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Secure network coding with adaptive and active attack

Masahito Hayashi

TL;DR

This work surveys secure network coding under adaptive and active attacks, focusing on one-hop relay and unicast relay networks. It analyzes two randomness formulations (intermediate-node randomness allowed vs disallowed) and three code families (scalar-linear, vector-linear, and non-linear), deriving capacity results $C_1$ and $C_2$ and presenting concrete constructions including anti-Latin square codes and layered vector-linear schemes. The results show when randomness at intermediate nodes increases capacity, provide explicit capacity formulas for unicast networks, and establish that adaptive/active attacks do not always enhance an adversary’s capability for certain non-local linear codes; they also reveal cases where non-linear and vector-linear codes are necessary to achieve secrecy. The discussion highlights open problems in anti-Latin code decodability and potential extensions to multicast settings, outlining directions for future secure network-code design under powerful adversaries.

Abstract

Ning Cai and the author jointly studied secure network codes over adaptive and active attacks, which were rarely studied until these seminal papers. This paper reviews the result for secure network code over adaptive and active attacks. We focus on two typical network models, a one-hop relay network and a unicast relay network.

Secure network coding with adaptive and active attack

TL;DR

This work surveys secure network coding under adaptive and active attacks, focusing on one-hop relay and unicast relay networks. It analyzes two randomness formulations (intermediate-node randomness allowed vs disallowed) and three code families (scalar-linear, vector-linear, and non-linear), deriving capacity results and and presenting concrete constructions including anti-Latin square codes and layered vector-linear schemes. The results show when randomness at intermediate nodes increases capacity, provide explicit capacity formulas for unicast networks, and establish that adaptive/active attacks do not always enhance an adversary’s capability for certain non-local linear codes; they also reveal cases where non-linear and vector-linear codes are necessary to achieve secrecy. The discussion highlights open problems in anti-Latin code decodability and potential extensions to multicast settings, outlining directions for future secure network-code design under powerful adversaries.

Abstract

Ning Cai and the author jointly studied secure network codes over adaptive and active attacks, which were rarely studied until these seminal papers. This paper reviews the result for secure network code over adaptive and active attacks. We focus on two typical network models, a one-hop relay network and a unicast relay network.
Paper Structure (13 sections, 9 theorems, 18 equations, 3 figures, 1 table)

This paper contains 13 sections, 9 theorems, 18 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Security model and coding model
  3. Two kinds of formulations over single source and single terminal network model
  4. Unconventional attack models
  5. Problem over one-hop relay network
  6. Non-linear codes over one-hop relay network
  7. Active attack to non-linear code over one-hop relay network
  8. Adaptive attack to non-linear code over one-hop relay network
  9. Vector-linear codes over one-hop relay network
  10. Non-local linear codes over unicast relay network
  11. Capacity formula
  12. Ideas for proof
  13. Conclusion

Key Result

lemma thmcounterlemma

For $r$-wiretap network, we have $\square$

Figures (3)

  • Figure 1: $r$-wiretap network with equality of the second inequality in \ref{['E9-2B']}. Node 1 is the source node and Node 6 is the terminal node. Node 5 is a pseudo source node. Thus, $\mathop{\rm mincut}\nolimits_2=2$ and $\mathop{\rm mincut}\nolimits_1=3$. When intermediate nodes are allowed to generate random variables, the presented code achieves $\mathop{\rm mincut}\nolimits_1-r$ when $r=2$. The source node (Node 1) has the message $M$ and two scramble variables $L_1,L_2$. The pseudo source node (Node 5) has another scramble variable $L_3$. Even when Eve wiretaps arbitrary two edges, she cannot get arbitrary information for the message $M$.
  • Figure 2:
  • Figure 5: Unicast relay network

Theorems & Definitions (9)

  • lemma thmcounterlemma: CH
  • corollary thmcountercorollary: CH
  • theorem thmcountertheorem: HOKC
  • lemma thmcounterlemma: HC21b
  • lemma thmcounterlemma: HC21b
  • theorem thmcountertheorem: CH
  • lemma thmcounterlemma: CH-cor
  • lemma thmcounterlemma: CH
  • lemma thmcounterlemma