Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Security for adversarial wiretap channels

Esther Hänggi, Iyán Méndez Veiga, Ligong Wang

TL;DR

The explicit and computationally efficient construction of information-theoretically secure coding schemes which use the inverse of an extractor and an error-correcting code are analyzed, showing that they can achieve secrecy capacity on channels where an adversary can pick a sequence of ``states'' governing the channel's behavior.

Abstract

We consider the wiretap channel, where the individual channel uses have memory or are influenced by an adversary. We analyze the explicit and computationally efficient construction of information-theoretically secure coding schemes which use the inverse of an extractor and an error-correcting code. These schemes are known to achieve secrecy capacity on a large class of memoryless wiretap channels. We show that this also holds for certain channel types with memory. In particular, they can achieve secrecy capacity on channels where an adversary can pick a sequence of ``states'' governing the channel's behavior, as long as, given every possible state, the channel is strongly symmetric.

Security for adversarial wiretap channels

TL;DR

The explicit and computationally efficient construction of information-theoretically secure coding schemes which use the inverse of an extractor and an error-correcting code are analyzed, showing that they can achieve secrecy capacity on channels where an adversary can pick a sequence of ``states'' governing the channel's behavior.

Abstract

We consider the wiretap channel, where the individual channel uses have memory or are influenced by an adversary. We analyze the explicit and computationally efficient construction of information-theoretically secure coding schemes which use the inverse of an extractor and an error-correcting code. These schemes are known to achieve secrecy capacity on a large class of memoryless wiretap channels. We show that this also holds for certain channel types with memory. In particular, they can achieve secrecy capacity on channels where an adversary can pick a sequence of ``states'' governing the channel's behavior, as long as, given every possible state, the channel is strongly symmetric.
Paper Structure (20 sections, 20 theorems, 66 equations, 7 figures)

This paper contains 20 sections, 20 theorems, 66 equations, 7 figures.

Table of Contents

  1. The Wiretap Channel
  2. Our Contribution
  3. Outline:
  4. Background and Previous Results
  5. Notation
  6. Properties of Distributions
  7. Extractors
  8. Codes and Channels
  9. Modelling Secure Message Transmission in the Wiretap Scenario
  10. Protocols from tessaroarxiv Using an Inverter of an Extractor
  11. Security Bound
  12. Simple Security Bound
  13. Example: Adversarially Selected Set of Bits (Wiretap II)
  14. Smoothing
  15. Example: Reaching Capacity for the Binary Symmetric Channel
  16. ...and 5 more sections

Key Result

theorem 1

Let $Z_1$,…, $Z_n$ be i.i.d. according to $P_Z$. Then, for any $\varepsilon>0$, where $Z$ is distributed according to $P_Z$.

Figures (7)

  • Figure 1: Concept of the wiretap channel.
  • Figure 2: The real (right) and ideal (left) message transmission system. The ideal system $\mathcal{S}_{\mathrm{ideal}}$ outputs the sender's message to the receiver and nothing to the eavesdropper.
  • Figure 3: We introduce an intermediate system which replaces the receiver's output by the input.
  • Figure 4: The protocol on the sender's side of the seeded wiretap scheme (left) and the unseeded wiretap scheme (right). The seed and additional randomness are chosen uniformly at random.
  • Figure 5: The largest probabilities allow to bound the guessing probability. The example shows the probability distribution of a binary symmetric channel with crossover probability $p_A=0.2$ with $4$ values of $V$ (denoted by different colors) and $16$ output values $Z^{(n)}$. The histogram on the left depicts the output probabilities from different inputs, the one on the right shows the selected $|\mathcal{Z}|^n$ highest probabilities, $4=16/4$ from each input $V$, which allow to bound the guessing probability.
  • ...and 2 more figures

Theorems & Definitions (52)

  • definition 1
  • definition 2
  • definition 3: Guessing probability of $V$ given $Z$
  • definition 4: min-entropy of $V$ given $Z$
  • theorem 1: Asymptotic equipartition property (see, e.g. coverthomas)
  • definition 5: Strong extractor
  • definition 6: Two-universal function family
  • theorem 2: Left-over hash lemma ILLHILLbiometrics
  • definition 7: Inverter
  • definition 8: Error-correcting code
  • ...and 42 more