pith. machine review for the scientific record. sign in

arxiv: 2605.06751 · v2 · submitted 2026-05-07 · 💻 cs.IT · cs.CR· math.IT

Recognition: no theorem link

Cryptographic and Information-theoretic Security Capacities for General Arbitrarily Varying Wiretap Channels

Holger Boche , Ning Cai , Yiqi Chen , Marc Geitz
Authors on Pith no claims yet

Pith reviewed 2026-05-12 03:42 UTC · model grok-4.3

classification 💻 cs.IT cs.CRmath.IT
keywords arbitrarily varying wiretap channelstrong secrecysemantic secrecycapacityinformation theoretic securitycryptographic securitygeneral arbitrarily varying wiretap channel
0
0 comments X

The pith

For Arbitrarily Varying Wiretap Channels, strong secrecy capacity equals semantic secrecy capacity under both average and maximal error criteria.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper compares capacities of Arbitrarily Varying Wiretap Channels under different error and secrecy constraints. It establishes that average error probability combined with strong secrecy gives the same capacity as maximal error probability combined with semantic secrecy. This does not hold for arbitrary communication systems, as shown by a counterexample. For General Arbitrarily Varying Wiretap Channels, semantic security matches other cryptographic measures in capacity. A bound is given on the gap between strong and semantic secrecy capacities that vanishes for sub-double-exponential jammer selections.

Core claim

The average error and strong secrecy capacity of an AVWC is always equal to its maximal error and semantic secrecy capacity. However, this equivalence does not hold for all general communication systems, and we prove this by a counterexample. For the GAVWC, semantic security and the other cryptographic security measures considered achieve the same capacity values. Finally, we bound the gap between the strong secrecy capacity and the semantic secrecy capacity for the GAVWC. The gap vanishes if the choice of the jammer is sub-double-exponential with respect to the block length n.

What carries the argument

Equivalence of capacities defined via average error with strong secrecy versus maximal error with semantic secrecy for AVWCs and GAVWCs.

If this is right

  • The capacity is the same whether one uses average or maximal error probability when paired with the corresponding secrecy notion.
  • For general systems beyond AVWCs, such equivalences may fail as demonstrated by the counterexample.
  • Semantic secrecy is sufficient to achieve the strong secrecy capacity in GAVWCs.
  • The difference between strong and semantic secrecy capacities is bounded and can be made to vanish under sub-double-exponential jammer growth.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Semantic secrecy may be easier to analyze or achieve in practice while still guaranteeing the full capacity.
  • The sub-double-exponential condition suggests that for adversaries with reasonable computational limits, the capacities coincide.
  • The counterexample could be used to test similar equivalences in other channel models like broadcast channels or multiple access channels.

Load-bearing premise

The alphabets for channel inputs, outputs, and states are finite, and the channel is memoryless but arbitrarily varying.

What would settle it

Observing a difference in capacities for an AVWC under the two sets of criteria, or a GAVWC where the gap does not vanish for sub-double-exponential jammer choices.

Figures

Figures reproduced from arXiv: 2605.06751 by Holger Boche, Marc Geitz, Ning Cai, Yiqi Chen.

Figure 1
Figure 1. Figure 1: A GAVWC with distinguishing security: For an arbitrary pair of messages (𝑈0, 𝑈1 ), Eve cannot distinguish which one is sent. The aforementioned attacks can substantially deteriorate the information security of a protocol. To fulfill the confidentiality and reliability requirements of the protocol, defense against advanced active attackers is always the focus of cryptographic and information-theoretic resea… view at source ↗
Figure 2
Figure 2. Figure 2: Communication system with a jammer B. Insights into cryptographic problems In physical communication channels, as shown in [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
read the original abstract

