Pith. sign in

REVIEW 3 major objections 3 minor 47 references

Asymptotically Optimal Secure Aggregation for Wireless Federated Learning with Multiple Servers

T0 review · 3 major / 3 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The paper claims that a Lagrange-coded, artificial-noise-aligned multi-server aggregation scheme achieves uplink normalized delivery time within a factor of 4 of the information-theoretic lower bound for all user/server counts, and is…

desk verdict Real achievable scheme with a repairable but genuine hole in the converse; the optimality claim is not proven as submitted. read the letter →

arxiv 2506.23680 v1 pith:4PO7IFJE submitted 2025-06-30 cs.IT math.IT

Zhenhao Huang , Kai Liang , Yuanming Shi , Songze Li , Youlong Wu This is my paper · ORCID
classification cs.ITmath.IT MSC 94A1594A62
keywords secureaggregationwirelessfederatedlearningnormalizeddeliverytimeLagrangecodingartificialnoisealignmentinformation-theoreticprivacymulti-serversystemsinterference
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper asks how long it takes to securely aggregate private gradients in federated learning over a wireless channel, where the aggregation must be computed without any server learning the individual gradients or even the aggregate itself. It proposes a scheme in which each user encodes its gradient into $K$ shares using polynomial interpolation, one share for each of $K$ servers, and the servers only forward sums of their received shares while users send artificial noise to prevent eavesdropping servers from decoding the shares. The paper proves information-theoretic privacy and derives the communication latency in normalized delivery time (NDT); with $r=K-1$ segments, the uplink NDT is $(M/(K-1)+1)\cdot M/(M-1)$ and the downlink NDT is $(M+K-1)/(K-1)$. It also establishes a lower bound on NDT and shows that the uplink NDT is within a multiplicative factor of 4 of that lower bound for all $K$ and $M$, and asymptotically optimal when the number of servers is much larger than the number of users. A sympathetic reader would care because it suggests that adding more servers can simultaneously protect privacy and reduce latency in wireless federated learning.

What carries the argument

The central object is the Lagrange-coded secret-sharing polynomial $G_i(x)$ together with the artificial-noise-alignment beamforming design for the resulting $K\times(M-1)$ X-network with confidential messages. Each user encodes $r=K-1$ gradient parts plus one random mask into a degree-$r$ polynomial; the $K$ evaluations at points $\alpha_j$ become the confidential messages, and the sum polynomial $F(x)=\sum_i G_i(x)$ makes the aggregate recoverable by interpolation at $\beta_k$. The noise-alignment construction, based on the secure degrees-of-freedom result for X-networks, lets each server decode only its own message while all other messages are aligned with artificial noise, which both provides privacy and yields the DoF that determines the NDT.

What would settle it

For $K=3$, take a user's encoded messages $c_1=m$, $c_2=g+m$, and $c_3=\emptyset$; then the left side of equation (38) equals $2A$ bits while the right side equals $4A/3$ bits, so the asserted Han's-inequality step fails. Checking such an assignment shows the converse proof does not establish the claimed lower bound, leaving the asymptotic-optimality claim unsupported.

Watch

Extended reading notes

Core claim

The central claim is Theorem 3: with $r=K-1$, the proposed scheme achieves uplink NDT $\Delta_{\mathrm{up}} = (M/(K-1)+1)\cdot M/(M-1)$ for $K\ge 3$ and downlink NDT $\Delta_{\mathrm{down}} = (M+K-1)/(K-1)$, which are asymptotically optimal when $K\gg M$ (and $M\gg 0$ for uplink), and the uplink NDT is within a multiplicative gap of 4 of the lower bound $\Delta_{\mathrm{up}}^{\mathrm{lb}} = \max\{M,K\}/(K-1)$ for all $K,M$. The scheme works by having each user split its gradient into $r=K-1$ parts, build a degree-$r$ Lagrange polynomial $G_i(x)$ whose evaluations at $\beta_1,\dots,\beta_r$ are the parts, and send the $K$ evaluations at $\alpha_1,\dots,\alpha_K$ as confidential messages to the $K$ servers; the servers, using artificial noise alignment, decode only their own message and forward the sum of the messages, so each server holds one evaluation of the aggregate polynomial $F(x)=\sum_i G_i(x)$. After $K$ such evaluations, every user interpolates $F$ and reads off the aggregated gradient at the $\beta$-points. The privacy guarantee is information-theoretic: the equivocation at each server tends to 1, and the paper shows the servers cannot infer the local gradients or the aggregate value.

