Pith. sign in

REVIEW 2 major objections 5 minor 42 references

A General Coding Framework for Adaptive Private Information Retrieval

T0 review · 2 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read Any feasible PIR coding framework yields an adaptive scheme that matches the best known rate for every straggler count, without knowing the count in advance.

desk verdict Adaptive PIR for coded storage with unknown straggler counts: a sound framework theorem and query-array construction, with one existence lemma that is asserted rather than proved and should be completed before acceptance. read the letter →

arxiv 2506.07787 v1 pith:UXNFQNZ7 submitted 2025-06-09 cs.IT math.IT

Jinbao Zhu , Xiaohu Tang This is my paper
classification cs.ITmath.IT MSC 94A6068P20
keywords adaptiveprivateinformationretrievalstragglertoleranceT-colludingprivacyX-secureK-codedstoragefeasiblePIRcodingframeworkLagrangecodesratefinitefieldsize
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 whether a user can retrieve one file from an $N$-server system, protected by $T$-server collusion privacy and $X$-secure $K$-coded storage, without knowing in advance how many servers are slow or silent. It answers yes: any 'feasible PIR coding framework' over a finite field $\mathbb{F}_q$ yields an adaptive scheme that achieves rate $1-\frac{K+X+T-1}{N-S}$ simultaneously for every straggler count $0\le S\le N-(K+X+T)$, matching the best known rate for the case where $S$ is known. The paper also gives a Lagrange-code implementation of such a framework, so the adaptive scheme works over any finite field of size $q\ge N+\max\{K, N-(K+X+T-1)\}$. If correct, the result removes a restrictive assumption in earlier schemes and supports the conjectured asymptotic optimality of this rate.

What carries the argument

The load-bearing object is the feasible PIR coding framework (Definition 2): a set of evaluation points $\alpha_0,\ldots,\alpha_{N-1}$ and encoding functions for storage and queries such that four conditions hold. $\tilde{F}0$ makes any $K+X$ servers reconstruct the files; $\tilde{F}1$ makes the noise matrices nonsingular so that $X$ servers learn nothing about the files and $T$ servers learn nothing about the desired index; $\tilde{F}2$ lets a requested partial file be decoded from any $N-(\lambda-r)$ responses; and $\tilde{F}3$ — the key adaptive ingredient — lets the partial file still be decoded from fewer responses once any $d$ of its rows are already known. The paper's adaptive scheme stacks these frameworks through a query array of $\lambda$ subarrays satisfying conditions C0–C3, with the $h$-th subarray compensating the missing responses of the earlier layers. The implementation section constructs storage and query functions as Lagrange interpolating polynomials whose evaluation points obey constraints P0–P3.

What would settle it

Run the Lagrange construction for a concrete larger instance, say $N=10,K=X=T=2$, and check the decoding condition $\tilde{F}3$: for a partial file with $r$ rows, after obtaining $d$ rows, are the claimed $N-(\lambda-r+d)$ responses sufficient to interpolate the answer polynomial? A single parameter set where interpolation fails, or where the required responses exceed the claimed count, would refute Theorem 2's existence claim.

Watch

Extended reading notes

Core claim

The paper's central claim is Theorem 1: any feasible PIR coding framework over $\mathbb{F}_q$ can be converted into an adaptive PIR scheme that tolerates $S$ stragglers simultaneously for all $0\le S\le N-(K+X+T)$, at retrieval rate $1-\frac{K+X+T-1}{N-S}$ over the same field. Theorem 2 asserts such a framework exists for any prime power $q$ with $q\ge N+\max\{K,\lambda\}$, where $\lambda=N-(K+X+T-1)$, via Lagrange interpolation. The adaptive guarantee comes from a layered query array: layer $h$ compensates the missing responses of the first $h$ layers when $S=h$ stragglers appear, so the user only waits for responses from the fastest $N-S$ servers and still retrieves the file at the rate appropriate to the actual $S$.