We compare the strong secrecy capacities of Arbitrarily Varying Wiretap Channels (AVWCs) and General Arbitrarily Varying Wiretap Channels (GAVWCs) with their capacities under semantic secrecy constraint and other equivalent cryptographic secrecy constraints. It turns out that the average error and strong secrecy capacity of an AVWC is always equal to its maximal error and semantic secrecy capacity. However, this equivalence does not hold for all general communication systems, and we prove this by a counterexample. We also show that, for the GAVWC, semantic security and the other cryptographic security measures considered achieve the same capacity values. Finally, we bound the gap between the strong secrecy capacity and the semantic secrecy capacity for the GAVWC. The gap vanishes if the choice of the jammer is sub-double-exponential with respect to the block length n, which gives a sufficient condition for the strong and semantic secrecy capacities to be equal for GAVWCs.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The paper compares strong secrecy capacities of Arbitrarily Varying Wiretap Channels (AVWCs) and General Arbitrarily Varying Wiretap Channels (GAVWCs) against semantic secrecy and related cryptographic constraints. It proves that for AVWCs the average-error strong-secrecy capacity equals the maximal-error semantic-secrecy capacity, supplies a counterexample showing the equivalence fails for general communication systems, establishes that semantic security and other cryptographic measures yield identical capacities for GAVWCs, and derives an upper bound on the gap between strong and semantic secrecy capacities for GAVWCs that vanishes when the jammer selection is sub-double-exponential in block length n.

Significance. If the derivations hold, the results clarify when information-theoretic and cryptographic secrecy notions coincide for adversarial wiretap channels, a setting relevant to robust secure communication. The counterexample isolates the special structure of AVWCs, while the gap bound supplies a concrete sufficient condition for capacity equality under standard finite-alphabet memoryless assumptions and random-coding arguments.

minor comments (3)
  1. §2 (channel definitions): the distinction between the AVWC and GAVWC state alphabets and the auxiliary channels used in the capacity expressions should be stated more explicitly to make the subsequent proofs easier to follow.
  2. The counterexample construction (presumably §3) would benefit from an explicit verification that the chosen auxiliary channels satisfy the finite-alphabet hypothesis without introducing hidden dependencies on n.
  3. The gap-bound derivation (presumably §5) relies on sub-double-exponential jammer scaling; a brief remark on whether this scaling is necessary or merely sufficient would strengthen the presentation.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the positive recommendation for minor revision. The referee's summary accurately reflects the main results of the paper.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The paper establishes equivalences between average-error/strong-secrecy and maximal-error/semantic-secrecy capacities for AVWCs, shows the equivalence fails for general systems via counterexample, equates cryptographic measures for GAVWCs, and bounds the strong-vs-semantic gap (vanishing under sub-double-exponential jammer scaling). All steps rely on standard random coding, typicality, and finite-alphabet memoryless AV structure with auxiliary channels; none of the capacity expressions are defined in terms of themselves, no fitted parameters are relabeled as predictions, and no load-bearing self-citations or imported uniqueness theorems appear in the provided derivation chain. The results are externally falsifiable against the stated channel models and do not reduce to their inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The results rest on standard information-theoretic axioms for finite-alphabet channels and the definition of arbitrarily varying channels; no new free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Finite input, output, and state alphabets for the channel model
    Required for the capacity expressions and the sub-double-exponential condition to be well-defined.
  • domain assumption Standard memoryless but arbitrarily varying structure
    Invoked throughout the comparison of secrecy capacities.

pith-pipeline@v0.9.0 · 5474 in / 1419 out tokens · 37083 ms · 2026-05-12T03:42:12.919423+00:00 · methodology

Review history (2 revisions) →

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

41 extracted references · 41 canonical work pages

  1. [1]

    Information-theoretic key agreement: From weak to strong secrecy for free,

    U. Maurer and S. Wolf, “Information-theoretic key agreement: From weak to strong secrecy for free,” inInternational Conference on the Theory and Applications of Cryptographic Techniques, pp. 351–368, Springer, 2000

    work page 2000

  2. [2]

    The wire-tap channel,

    A. D. Wyner, “The wire-tap channel,”Bell System Technical Journal, vol. 54, no. 8, pp. 1355–1387, 1975

    work page 1975

  3. [3]