Load-bearing premise

The claimed optimality rests on a mathematical inequality about how much the shares a server receives reveal about the shares of other servers; that inequality holds for the paper's linear encoding but not for arbitrary encodings, so the general lower bound is not proven.

Editorial extensions

If this is right

  • If the optimality results hold, then in the $K\gg M$ regime the latency overhead of privacy is negligible: secure aggregation costs essentially the same normalized delivery time as the information-theoretic lower bound.
  • The factor-4 gap guarantee for all $K$ and $M$ means the upload strategy is order-optimal even when the number of users and servers are comparable, so no order-level latency improvement is available from a different scheme.
  • Because both uplink and downlink NDT fall monotonically with $K$, adding servers is a proven lever for latency reduction in multi-server wireless federated learning, not just a privacy safeguard.
  • The downlink NDT formula implies that the cost of broadcasting the aggregate to users grows only linearly with the user-server ratio $M/K$, so the scheme scales to large user populations when many servers are available.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The questionable Han's-inequality step in the converse suggests a possible weaker lower bound for arbitrary encodings; if so, there may exist schemes outside the Lagrange-code family that beat the proposed latency, particularly when $K$ is not much larger than $M$.
  • The paper's Remark 4 points toward blind interference alignment as a way to drop the CSIT requirement; quantifying the latency cost of that replacement is a natural extension the authors do not carry out.
  • One testable extension is to let $r$ be smaller than $K-1$: the formulas suggest a tradeoff between the number of shares (and thus privacy or robustness) and NDT, which the paper does not fully optimize.
  • The full-duplex assumption for servers is used to justify extra alignment conditions; a half-duplex variant would relax those conditions and could yield a different (improved) downlink NDT, but the paper only notes this in passing.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 3 minor

Summary. The paper studies a wireless federated learning system with M users and K semi-honest servers, in which users want to recover the sum of their local gradients while the servers learn neither the individual gradients nor the aggregate. The proposed scheme combines Lagrange-coded multi-secret sharing (each user encodes its gradient into K messages) with artificial-noise alignment over an M×K X-network. The paper derives achievable uplink and downlink NDTs (Theorem 1), states an information-theoretic privacy guarantee (Section IV-B), gives a converse lower bound on NDT (Theorem 2), and claims asymptotic optimality for K≫M plus a multiplicative gap of at most 4 for the uplink (Theorem 3).

Significance. The problem is timely and the proposed architecture is natural. The paper provides an explicit achievability construction with a concrete complexity analysis, and the privacy proof follows a standard equivocation argument. If Theorem 2 were established, the claimed NDT bounds would give a useful order-optimal characterization for private multi-server wireless aggregation and would improve on single-server baselines. The main caveat is that the converse proof, which is the load-bearing part of the optimality claims, contains an invalid entropy inequality; the theorem is probably repairable, but as printed the proof is incomplete.

