Secure Network Function Computation for Linear Functions, Part II: Target-Function Security

2025-04-24

AI Summary

This paper investigates secure computation of linear target functions over directed acyclic networks under eavesdropping: ensuring correct function evaluation at the sink while leaking no information about the target function—termed *target-function security*—given that an eavesdropper may access any subset from a prescribed collection of wire sets. We first formalize this security model, then derive nontrivial upper bounds on the secure computing capacity for arbitrary network topologies and eavesdropping capabilities. We establish algebraic conditions under which target-function security is equivalent to source security. Leveraging linear network coding, information-theoretic analysis, and finite-field constructions, we obtain tight upper and lower bounds on the linearly computable secure capacity. Furthermore, we propose a universal linear secure coding scheme and extend the source-security framework from Part I to achieve target-function security.

Technology Category

• Machine Learning: Probabilistic Circuits and Graphical Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Planning, Routing, and Scheduling: Scheduling under Uncertainty

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

In this Part II of a two-part paper, we put forward secure network function computation, where in a directed acyclic network, a sink node is required to compute a target function of which the inputs are generated as source messages at multiple source nodes, while a wiretapper, who can access any one but not more than one wiretap set in a given collection of wiretap sets, is not allowed to obtain any information about a security function of the source messages. In Part I of the two-part paper, we have investigated securely computing linear functions with the wiretapper who can eavesdrop any edge subset up to a certain size r, referred to as the security level, where the security function is the identity function. The notion of this security is called source security. In the current paper, we consider another interesting model which is the same as the above one except that the security function is identical to the target function, i.e., we need to protect the information on the target function from being leaked to the wiretapper. The notion of this security is called target-function security. We first prove a non-trivial upper bound on the secure computing capacity, which is applicable to arbitrary network topologies and arbitrary security levels. In particular, when the security level r is equal to 0, the upper bound reduces to the computing capacity without security consideration. Further, from an algebraic point of view, we prove two equivalent conditions for target-function security and source security for the existence of the corresponding linear function-computing secure network codes. With them, for any linear function over a given finite field, we develop a code construction of linear secure network codes for target-function security and thus obtain a lower bound on the secure computing capacity; and also generalize the code construction developed in Part I for source security.

Problem

• Secure computation of linear functions in networks with eavesdroppers
• Protecting target-function information from wiretapper access
• Developing bounds and codes for secure network function computation

Innovation

• Secure network function computation for target-function security
• Upper bound on secure computing capacity for arbitrary networks
• Linear secure network codes for target-function security