Load-bearing premise

The paper's existence guarantee rests on the claim that the Lagrange-code construction satisfies conditions F0–F3 for all parameters, but that feasibility is asserted by reference to earlier work and only demonstrated by example (Appendix B) rather than proved in this paper; if the construction fails for some $N,K,X,T$, Theorem 2's existence claim collapses, though Theorem 1's reduction would remain valid.

Editorial extensions

If this is right

  • A user retrieving a file no longer needs to know the number of stragglers in advance; the same queries and responses work for any $S$ in the allowed range.
  • For every $S$, the achieved rate $1-\frac{K+X+T-1}{N-S}$ equals the best previously known rate for the known-$S$ setting, so adaptivity comes at no rate penalty.
  • The finite field size required, $q\ge N+\max\{K,\lambda\}$, matches the field size of the best known non-adaptive scheme, so adaptivity adds no field-size overhead.
  • The construction includes earlier adaptive PIR schemes as special cases: setting $X=0,T=1$ recovers coded-storage adaptive PIR, and setting $X=0,K=1$ recovers $T$-colluding adaptive PIR with replicated storage.
  • With the Lagrange implementation, waiting for responses from an additional $2B$ servers gives robustness against up to $B$ Byzantine servers, at rate $1-\frac{K+X+T+2B-1}{N-S}$.

Reading between the lines

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

  • The reduction in Theorem 1 means that any future construction satisfying F0–F3, for example via cross-subspace alignment codes, would automatically yield an adaptive scheme with the same rate and field size; the paper's contribution is therefore a template as much as a single scheme.
  • The file length is $K\lambda\cdot\mathrm{lcm}(1,2,\ldots,\lambda)$, which grows superexponentially in $\lambda$; a natural next step, not addressed here, is whether the query array can be shortened so that the required file length becomes linear in $\lambda$.
  • Because the query array is described purely combinatorially by conditions C0–C3, the adaptive construction could likely be exported to other distributed-computation settings, such as secure multiparty computation or federated submodel learning, where stragglers are also unknown in advance.
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

2 major / 5 minor

Summary. The paper studies T-colluding private information retrieval from an X-secure K-coded distributed storage system in which the number and identities of stragglers are unknown in advance and may vary over time. It introduces the concept of a "feasible PIR coding framework" (Definition 2), specified by conditions F0–F3, and proves in Theorem 1 that any such framework over a finite field F_q yields an adaptive PIR scheme achieving rate 1 - (K+X+T-1)/(N-S) simultaneously for all 0 ≤ S ≤ N-(K+X+T). The adaptive scheme is built from a λ × P query array satisfying conditions C0–C3 (Algorithm 1 and Lemma 3). The paper then claims, in Lemma 2 and Theorem 2, that a Lagrange-code implementation provides such a feasible framework for every prime power q ≥ N + max{K, N-(K+X+T-1)}. The proof of Theorem 1 and the query-array lemma are detailed; the existence half rests on Lemma 2, whose general proof is not supplied.

Significance. If it holds, the main result is a meaningful conceptual advance: the user no longer needs to know the actual number of stragglers before starting retrieval, and the achieved rate matches the best known rate of known-S schemes from [13] and [15]. The reduction in Theorem 1 is an elegant abstraction, and the query-array construction in Section IV-C is explicit and appears correct; the detailed examples in Sections III-A and IV-B are also useful. The paper correctly identifies the relationship to the earlier adaptive schemes [16] and [17]. The principal weakness is that Theorem 2, the unconditional existence claim, depends on Lemma 2, and the feasibility of the Lagrange implementation is not proved for general parameters beyond a single example. Thus the paper currently establishes a conditional general framework plus one illustrated instance, rather than a fully supported existence theorem.