major comments (3)
  1. [Appendix A, Eq. (38)] The inequality H(c_{K\{j},i}|c_{j,i}) ≤ (K−1)/K ∑_{k=1}^K H(c_{k,i}) is claimed to follow from Han's inequality, but it is not a general consequence of the model and is false for valid schemes. For K=3, take c_{1,i}=n_i, c_{2,i}=g_i+n_i, c_{3,i}=∅ with uniform independent g_i,n_i. Each server's observation is either a one-time-padded value or nothing, so the per-server privacy constraint holds, and the user can recover g_i from c_{2,i}−c_{1,i}; the same construction for all users permits recovery of ∑ g_i from the summed shares. Yet for j=3 the left side equals H(c_{1,i},c_{2,i}|c_{3,i})=2A while the right side equals (2/3)(A+A+0)=4A/3. Thus the step leading to (38) is invalid, and the derivation of (39) and the bound Δ_up^lb is not established as printed. A repair appears to be available: from the preceding chain one has A ≤ H(c_{K\{j},i}|c_{j,i})+ε for each j; summing over j gives K A ≤ ∑_j H(c_{K\{j},i}|c_{j,i})+Kε = K H(c_{[K],i})−∑_k H(c_{k,i})+Kε ≤ (K−1)∑_k H(c_{k,i})+Kε, which implies the same final bound. The manuscript should replace (38) with this argument.
  2. [Appendix A, Eq. (44)] The downlink converse uses the same invalid step, H(\tilde{c}_{t,K\{j}}|\tilde{c}_{t,j}) ≤ (K−1)/K ∑_{k=1}^K H(\tilde{c}_{t,k}), with the same citation to Han's inequality. Since the downlink lower bound Δ_down^lb = K/(K−1) in Theorem 2 relies on (44), this part of the converse is also unproven as printed. The same summing-over-j repair applies here as well.
  3. [Theorem 3] Because Theorem 3's asymptotic optimality and gap-4 claims are derived by comparing the achievable NDTs to the lower bounds of Theorem 2, the optimality statements are contingent on the repair of the converse. If the repair described above is adopted, the comparison in the proof of Theorem 3 goes through unchanged; without it, the claimed optimality is not supported.
minor comments (3)
  1. [Section III-A] The text says 'server j ∈ [4] first recovers confidential messages {c_{j,1},...,c_{j,4}}' but the example has M=5 users; the set should be {c_{j,1},...,c_{j,5}}, as the sum immediately below correctly reflects.
  2. [Eq. (7)] The product notation Ö_{l=1}^{[r+1]\{k}} is nonstandard and should be written as ∏_{l∈[r+1]\{k}}.
  3. [Definition 3] Definition 3 states 'lim_{A,P→∞} Δ_j^{g_M} = 1−ε for arbitrary small positive ε' while Section IV-B concludes the limit equals 1; the role of ε should be clarified, for example by stating that the limit is 1 and the ε is used only in finite-precision statements.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the NDT achievability and privacy claims rest on external DoF and coding results, while the invalid Han's-inequality step in Appendix A is a repairable proof error rather than a self-referential reduction.

full rationale

The claimed achievability (Theorem 1) is derived from the proposed Lagrange-coded secret sharing and from Lemma 1, which is taken from the external X-network secure-DoF result [39]; the NDT expressions then follow by substituting the explicit block lengths into Definition 2. The privacy proof in Section IV-B uses the MDS/Lagrange structure to cancel the randomness (Eq. (24)) and the artificial-noise alignment subspaces from [39] to show that each server's mutual information is o(log P); these are independent ingredients, not the target NDT claims. Theorem 3 is then pure algebra comparing the achievable NDT with Theorem 2. The one serious defect is in Appendix A: Eq. (38) is not a consequence of Han's inequality, and the displayed bound H(c_{K\{j},i}|c_{j,i}) <= (K-1)/K sum_k H(c_{k,i}) is false for a valid three-server scheme with c1=n, c2=g+n, c3=empty, which still satisfies the model's correctness and privacy requirements. This makes the printed converse proof invalid, but it is a mathematical correctness gap rather than circularity: the step is an attempted universal entropy bound, not a fitted parameter, a definitional identity, or an imported self-citation, and the argument is repairable by summing the preceding per-j bounds before applying Han's inequality in its valid form. Self-citations ([1], [36], [42], [46]) appear but are not load-bearing: [39] and [42] are external results, and [42] is a standard Lagrange-coding construction. Thus no central claim reduces to its own inputs by construction, and the circularity score is 0.