    Broadcast channels with confidential messages,

    I. Csisz ´ar and J. K ¨orner, “Broadcast channels with confidential messages,”IEEE Transactions on Information Theory, vol. 24, no. 3, pp. 339–348, 1978

    work page 1978

  4. [4]

    Common randomness and secret key generation with a helper,

    I. Csisz ´ar and P. Narayan, “Common randomness and secret key generation with a helper,”IEEE Transactions on Information Theory, vol. 46, no. 2, pp. 344–366, 2000

    work page 2000

  5. [5]

    Strong secrecy from channel resolvability,

    M. R. Bloch and J. N. Laneman, “Strong secrecy from channel resolvability,”IEEE Transactions on Information Theory, vol. 59, no. 12, pp. 8077–8098, 2013

    work page 2013

  6. [6]

    Multiple access wiretap channels with strong secrecy,

    M. H. Yassaee and M. R. Aref, “Multiple access wiretap channels with strong secrecy,” in2010 IEEE Information Theory Workshop, pp. 1–5, IEEE, 2010

    work page 2010

  7. [7]

    Secrecy results for compound wiretap channels,

    I. Bjelakovi ´c, H. Boche, and J. Sommerfeld, “Secrecy results for compound wiretap channels,”Problems of Information Transmission, vol. 49, no. 1, pp. 73–98, 2013

    work page 2013

  8. [8]

    Strong secrecy for cooperative broadcast channels,

    Z. Goldfeld, G. Kramer, H. H. Permuter, and P. Cuff, “Strong secrecy for cooperative broadcast channels,”IEEE Transactions on Information Theory, vol. 63, no. 1, pp. 469–495, 2016

    work page 2016

  9. [9]

    Strongly secure communications over the two-way wiretap channel,

    A. J. Pierrot and M. R. Bloch, “Strongly secure communications over the two-way wiretap channel,”IEEE Transactions on Information Forensics and Security, vol. 6, no. 3, pp. 595–605, 2011

    work page 2011

  10. [10]

    The secrecy capacity of compound gaussian mimo wiretap channels,

    R. F. Schaefer and S. Loyka, “The secrecy capacity of compound gaussian mimo wiretap channels,”IEEE Transactions on Information Theory, vol. 61, no. 10, pp. 5535–5552, 2015

    work page 2015

  11. [11]

    Strong secrecy for interference channels based on channel resolvability,

    Z. Wang, R. F. Schaefer, M. Skoglund, M. Xiao, and H. V . Poor, “Strong secrecy for interference channels based on channel resolvability,”IEEE Transactions on Information Theory, vol. 64, no. 7, pp. 5110–5130, 2018

    work page 2018

  12. [12]

    Wiretap channels with causal state information: Strong secrecy,

    T. S. Han and M. Sasaki, “Wiretap channels with causal state information: Strong secrecy,”IEEE Transactions on Information Theory, vol. 65, no. 10, pp. 6750–6765, 2019

    work page 2019

  13. [13]

    On the fundamental limits of integrated sensing and communications under logarithmic loss,

    J. Chen, L. Yu, Y . Li, W. Shi, Y . Ge, and W. Tong, “On the fundamental limits of integrated sensing and communications under logarithmic loss,”arXiv preprint arXiv:2502.08502, 2025

    work page arXiv 2025

  14. [14]

    Semantic security for the wiretap channel,

    M. Bellare, S. Tessaro, and A. Vardy, “Semantic security for the wiretap channel,” inAnnual cryptology conference, pp. 294–311, Springer, 2012

    work page 2012

  15. [15]

    Probabilistic encryption,

    S. Goldwasser and S. Micali, “Probabilistic encryption,”J. Comput. Syst. Sci., vol. 28, pp. 270–299, 1984

    work page 1984

  16. [16]