major comments (2)
  1. [Section III-B, Lemma 2, Appendix B] Lemma 2 asserts that the Lagrange-code construction is a feasible PIR coding framework for all parameter triples, but no general proof is given. The text states that feasibility "can be readily established" by arguments in [32] and [14], and Appendix B verifies the conditions only for the single parameter set N=8, K=X=T=2. In particular, condition F3—decoding a partial file of size r from any N-(λ-r+d) responses together with any d known rows, for arbitrary d ∈ [1:r)—is stronger than the standard decoding guarantees of the cited references, and the paper does not show that those references imply it for general r. Since Theorem 2 follows immediately from Lemma 2, the existence claim is currently unsupported beyond the example. I recommend adding a complete proof of F0–F3 for the Lagrange construction; the degree count of the answer polynomial (degree r+K+X+T-2) together with the distinctness constraints P0–P3 suggests the claim is true, but the argument must be written out.
  2. [Section IV-D, Eq. (67)] The privacy proof invokes Lemma 4 to conclude I(θ; Q_T) = 0, but Lemma 4 is a statement about hiding random secrets behind random noise, whereas the query functions in (59) for m=θ contain the deterministic term v_T rather than a random secret. The lemma therefore does not apply directly. The conclusion is nevertheless correct: for each (m,i,k), the T evaluations of v_0, ..., v_{T-1} at any colluding set form an invertible matrix, so the evaluation vector is uniform over F_q^T for every θ, and the vectors are independent across m. The proof should be rewritten with this direct argument, or with a version of Lemma 4 that explicitly covers a fixed nonzero coefficient.
minor comments (5)
  1. [Theorems 1–2 and Remark 3] There are several typos: "finite filed" appears in Theorem 1, Theorem 2, and Remark 3, and the theorems begin with "F or" instead of "For". Please correct these throughout.
  2. [Notation section] In the Notation section, the sentence "Define AS as {As0, As1, ..., Asn-1}" appears to use the symbol A before it is defined; please clarify the intended notation.
  3. [Definition 2] In Definition 2, the calligraphic symbol K is used both for the storage parameter K and for a subset of servers of size K+X; this is potentially confusing and should be renamed, for example to S.
  4. [Remark 1] Remark 1 asserts that the CSA-code construction also satisfies F0–F3, but it provides only a high-level explanation and no formal verification. Since this remark is not used in the main theorems, it should either be proved or explicitly labeled as a sketch.
  5. [Appendix C] Equation (80) relies on a convention for indexing the columns of U contiguously across subarrays; this convention should be stated explicitly before the equation for readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular reduction found: the adaptive rate follows from the query-array sizes by a telescoping sum, the framework is an explicit hypothesis rather than a disguised conclusion, and the only flagged weakness is an unproved feasibility assertion that is a correctness gap, not circularity.

full rationale

The paper's central derivation is a conditional reduction, not a circular one. Definition 2 introduces a feasible PIR coding framework as a set of explicit conditions F0-F3, and Theorem 1 shows that any object satisfying those conditions yields an adaptive PIR scheme. The decoding correctness of the adaptive scheme does invoke F3, but F3 is an assumed property of the framework, not a restatement of the target rate or of the adaptive guarantee; the framework is defined before and independently of the query-array construction. The retrieval rate is computed arithmetically from the query-array column counts: sum_{h=0}^S Gamma_h = P/(lambda-S) by the telescoping identity 1/((lambda-h)(lambda-h+1)) = 1/(lambda-h) - 1/(lambda-h+1), giving R_S = PK / ((N-S)K P/(lambda-S)) = 1 - (K+X+T-1)/(N-S). No parameter is fitted to data, and the rate is not an input to the framework. The query-array conditions C0-C3 are proved in Lemma 3 and Appendix C, independently of F0-F3. The only substantive concern is Section III-B / Lemma 2: the general feasibility of the Lagrange-code implementation is asserted by saying it 'can be readily established by following arguments similar to those in [32] and [14]', with Appendix B verifying only the N=8, K=X=T=2 example. This is an omitted or deferred proof and a correctness risk for Theorem 2, but it is not a circular reduction: no equation in the paper makes Lemma 2 equivalent to the adaptive rate or to Definition 2 by construction, and the cited works are prior, independently stated results rather than a conclusion of this paper. Under the hard rule requiring a specific reduction, this does not qualify as circularity.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The central construction has no fitted parameters. It relies on the existence of a feasible PIR coding framework (which is proven only via a deferred reference and an example), on finite-field interpolation theorems, and on the ramp-storage model. The query array is constructed rather than postulated.