Assumptions & free parameters 1 free parameters · 6 assumptions · 0 invented entities

The scheme relies on standard finite-field secret sharing and known interference alignment results; no new physical entities are introduced. The main input from prior work is the secure DoF theorem of [39], which is not re-derived. The free parameter r is a design choice in the coding scheme, not a fitted constant.

free parameters (1)
  • r (number of gradient segments) = K-1
    Design parameter in Lagrange coding. The NDT formulas scale as 1/r, and the paper sets r=K-1 to minimize latency for the optimality claims. Not fitted to data, but a hand-chosen parameter.
assumptions (6)
  • domain assumption Channel coefficients are i.i.d. across time and users, and both users and servers know CSI perfectly.
    Section II system model. Needed for the interference alignment construction and for the secure DoF expressions.
  • domain assumption The secure sum DoF of the M x K X-network with confidential messages is as stated in Lemma 1 (Theorem 2 of [39]).
    Section III-B uses this result to compute the achievable NDT. It is a prior result, not re-derived in this paper.
  • domain assumption There exist beamforming matrices satisfying the alignment conditions (11) and (16) for generic channel realizations.
    The construction is given in Section III-B and existence is established in [39]. The paper relies on this existence for the DoF claims.
  • domain assumption Gradients are independent and uniformly distributed over the finite field.
    Stated in Section II and Definition 3. Required for the converse proof and the equivocation analysis. The authors note it is not needed for achievability.
  • domain assumption Servers are semi-honest and non-colluding; each server is an eavesdropper for messages intended to other servers in both uplink and downlink.
    Section II threat model. The privacy guarantee is per-server only; colluding servers are not considered, and the conference version explicitly dropped collusion.
  • domain assumption Servers operate in full-duplex mode during the downlink.
    Remark 2. Needed for the downlink alignment conditions at the servers, which prevent a server from overhearing other servers' downlink transmissions.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Asymptotically Optimal Secure Aggregation for Wireless Federated Learning with Multiple Servers." pith.science (2026). https://pith.science/paper/4PO7IFJE

@misc{pith2026250623680,
  author       = {Pith},
  title        = {Pith review of: Asymptotically Optimal Secure Aggregation for Wireless Federated Learning with Multiple Servers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4PO7IFJE}},
  note         = {Machine review of arXiv:2506.23680}
}
abstract

In this paper, we investigate the transmission latency of the secure aggregation problem in a \emph{wireless} federated learning system with multiple curious servers. We propose a privacy-preserving coded aggregation scheme where the servers can not infer any information about the distributed users' local gradients, nor the aggregation value. In our scheme, each user encodes its local gradient into $\sK$ confidential messages intended exclusively for different servers using a multi-secret sharing method, and each server forwards the summation of the received confidential messages, while the users sequentially employ artificial noise alignment techniques to facilitate secure transmission. Through these summations, the user can recover the aggregation of all local gradients. We prove the privacy guarantee in the information-theoretic sense and characterize the uplink and downlink communication latency measured by \emph{normalized delivery time} (NDT), both of which decrease monotonically with the number of servers $\sK$ while increasing over most of the range of the number of users $\sM$. Finally, we establish a lower bound on the NDT of the considered system and theoretically prove that the scheme achieves the optimal uplink and downlink NDT under the conditions $\sK \gg \sM \gg 0$ and $\sK \gg \sM$, respectively. For arbitrary $\sK$ and $\sM$, the proposed scheme achieves the optimal uplink NDT within a multiplicative gap of $4$.

Figures

Figures reproduced from arXiv: 2506.23680 by the authors.

