The paper introduces a general secure network function computation model and, using information-theoretic methods, establishes the first upper bound on secure computation capacity applicable to arbitrary network topologies, arbitrary target and secure functions, and arbitrary security levels. For two classes of linear function models, it develops linear-time algorithms to compute this upper bound, reveals necessary and sufficient conditions for the equivalence between computability and security, and provides an explicit upper bound on the required finite field size. Furthermore, the authors construct efficient coding schemes that achieve non-trivial lower bounds on secure computation capacity.

Abstract

Secure network function computation is a critical research direction in network coding, which aims to ensure that the target function is correctly computed at the sink node while preventing the wiretapper from obtaining any information about the security function. In this paper, we focus on the general secure network function computation model, where the target function f and the security function ζ are arbitrary, and the wiretapper can eavesdrop on any subset of edges with size at most a given security level. Using information-theoretic techniques, we establish a nontrivial upper bound on the secure computing capacity, which is applicable to arbitrary networks, arbitrary target and security functions, and arbitrary security levels. This upper bound is shown to degenerate to the existing bounds in the literature when the target and security functions are specific forms. Furthermore, we consider two specific models: one where the target function is vector-linear and the security function is the identity function, and another where both functions are vector-linear. For the former, we derive a simplified form of the upper bound on the secure computing capacity via order-theoretic methods and propose an efficient algorithm to compute this bound with linear time complexity in the number of network edges. For the latter, we characterize the equivalent conditions for the computability and security of linear secure network codes, develop two constructive schemes for such codes, and derive an upper bound on the minimal finite field size required for the constructions, thereby obtaining a nontrivial lower bound on the secure computing capacity.

Problem

• secure network function computation
• target function
• security function
• network coding
• wiretapper

Innovation

• secure network coding
• network function computation
• information-theoretic security
• vector-linear functions
• computing capacity bounds