Efficient and Secure Message Transmission over Adversarial Wiretap Channels

Core Concepts

The paper presents an efficient and computationally secure coding scheme for message transmission over wiretap channels, where the individual channel uses can have memory or be influenced by an adversary.

Abstract

The paper considers the wiretap channel problem, where two honest parties (sender and receiver) communicate over a noisy channel, while an eavesdropper obtains a noisier version of the transmitted messages. The goal is to achieve both correctness (low probability of decoding error at the receiver) and secrecy (the eavesdropper learns nothing about the message).
The key contributions are:

A new security analysis of an explicit and computationally efficient coding scheme that uses the inverse of an extractor and an error-correcting code. This scheme is shown to achieve secrecy capacity on a large class of memoryless wiretap channels, and the analysis is extended to certain channel types with memory.

The scheme remains secure even when the individual channel uses can differ or have memory, and the adversary is allowed to choose the exact channel from a set (e.g., the order of the channels).

A general reduction from security for uniform random messages to security for arbitrary message distributions, applicable to schemes with a linear inverter of an extractor combined with a linear error-correcting code.

Application of the techniques to prove security for the arbitrarily varying wiretap channel with type-constrained states, where the adversary can choose the state sequence.

The analysis shows that the scheme can reach secrecy capacity in many cases, including the binary symmetric channel, the wiretap channel II, and the arbitrarily varying wiretap channel with strongly symmetric individual channels.

Stats

The secrecy capacity of the wiretap channel is given by the formula:
Csec = max_PVX (I(V; Y) - I(V; Z))
For the case of binary symmetric channels, the secrecy capacity is Csec = h(pA) - h(pR), where pA and pR are the error probabilities of the adversarial and receiver channels, respectively.

Quotes

"The new analysis has two advantages. First, it yields tighter nonasymptotic bounds for memoryless channels. Second, it applies to certain channel models that are not memoryless, for example, channels where the adversary can choose the behavior of ChA subject to certain constraints."
"We prove security for random-messages for channels where every input leads to the same output distribution (upon relabelling) and where the output distribution follows an asymptotic equipartition property. This is the case for many distributions which are not identical and independent/memoryless."
"We give a general reduction from security for uniform random messages to security for arbitrary message distributions. Our reduction applies to schemes with a linear inverter of an extractor combined with a linear error-correcting code."

Key Insights Distilled From

Security for adversarial wiretap channels

by Esth... at arxiv.org 04-03-2024

https://arxiv.org/pdf/2404.01760.pdf

Deeper Inquiries

How can the techniques presented in this paper be extended to handle more general channel models, such as channels with memory that do not satisfy the strong symmetry condition

The techniques presented in the paper can be extended to handle more general channel models by considering channels with memory that do not satisfy the strong symmetry condition. One approach could be to incorporate the concept of smoothing into the analysis, as demonstrated in the paper. By focusing on the ε-smooth version of the min-entropy, it becomes possible to bound the guessing probability for a wider range of channel types. This smoothing technique allows for a more flexible and robust analysis of the security of wiretap channels with varying characteristics, including those with memory and asymmetric properties. Additionally, exploring the use of different types of error-correcting codes and extractors that are suitable for channels with memory could further enhance the applicability of the techniques to a broader set of channel models.

What are the implications of the security results for practical applications of wiretap channels, such as secure communication in the presence of eavesdroppers

The security results for wiretap channels have significant implications for practical applications involving secure communication in the presence of eavesdroppers. By providing explicit and computationally efficient construction of information-theoretically secure coding schemes, the paper offers a valuable framework for ensuring the confidentiality of communication between parties in the presence of potential adversaries. The ability to achieve secrecy capacity on a variety of channel types, including those with memory or influenced by adversaries, enhances the practical relevance of the techniques presented. This can be particularly beneficial in scenarios where secure communication is crucial, such as in sensitive data transmission, financial transactions, or confidential information exchange.

Can the ideas behind the invertible extractor-based schemes be applied to other cryptographic primitives beyond the wiretap channel, such as secure multi-party computation or oblivious transfer

The ideas behind the invertible extractor-based schemes presented in the paper can indeed be applied to other cryptographic primitives beyond the wiretap channel. For instance, these techniques could be adapted for use in secure multi-party computation (MPC) protocols, where multiple parties wish to jointly compute a function over their private inputs while preserving the privacy of individual data. By incorporating invertible extractors and error-correcting codes into the design of MPC schemes, it may be possible to enhance the security and privacy guarantees of the protocol. Similarly, the concept of extractors and error-correcting codes could also be explored in the context of oblivious transfer protocols, where one party transfers information to another party in a way that ensures the sender remains oblivious to the receiver's choice. This application could benefit from the secure and efficient transmission of information, as demonstrated in the wiretap channel context.