Figure 1
Figure 1. Aggregation over wireless network with multi-server. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. The uplink transmission over the wireless network. For server [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Uplink and Downlink NDTs versus M when 𝑟 = K−1. lower uplink NDT except the case K = 2 (see [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: The comparison of achievable NDT and the converse [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

47 extracted references · 34 canonical work pages

  1. [1]

    Secure gradient aggregation for wireless multi-server federated learning,

    Z. Huang, S. Li, K. Liang, and Y . Wu, “Secure gradient aggregation for wireless multi-server federated learning,” in 2023 IEEE International Symposium on Information Theory (ISIT) , 2023, pp. 2404–2409

    work page 2023

  2. [2]

    Toward an intelligent edge: Wireless communication meets machine learning,

    G. Zhu, D. Liu, Y . Du, C. You, J. Zhang, and K. Huang, “Toward an intelligent edge: Wireless communication meets machine learning,” IEEE Communications Magazine , vol. 58, no. 1, pp. 19–25, 2020

    work page 2020

  3. [3]

    Communication- efficient edge ai: Algorithms and systems,

    Y . Shi, K. Yang, T. Jiang, J. Zhang, and K. B. Letaief, “Communication- efficient edge ai: Algorithms and systems,” IEEE Communications Surveys & Tutorials, vol. 22, no. 4, pp. 2167–2191, 2020

    2020

  4. [4]

    Task- oriented communications for 6g: Vision, principles, and technologies,

    Y . Shi, Y . Zhou, D. Wen, Y . Wu, C. Jiang, and K. B. Letaief, “Task- oriented communications for 6g: Vision, principles, and technologies,” IEEE Wireless Communications, vol. 30, no. 3, pp. 78–85, 2023

    work page 2023

  5. [5]

    Edge artificial intelligence for 6g: Vision, enabling technologies, and applications,

    K. B. Letaief, Y . Shi, J. Lu, and J. Lu, “Edge artificial intelligence for 6g: Vision, enabling technologies, and applications,” IEEE Journal on Selected Areas in Communications , vol. 40, no. 1, pp. 5–36, 2021

    work page 2021

  6. [6]

    Private retrieval, computing, and learning: Recent progress and future challenges,

    S. Ulukus, S. Avestimehr, M. Gastpar, S. A. Jafar, R. Tandon, and C. Tian, “Private retrieval, computing, and learning: Recent progress and future challenges,” IEEE Journal on Selected Areas in Communications , vol. 40, no. 3, pp. 729–748, 2022

    work page 2022

  7. [7]

    Trusted ai in multiagent systems: An overview of privacy and security for distributed learning,

    C. Ma, J. Li, K. Wei, B. Liu, M. Ding, L. Yuan, Z. Han, and H. V . Poor, “Trusted ai in multiagent systems: An overview of privacy and security for distributed learning,” Proceedings of the IEEE , vol. 111, no. 9, pp. 1097–1132, 2023

    work page 2023

  8. [8]

    Communication-efficient learning of deep networks from decentralized data,

    B. McMahan, E. Moore, D. Ramage, S. Hampson, and B. A. y Arcas, “Communication-efficient learning of deep networks from decentralized data,” in Artificial intelligence and statistics . PMLR, 2017, pp. 1273– 1282

    2017

Show all 47 references
  1. [9]

    Advances and open problems in federated learning,

    P. Kairouz, H. B. McMahan, B. Avent21, A. Bellet, M. Bennis19, A. N. Bhagoji13, K. Bonawitz, Z. Charles, G. Cormode23, R. Cummingset al., “Advances and open problems in federated learning,” arXiv preprint arXiv:1912.04977, 2019

    1912 arXiv

  2. [10]

    Inverting gradients - how easy is it to break privacy in federated learning?

    J. Geiping, H. Bauermeister, H. Dr ¨oge, and M. Moeller, “Inverting gradients - how easy is it to break privacy in federated learning?” in Proceedings of the 34th International Conference on Neural Information Processing Systems , ser. NIPS’20. Red Hook, NY , USA: Curran Assoc...