assumptions (4)
  • domain assumption The storage system is an optimal ramp scheme satisfying secrecy (1), reliability (2), and storage overhead (3).
    Invoked in Section II and Definition 1 as the model for X-secure K-coded storage; the adaptive PIR scheme is built on top of this model.
  • ad hoc to paper There exists a feasible PIR coding framework satisfying conditions F0-F3 over Fq.
    Definition 2 introduces this as the key building block; the paper's existence proof for the Lagrange-code implementation is deferred to prior work [14], [32] and only exemplified in Appendix B.
  • standard math Lagrange interpolation and Cauchy-Vandermonde matrix invertibility (Lemma 5 and [13, Lemma 1]) over finite fields.
    Used in Section III-B and Appendix B to verify F0-F3 for the Lagrange-code implementation and to argue the feasibility of the coding framework.
  • ad hoc to paper The query array constructed in Algorithm 1 satisfies conditions C0-C3.
    Lemma 3 proves this within the paper, but the specific construction is custom-designed to enable the adaptive decoding argument.

how reviews work

0 comments
Cite this review

Pith. "Pith review of A General Coding Framework for Adaptive Private Information Retrieval." pith.science (2026). https://pith.science/paper/UXNFQNZ7

@misc{pith2026250607787,
  author       = {Pith},
  title        = {Pith review of: A General Coding Framework for Adaptive Private Information Retrieval},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UXNFQNZ7}},
  note         = {Machine review of arXiv:2506.07787}
}
abstract

The problem of $T$-colluding private information retrieval (PIR) enables the user to retrieve one out of $M$ files from a distributed storage system with $N$ servers without revealing anything about the index of the desired file to any group of up to $T$ colluding servers. In the considered storage system, the $M$ files are stored across the $N$ distributed servers in an $X$-secure $K$-coded manner such that any group of up to $X$ colluding servers learns nothing about the files; the storage overhead at each server is reduced by a factor of $\frac{1}{K}$ compared to the total size of the files; and the files can be reconstructed from any $K+X$ servers. However, in practical scenarios, when the user retrieves the desired file from the distributed system, some servers may respond to the user very slowly or not respond at all. These servers are referred to as \emph{stragglers}, and particularly their identities and numbers are unknown in advance and may change over time. This paper considers the adaptive PIR problem that can be capable of tolerating the presence of a varying number of stragglers. We propose a general coding method for designing adaptive PIR schemes by introducing the concept of a \emph{feasible PIR coding framework}. We demonstrate that any \emph{feasible PIR coding framework} over a finite field $\mathbb{F}_q$ with size $q$ can be used to construct an adaptive PIR scheme that achieves a retrieval rate of $1-\frac{K+X+T-1}{N-S}$ simultaneously for all numbers of stragglers $0\leq S\leq N-(K+X+T)$ over the same finite field. Additionally, we provide an implementation of the \emph{feasible PIR coding framework}, ensuring that the adaptive PIR scheme operates over any finite field $\mathbb{F}_q$ with size $q\geq N+\max\{K, N-(K+X+T-1)\}$.