    Semantic security via seeded modular coding schemes and ramanujan graphs,

    M. Wiese and H. Boche, “Semantic security via seeded modular coding schemes and ramanujan graphs,”IEEE Transactions on Information Theory, vol. 67, no. 1, pp. 52–80, 2020

    work page 2020

  17. [17]

    Experimental validation of information-theoretic physical layer security,

    J. V oichtleitner, M. Wiese, A. Frank, and H. Boche, “Experimental validation of information-theoretic physical layer security,”IEEE Transactions on Information Forensics and Security, 2026

    work page 2026

  18. [18]

    Semantic security for quantum wiretap channels,

    H. Boche, M. Cai, C. Deppe, R. Ferrara, and M. Wiese, “Semantic security for quantum wiretap channels,”Journal of Mathematical Physics, vol. 63, no. 9, 2022

    work page 2022

  19. [19]

    Semantic security with infinite-dimensional quantum eavesdropping channel,

    M. Frey, I. Bjelakovi ´c, J. N ¨otzel, and S. Sta ´nczak, “Semantic security with infinite-dimensional quantum eavesdropping channel,”IEEE Transactions on Information Theory, vol. 71, no. 4, pp. 2662–2697, 2025

    work page 2025

  20. [20]

    Semantic-security capacity for wiretap channels of type ii,

    Z. Goldfeld, P. Cuff, and H. H. Permuter, “Semantic-security capacity for wiretap channels of type ii,”IEEE Transactions on Information Theory, vol. 62, no. 7, pp. 3863–3879, 2016

    work page 2016

  21. [21]

    Arbitrarily varying wiretap channels with type constrained states,

    Z. Goldfeld, P. Cuff, and H. H. Permuter, “Arbitrarily varying wiretap channels with type constrained states,”IEEE Transactions on Information Theory, vol. 62, no. 12, pp. 7216–7244, 2016

    work page 2016

  22. [22]

    Semantically secure lattice codes for the gaussian wiretap channel,

    C. Ling, L. Luzzi, J.-C. Belfiore, and D. Stehl ´e, “Semantically secure lattice codes for the gaussian wiretap channel,”IEEE Transactions on Information Theory, vol. 60, no. 10, pp. 6399–6416, 2014

    work page 2014

  23. [23]

    Semantically secure lattice codes for compound mimo channels,

    A. Campello, C. Ling, and J.-C. Belfiore, “Semantically secure lattice codes for compound mimo channels,”IEEE Transactions on Information Theory, vol. 66, no. 3, pp. 1572–1584, 2019

    work page 2019

  24. [24]

    Arbitrary jamming can preclude secure communication,

    E. MolavianJazi, M. Bloch, and J. N. Laneman, “Arbitrary jamming can preclude secure communication,” in2009 47th Annual Allerton Conference on Communication, Control, and Computing (Allerton), pp. 1069–1075, IEEE, 2009

    work page 2009

  25. [25]

    Capacity results for arbitrarily varying wiretap channels,

    I. Bjelakovi ´c, H. Boche, and J. Sommerfeld, “Capacity results for arbitrarily varying wiretap channels,” inInformation Theory, Combinatorics, and Search Theory, pp. 123–144, Springer, 2013

    work page 2013

  26. [26]

    A channel under simultaneous jamming and eavesdropping attack—correlated random coding capacities under strong secrecy criteria,

    M. Wiese, J. N ¨otzel, and H. Boche, “A channel under simultaneous jamming and eavesdropping attack—correlated random coding capacities under strong secrecy criteria,”IEEE Transactions on Information Theory, vol. 62, no. 7, pp. 3844–3862, 2016

    work page 2016

  27. [27]

    The arbitrarily varying wiretap channel—secret randomness, stability, and super-activation,

    J. N ¨otzel, M. Wiese, and H. Boche, “The arbitrarily varying wiretap channel—secret randomness, stability, and super-activation,”IEEE Transactions on Information Theory, vol. 62, no. 6, pp. 3504–3531, 2016

    work page 2016

  28. [28]