    2020

  3. [11]

    Beyond inferring class representatives: User-level privacy leakage from federated learning,

    Z. Wang, M. Song, Z. Zhang, Y . Song, Q. Wang, and H. Qi, “Beyond inferring class representatives: User-level privacy leakage from federated learning,” in IEEE INFOCOM 2019 - IEEE Conference on Computer Communications, 2019, pp. 2512–2520

    2019

  4. [12]

    Deep leakage from gradients,

    L. Zhu, Z. Liu, and S. Han, “Deep leakage from gradients,” Advances in neural information processing systems , vol. 32, 2019

    2019

  5. [13]

    Differentially private federated learning: A client level perspective,

    R. C. Geyer, T. Klein, and M. Nabi, “Differentially private federated learning: A client level perspective,” arXiv preprint arXiv:1712.07557 , 2017

    2017 arXiv

  6. [14]

    Ldp-fl: Practical private aggregation in federated learning with local differential privacy,

    L. Sun, J. Qian, and X. Chen, “Ldp-fl: Practical private aggregation in federated learning with local differential privacy,” arXiv preprint arXiv:2007.15789, 2020

    2007 arXiv

  7. [15]

    The algorithmic foundations of differential privacy,

    C. Dwork, A. Roth et al. , “The algorithmic foundations of differential privacy,” Foundations and Trends® in Theoretical Computer Science , vol. 9, no. 3–4, pp. 211–407, 2014

    2014

  8. [16]

    Wireless federated learning with local differential privacy,

    M. Seif, R. Tandon, and M. Li, “Wireless federated learning with local differential privacy,” in 2020 IEEE International Symposium on Information Theory (ISIT) . IEEE, 2020, pp. 2604–2609

    2020

  9. [17]

    Privacy for free: Wireless federated learning via uncoded transmission with adaptive power control,

    D. Liu and O. Simeone, “Privacy for free: Wireless federated learning via uncoded transmission with adaptive power control,” IEEE Journal on Selected Areas in Communications, vol. 39, no. 1, pp. 170–185, 2020

    2020

  10. [18]

    Harnessing wireless channels for scalable and privacy-preserving federated learning,

    A. Elgabli, J. Park, C. B. Issaid, and M. Bennis, “Harnessing wireless channels for scalable and privacy-preserving federated learning,” IEEE Transactions on Communications, vol. 69, no. 8, pp. 5194–5208, 2021

    2021

  11. [19]

    Differentially private federated learning via reconfigurable intelligent surface,

    Y . Yang, Y . Zhou, Y . Wu, and Y . Shi, “Differentially private federated learning via reconfigurable intelligent surface,” IEEE Internet of Things journal, vol. 9, no. 20, pp. 19 728–19 743, 2022

    2022

  12. [20]

    Practical secure aggregation for federated learning on user-held data,

    K. Bonawitz, V . Ivanov, B. Kreuter, A. Marcedone, H. B. McMa- han, S. Patel, D. Ramage, A. Segal, and K. Seth, “Practical secure aggregation for federated learning on user-held data,” arXiv preprint arXiv:1611.04482, 2016

    2016 arXiv

  13. [21]

    Practical secure aggregation for privacy-preserving machine learning,

    ——, “Practical secure aggregation for privacy-preserving machine learning,” in Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security , ser. CCS ’17. New York, NY , USA: Association for Computing Machinery, 2017, p. 1175–1191. [Online]. Available...

    2017

  14. [22]

    Privacy-preserving deep learning via additively homomorphic encryption,

    Y . Aono, T. Hayashi, L. Wang, S. Moriaiet al., “Privacy-preserving deep learning via additively homomorphic encryption,” IEEE transactions on information forensics and security, vol. 13, no. 5, pp. 1333–1345, 2017

    2017

  15. [23]

    Secure single-server aggregation with (poly) logarithmic overhead,

    J. H. Bell, K. A. Bonawitz, A. Gasc ´on, T. Lepoint, and M. Raykova, “Secure single-server aggregation with (poly) logarithmic overhead,” in Proceedings of the 2020 ACM SIGSAC Conference on Computer and Communications Security, 2020, pp. 1253–1269

    2020

  16. [24]

    Fast- secagg: Scalable secure aggregation for privacy-preserving federated learning,