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

42 extracted references · 41 canonical work pages

  1. [16]

    Robust private inform ation retrieval on coded data,

    R. Tajeddine and S. El Rouayheb, “Robust private inform ation retrieval on coded data,” in 2017 IEEE International Symposium on Information Theory (ISIT) , pp. 1903–1907, IEEE, 2017

    work page 2017

  2. [17]

    Staircase-pir: Universal ly robust private information retrieval,

    R. Bitar and S. El Rouayheb, “Staircase-pir: Universal ly robust private information retrieval,” in 2018 IEEE Information Theory W orkshop (ITW), pp. 1–5, IEEE, 2018

    work page 2018

  3. [15]

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

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

    work page 2022

  4. [32]

    Symmetric private pol ynomial computation from lagrange encoding,

    J. Zhu, Q. Y an, X. Tang, and S. Li, “Symmetric private pol ynomial computation from lagrange encoding,” IEEE Transactions on Information Theory, vol. 68, no. 4, pp. 2704–2718, 2022

    work page 2022

  5. [14]

    Multi-user blind symmetric private information retrieval from coded servers,

    J. Zhu, Q. Y an, and X. Tang, “Multi-user blind symmetric private information retrieval from coded servers,” IEEE Journal on Selected Areas in Communications , vol. 40, no. 3, pp. 815–831, 2022

    work page 2022

  6. [13]

    X-secure t-private information retrieval from mds coded storage with byzantine and unrespo nsive servers,

    Z. Jia and S. A. Jafar, “X-secure t-private information retrieval from mds coded storage with byzantine and unrespo nsive servers,” IEEE Transactions on Information Theory , vol. 66, no. 12, pp. 7427–7438, 2020

    work page 2020

  7. [1]

    Pri vate information retrieval,

    B. Chor, O. Goldreich, E. Kushilevitz, and M. Sudan, “Pri vate information retrieval,” in Proceedings of IEEE 36th Annual F oundations of Computer Science , pp. 41–50, 1995. 36

    work page 1995

  8. [2]

    Pri vate information retrieval,

    B. Chor, E. Kushilevitz, O. Goldreich, and M. Sudan, “Pri vate information retrieval,” Journal of the ACM (JACM) , vol. 45, no. 6, pp. 965– 981, 1998

    work page 1998

Show all 42 references
  1. [3]

    The capacity of private informati on retrieval,

    H. Sun and S. A. Jafar, “The capacity of private informati on retrieval,” IEEE Transactions on Information Theory , vol. 63, no. 7, pp. 4075– 4088, 2017

    2017

  2. [4]

    Optimal download cost of private i nformation retrieval for arbitrary message length,

    H. Sun and S. A. Jafar, “Optimal download cost of private i nformation retrieval for arbitrary message length,” IEEE Transactions on Information F orensics and Security, vol. 12, no. 12, pp. 2920–2932, 2017

    2017

  3. [5]

    Capacity-achieving privat e information retrieval codes with optimal message size and upload cost,

    C. Tian, H. Sun, and J. Chen, “Capacity-achieving privat e information retrieval codes with optimal message size and upload cost,” IEEE Transactions on Information Theory , vol. 65, no. 11, pp. 7613–7627, 2019

    2019

  4. [6]

    Private retrieval, computing, and learnin g: Recent progress and future challenges,

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

    2022

  5. [7]

    Private information retrieval and its extensions: An introduction, open proble ms, future directions,

    S. Vithana, Z. Wang, and S. Ulukus, “Private information retrieval and its extensions: An introduction, open proble ms, future directions,” IEEE BITS the Information Theory Magazine , vol. 3, no. 4, pp. 67–85, 2023

    2023

  6. [8]

    A guided walk throug h coded private information retrieval,

    R. G. D’Oliveira and S. El Rouayheb, “A guided walk throug h coded private information retrieval,” IEEE BITS the Information Theory Magazine, vol. 3, no. 4, pp. 51–66, 2023

    2023

  7. [9]

    The tail at scale,

    J. Dean and L. A. Barroso, “The tail at scale,” Communications of the ACM , vol. 56, no. 2, pp. 74–80, 2013

    2013

  8. [10]

    Multi-task learning for straggler avoiding predictive j ob scheduling,

    N. J. Y adwadkar, B. Hariharan, J. E. Gonzalez, et al. , “Multi-task learning for straggler avoiding predictive j ob scheduling,” Journal of Machine Learning Research , vol. 17, no. 106, pp. 1–37, 2016

    2016

  9. [11]