    Strong secrecy of arbitrarily varying multiple access channels,

    Y . Chen, D. He, and Y . Luo, “Strong secrecy of arbitrarily varying multiple access channels,”IEEE Transactions on Information Forensics and Security, vol. 16, pp. 3662–3677, 2021

    work page 2021

  29. [29]

    Strong secrecy of arbitrarily varying wiretap channel with constraints,

    Y . Chen, D. He, C. Ying, and Y . Luo, “Strong secrecy of arbitrarily varying wiretap channel with constraints,”IEEE Transactions on Information Theory, vol. 68, no. 7, pp. 4700–4722, 2022

    work page 2022

  30. [30]

    Arbitrarily varying wiretap channels with non-causal side information at the jammer,

    C. R. Janda, M. Wiese, E. A. Jorswieck, and H. Boche, “Arbitrarily varying wiretap channels with non-causal side information at the jammer,”IEEE Transactions on Information Theory, vol. 69, no. 4, pp. 2635–2663, 2023

    work page 2023

  31. [31]

    On the security of public key protocols,

    D. Dolev and A. Yao, “On the security of public key protocols,”IEEE Transactions on information theory, vol. 29, no. 2, pp. 198–208, 1983

    work page 1983

  32. [32]

    Authenticated-encryption with associated-data,

    P. Rogaway, “Authenticated-encryption with associated-data,” inProceedings of the 9th ACM Conference on Computer and Communications Security, pp. 98–107, 2002

    work page 2002

  33. [33]

    Stronger security of authenticated key exchange,

    B. LaMacchia, K. Lauter, and A. Mityagin, “Stronger security of authenticated key exchange,” inInternational conference on provable security, pp. 1–16, Springer, 2007

    work page 2007

  34. [34]

    Authentication and authenticated key exchanges,

    W. Diffie, P. C. Van Oorschot, and M. J. Wiener, “Authentication and authenticated key exchanges,”Designs, Codes and cryptography, vol. 2, no. 2, pp. 107–125, 1992

    work page 1992

  35. [35]

    A cryptographic treatment of the wiretap channel,

    M. Bellare, S. Tessaro, and A. Vardy, “A cryptographic treatment of the wiretap channel,”arXiv preprint arXiv:1201.2205, 2012

    work page arXiv 2012

  36. [36]

    The capacity of the arbitrarily varying channel revisited: Positivity, constraints,

    I. Csisz ´ar and P. Narayan, “The capacity of the arbitrarily varying channel revisited: Positivity, constraints,”IEEE Transactions on Information Theory, vol. 34, no. 2, pp. 181–193, 1988

    work page 1988

  37. [37]

    Exponential error bounds for random codes in the arbitrarily varying channel,

    T. Ericson, “Exponential error bounds for random codes in the arbitrarily varying channel,”IEEE Transactions on Information Theory, vol. 31, no. 1, pp. 42–48, 1985

    work page 1985

  38. [38]

    Elimination of correlation in random codes for arbitrarily varying channels,

    R. Ahlswede, “Elimination of correlation in random codes for arbitrarily varying channels,”Probability Theory and Related Fields, vol. 44, no. 2, pp. 159–175, 1978

    work page 1978

  39. [39]

    Csisz ´ar and J

    I. Csisz ´ar and J. K ¨orner,Information Theory: Coding Theorems for Discrete Memoryless Systems. Cambridge University Press, 2011

    work page 2011

  40. [40]

    Localized error correction in projective space,

    N. Cai, “Localized error correction in projective space,”IEEE transactions on information theory, vol. 59, no. 6, pp. 3282–3294, 2013

    work page 2013

  41. [41]

    Message transmission over classical quantum channels with a jammer with side information: Message transmission capacity and resources,

    H. Boche, M. Cai, and N. Cai, “Message transmission over classical quantum channels with a jammer with side information: Message transmission capacity and resources,”IEEE Transactions on Information Theory, vol. 65, no. 5, pp. 2922–2943, 2018

    work page 2018