    S. Kadhe, N. Rajaraman, O. O. Koyluoglu, and K. Ramchandran, “Fast- secagg: Scalable secure aggregation for privacy-preserving federated learning,” arXiv preprint arXiv:2009.11248 , 2020

    2009 arXiv

  17. [25]

    Turbo-aggregate: Breaking the quadratic aggregation barrier in secure federated learning,

    J. So, B. G ¨uler, and A. S. Avestimehr, “Turbo-aggregate: Breaking the quadratic aggregation barrier in secure federated learning,”IEEE Journal on Selected Areas in Information Theory , vol. 2, no. 1, pp. 479–489, 2021

    2021

  18. [26]

    Lightsecagg: Rethinking secure aggregation in federated learning,

    C.-S. Yang, J. So, C. He, S. Li, Q. Yu, and S. Avestimehr, “Lightsecagg: Rethinking secure aggregation in federated learning,” arXiv preprint arXiv:2109.14236, 2021

    2021 arXiv

  19. [27]

    Information theoretic secure aggregation with user dropouts,

    Y . Zhao and H. Sun, “Information theoretic secure aggregation with user dropouts,” IEEE Transactions on Information Theory , vol. 68, no. 11, pp. 7471–7484, 2022

    2022

  20. [28]

    Distributed learning in wireless networks: Recent progress and future challenges,

    M. Chen, D. G ¨und¨uz, K. Huang, W. Saad, M. Bennis, A. V . Feljan, and H. V . Poor, “Distributed learning in wireless networks: Recent progress and future challenges,” IEEE Journal on Selected Areas in Communications, vol. 39, no. 12, pp. 3579–3605, 2021

    2021

  21. [29]

    Federated learning over wireless fading channels,

    M. M. Amiri and D. G ¨und¨uz, “Federated learning over wireless fading channels,” IEEE Transactions on Wireless Communications , vol. 19, no. 5, pp. 3546–3557, 2020

    2020

  22. [30]

    When wireless federated learning meets physical layer security: The fundamental limits,

    H. Zhang, C. Yang, and B. Dai, “When wireless federated learning meets physical layer security: The fundamental limits,” in IEEE INFOCOM 2022-IEEE Conference on Computer Communications Workshops (IN- FOCOM WKSHPS). IEEE, 2022, pp. 1–6

    2022

  23. [31]

    On safeguarding privacy and security in the framework of federated learning,

    C. Ma, J. Li, M. Ding, H. H. Yang, F. Shu, T. Q. Quek, and H. V . Poor, “On safeguarding privacy and security in the framework of federated learning,” IEEE network, vol. 34, no. 4, pp. 242–248, 2020

    2020

  24. [32]

    Federated learning with differential privacy: Algorithms and performance analysis,

    K. Wei, J. Li, M. Ding, C. Ma, H. H. Yang, F. Farokhi, S. Jin, T. Q. Quek, and H. V . Poor, “Federated learning with differential privacy: Algorithms and performance analysis,” IEEE transactions on information forensics and security, vol. 15, pp. 3454–3469, 2020

    2020

  25. [33]

    Securing secure aggregation: Mitigating multi-round privacy leakage in federated learn- ing,

    J. So, R. E. Ali, B. G ¨uler, J. Jiao, and A. S. Avestimehr, “Securing secure aggregation: Mitigating multi-round privacy leakage in federated learn- ing,” in Proceedings of the AAAI Conference on Artificial Intelligence , vol. 37, no. 8, 2023, pp. 9864–9873

    2023

  26. [34]

    How much privacy does federated learning with secure aggregation guarantee?