    The capacity of robust private in formation retrieval with colluding databases,

    H. Sun and S. A. Jafar, “The capacity of robust private in formation retrieval with colluding databases,” IEEE Transactions on Information Theory, vol. 64, no. 4, pp. 2361–2370, 2017

    2017

  10. [12]

    Private information retrieval from cod ed storage systems with colluding, byzantine, and unresponsive servers,

    R. Tajeddine, O. W. Gnilke, D. Karpuk, R. Freij-Hollant i, and C. Hollanti, “Private information retrieval from cod ed storage systems with colluding, byzantine, and unresponsive servers,” IEEE Transactions on information theory , vol. 65, no. 6, pp. 3898–3906, 2019

    2019

  11. [18]

    Staircase codes for secret sharing with optimal communication and read overheads,

    R. Bitar and S. El Rouayheb, “Staircase codes for secret sharing with optimal communication and read overheads,” IEEE Transactions on Information Theory , vol. 64, no. 2, pp. 933–943, 2017

    2017

  12. [19]

    Cross subspace alignmen t and the asymptotic capacity of x-secure t-private information retrieval,

    Z. Jia, H. Sun, and S. A. Jafar, “Cross subspace alignmen t and the asymptotic capacity of x-secure t-private information retrieval,” IEEE Transactions on Information Theory , vol. 65, no. 9, pp. 5783–5798, 2019

    2019

  13. [20]

    Private read update write (pr uw) in federated submodel learning (fsl): Communication ef ficient schemes with and without sparsification,

    S. Vithana and S. Ulukus, “Private read update write (pr uw) in federated submodel learning (fsl): Communication ef ficient schemes with and without sparsification,” IEEE Transactions on Information Theory , vol. 70, no. 2, pp. 1320–1348, 2024

    2024

  14. [21]

    Security of ramp schemes,

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

    1985

  15. [22]

    A combinatorial interp retation of ramp schemes,

    W.-A. Jackson and K. M. Martin, “A combinatorial interp retation of ramp schemes,” Australasian Journal of Combinatorics , vol. 14, pp. 51–60, 1996

    1996

  16. [23]

    On the size of shares for secret sharing schemes,

    R. M. Capocelli, A. De Santis, L. Gargano, and U. V accaro , “On the size of shares for secret sharing schemes,” Journal of Cryptology , vol. 6, no. 3, pp. 157–167, 1993

    1993

  17. [24]

    The size of a share must be large,

    L. Csirmaz, “The size of a share must be large,” Journal of cryptology , vol. 10, no. 4, pp. 223–231, 1997

    1997

  18. [25]

    How to share a secret,

    A. Shamir, “How to share a secret,” Communications of the ACM , vol. 22, no. 11, pp. 612–613, 1979

    1979

  19. [26]

    Safeguarding cryptographic keys,

    G. R. Blakley, “Safeguarding cryptographic keys,” in Managing Requirements Knowledge, International W orkshop on, pp. 313–313, IEEE Computer Society, 1979. 37

    1979

  20. [27]

    Lagrange coded computing: Optimal de sign for resiliency, security, and privacy,

    Q. Y u, S. Li, N. Raviv, S. M. M. Kalan, M. Soltanolkotabi, and S. A. Avestimehr, “Lagrange coded computing: Optimal de sign for resiliency, security, and privacy,” in The 22nd International Conference on Artificial Intelligen ce and Statistics , pp. 1215–1225, PMLR, 2019

    2019

  21. [28]

    Generalized lagrange coded computing : A flexible computation-communication tradeoff,

    J. Zhu and S. Li, “Generalized lagrange coded computing : A flexible computation-communication tradeoff,” in 2022 IEEE International Symposium on Information Theory (ISIT) , pp. 832–837, IEEE, 2022

    2022

  22. [29]

    Generalized lagran ge coded computing: A flexible computation-communication t radeoff for resilient, secure, and private computation,