    A. R. Elkordy, J. Zhang, Y . H. Ezzeldin, K. Psounis, and S. Avestimehr, “How much privacy does federated learning with secure aggregation guarantee?” Proceedings on Privacy Enhancing Technologies , vol. 1, pp. 510–526, 2023

    2023

  27. [35]

    X-secure t-private federated submodel learning with elastic dropout resilience,

    Z. Jia and S. A. Jafar, “X-secure t-private federated submodel learning with elastic dropout resilience,” IEEE Transactions on Information Theory, vol. 68, no. 8, pp. 5418–5439, 2022

    2022

  28. [36]

    Privacy-preserving coded schemes for multi-server federated learning with straggling links,

    K. Liang, S. Li, M. Ding, F. Tian, and Y . Wu, “Privacy-preserving coded schemes for multi-server federated learning with straggling links,” IEEE Transactions on Information Forensics and Security , 2024

    2024

  29. [37]

    Cache aided wireless networks: Tradeoffs between storage and latency,

    A. Sengupta, R. Tandon, and O. Simeone, “Cache aided wireless networks: Tradeoffs between storage and latency,” in 2016 Annual Conference on Information Science and Systems (CISS) , 2016, pp. 320– 325

    2016

  30. [38]

    On secrecy metrics for physi- cal layer security over quasi-static fading channels,

    B. He, X. Zhou, and A. L. Swindlehurst, “On secrecy metrics for physi- cal layer security over quasi-static fading channels,” IEEE Transactions on Wireless Communications, vol. 15, no. 10, pp. 6913–6924, 2016

    2016

  31. [39]

    Secure degrees of freedom of wireless x networks using artificial noise alignment,

    Z. Wang, M. Xiao, M. Skoglund, and H. V . Poor, “Secure degrees of freedom of wireless x networks using artificial noise alignment,” IEEE Transactions on communications , vol. 63, no. 7, pp. 2632–2646, 2015

    2015

  32. [40]

    Security of ramp schemes,

    G. R. Blakley and C. Meadows, “Security of ramp schemes,” in Advances in Cryptology: Proceedings of CRYPTO 84 4 . Springer, 1985, pp. 242–268

    1985

  33. [41]

    Communication complexity of secure com- putation,

    M. Franklin and M. Yung, “Communication complexity of secure com- putation,” in Proceedings of the twenty-fourth annual ACM symposium on Theory of computing , 1992, pp. 699–710

    1992

  34. [42]

    Lagrange coded computing: Optimal design for resiliency, security, and privacy,

    Q. Yu, S. Li, N. Raviv, S. M. M. Kalan, M. Soltanolkotabi, and S. A. Avestimehr, “Lagrange coded computing: Optimal design for resiliency, security, and privacy,” inThe 22nd International Conference on Artificial Intelligence and Statistics . PMLR, 2019, pp. 1215–1225. 13

    2019

  35. [43]

    Secure degrees of freedom of one-hop wireless networks,

    J. Xie and S. Ulukus, “Secure degrees of freedom of one-hop wireless networks,” IEEE Transactions on Information Theory , vol. 60, no. 6, pp. 3359–3378, 2014

    2014

  36. [44]

    Fast polynomial factorization and modular composition,

    K. S. Kedlaya and C. Umans, “Fast polynomial factorization and modular composition,” SIAM Journal on Computing , vol. 40, no. 6, pp. 1767–1802, 2011

    2011

  37. [45]

    Aiming perfectly in the dark- blind interference alignment through staggered antenna switching,

    T. Gou, C. Wang, and S. A. Jafar, “Aiming perfectly in the dark- blind interference alignment through staggered antenna switching,”IEEE Transactions on Signal Processing, vol. 59, no. 6, pp. 2734–2744, 2011

    2011

  38. [46]

    Coded computing for half-duplex wireless distributed computing systems via interference alignment,

    Z. Huang, K. Yuan, S. Ma, Y . Bi, and Y . Wu, “Coded computing for half-duplex wireless distributed computing systems via interference alignment,” IEEE Transactions on Wireless Communications , 2024

    2024

  39. [47]

    Blind interference alignment for mapreduce: Ex- ploiting side-information with reconfigurable antennas,

    Y . Lu and S. A. Jafar, “Blind interference alignment for mapreduce: Ex- ploiting side-information with reconfigurable antennas,” arXiv preprint arXiv:2404.09141, 2024

    2024

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.