    J. Zhu, H. Tang, S. Li, and Y . Chang, “Generalized lagran ge coded computing: A flexible computation-communication t radeoff for resilient, secure, and private computation,” IEEE Transactions on Communications , 2024

    2024

  23. [30]

    On the asymptotic capacity of x-s ecure t-private information retrieval with graph-based re plicated storage,

    Z. Jia and S. A. Jafar, “On the asymptotic capacity of x-s ecure t-private information retrieval with graph-based re plicated storage,” IEEE Transactions on Information Theory , vol. 66, no. 10, pp. 6280–6296, 2020

    2020

  24. [31]

    Double blind t-private in formation retrieval,

    Y . Lu, Z. Jia, and S. A. Jafar, “Double blind t-private in formation retrieval,” IEEE Journal on Selected Areas in Information Theory , vol. 2, no. 1, pp. 428–440, 2021

    2021

  25. [33]

    Private polynomial computat ion from lagrange encoding,

    N. Raviv and D. A. Karpuk, “Private polynomial computat ion from lagrange encoding,” IEEE Transactions on Information F orensics and Security, vol. 15, pp. 553–563, 2019

    2019

  26. [34]

    The asymptotic capacity of x-secure t -private linear computation with graph based replicated st orage,

    H. Jia and Z. Jia, “The asymptotic capacity of x-secure t -private linear computation with graph based replicated st orage,” IEEE Transactions on Information Theory , vol. 70, no. 7, pp. 5269–5288, 2024

    2024

  27. [35]

    Cross subspace alignment codes f or coded distributed batch computation,

    Z. Jia and S. A. Jafar, “Cross subspace alignment codes f or coded distributed batch computation,” IEEE Transactions on Information Theory, vol. 67, no. 5, pp. 2821–2846, 2021

    2021

  28. [36]

    Gcsa codes with noise alignment for secure coded multi-party batch matrix m ultiplication,

    Z. Chen, Z. Jia, Z. Wang, and S. A. Jafar, “Gcsa codes with noise alignment for secure coded multi-party batch matrix m ultiplication,” IEEE Journal on Selected Areas in Information Theory , vol. 2, no. 1, pp. 306–316, 2021

    2021

  29. [37]

    Improved constructions for secure multi-party batch matrix multiplication,

    J. Zhu, Q. Y an, and X. Tang, “Improved constructions for secure multi-party batch matrix multiplication,” IEEE Transactions on Communications, vol. 69, no. 11, pp. 7673–7690, 2021

    2021

  30. [38]

    Network coding for distributed storage sy stems,

    A. G. Dimakis, P . B. Godfrey, Y . Wu, M. J. Wainwright, and K. Ramchandran, “Network coding for distributed storage sy stems,” IEEE transactions on information theory , vol. 56, no. 9, pp. 4539–4551, 2010

    2010

  31. [39]

    Achievi ng maximum distance separable private information retriev al capacity with linear codes,

    S. Kumar, H.-Y . Lin, E. Rosnes, and A. G. i Amat, “Achievi ng maximum distance separable private information retriev al capacity with linear codes,” IEEE Transactions on Information Theory , vol. 65, no. 7, pp. 4243–4273, 2019

    2019

  32. [40]

    A new capacity-achiev ing private information retrieval scheme with (almost) opt imal file length for coded servers,

    J. Zhu, Q. Y an, C. Qi, and X. Tang, “A new capacity-achiev ing private information retrieval scheme with (almost) opt imal file length for coded servers,” IEEE Transactions on Information F orensics and Security , vol. 15, pp. 1248–1260, 2020

    2020

  33. [41]

    Towards practical pr ivate information retrieval from mds array codes,

    J. Li, D. Karpuk, and C. Hollanti, “Towards practical pr ivate information retrieval from mds array codes,” IEEE Transactions on Communications, vol. 68, no. 6, pp. 3415–3425, 2020

    2020

  34. [42]

    Roth, Introduction to coding theory

    R. Roth, Introduction to coding theory . Cambridge University Press, 2006

    2006

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.