Achievable Rate of Private Function Retrieval from MDS Coded Databases

Obead, Sarah A.; Kliewer, Joerg

doi:10.1109/isit.2018.8437655

Cited by 32 publications

(37 citation statements)

References 13 publications

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“…For functions which are linear combinations of the files, PC was studied in [16,25] for uncoded databases, and in [17,18] for coded databases. The case of non-linear functions, and especially polynomial functions of degree larger than one, was studied by the second author of the current work in [12], where a PC scheme was constructed for polynomial functions on systematically coded databases.…”

Section: B Private Computationmentioning

confidence: 99%

Private Polynomial Computation From Lagrange Encoding

Raviv

Karpuk

2020

IEEE Trans.Inform.Forensic Secur.

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Private computation is a generalization of private information retrieval, in which a user is able to compute a function on a distributed dataset without revealing the identity of that function to the servers. In this paper it is shown that Lagrange encoding, a powerful technique for encoding Reed-Solomon codes, enables private computation in many cases of interest. In particular, we present a scheme that enables private computation of polynomials of any degree on Lagrange encoded data, while being robust to Byzantine and straggling servers, and to servers colluding to attempt to deduce the identities of the functions to be evaluated. Moreover, incorporating ideas from the well-known Shamir secret sharing scheme allows the data itself to be concealed from the servers as well. Our results extend private computation to high degree polynomials and to data-privacy, and reveal a tight connection between private computation and coded computation.

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Section: B Private Computationmentioning

confidence: 99%

Private Polynomial Computation From Lagrange Encoding

Raviv

Karpuk

2020

IEEE Trans.Inform.Forensic Secur.

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“…where (18) holds because of the chain rule of entropy, (19) is due to the fact that conditioning reduces entropy, and we apply (17) to obtain (20).…”

Section: (V)mentioning

confidence: 99%

“…Note that the function is computed separately for the t-th row of all messages, t ∈ [β]. Therefore, similar to the PLC scheme in [17] and the MDS-coded PLC scheme in [20], we apply a permutation that is fixed across all coded symbols for the t-th row to maintain the dependency across the associated message elements. Let π(·) be a random permutation function over [β], and let…”

Section: B Generic Query Generationmentioning

confidence: 99%

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Private Polynomial Computation for Noncolluding Coded Databases

Obead

Lin

Rosnes

et al. 2019

2019 IEEE International Symposium on Information Theory (ISIT)

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Private computation in a distributed storage system (DSS) is a generalization of the private information retrieval (PIR) problem. In such setting a user wishes to compute a function of f messages stored in noncolluding coded databases while revealing no information about the desired function to the databases. We consider the problem of private polynomial computation (PPC). In PPC, a user wishes to compute a multivariate polynomial of degree at most g over f variables (or messages) stored in multiple databases. First, we consider the private computation of polynomials of degree g = 1, i.e., private linear computation (PLC) for coded databases. In PLC, a user wishes to compute a linear combination over the f messages while keeping the coefficients of the desired linear combination hidden from the database. For a linearly encoded DSS, we present a capacity-achieving PLC scheme and show that the PLC capacity, which is the ratio of the desired amount of information and the total amount of downloaded information, matches the maximum distance separable coded capacity of PIR for a large class of linear storage codes. Then, we consider private computation of higher degree polynomials, i.e., g > 1. For this setup, we construct two novel PPC schemes. In the first scheme we consider Reed-Solomon coded databases with Lagrange encoding, which leverages ideas from recently proposed star-product PIR and Lagrange coded computation. The second scheme considers the special case of coded databases with systematic Lagrange encoding. Both schemes yield improved rates compared to the best known schemes from the literature for a small number of messages, while asymptotically, as f → ∞, the systematic scheme gives a significantly better computation rate compared to all known schemes up to some storage code rate that depends on the maximum degree of the candidate polynomials.

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“…Interestingly, the obtained PLC capacity is equal to the PIR capacity of [6]. The extension to the coded case is addressed in [13], [14]. In [13], a PC This work is supported by US NSF grant CNS-1526547 and the Research Council of Norway (grant 240985/F20).…”

Section: Introductionmentioning

confidence: 99%

Capacity of Private Linear Computation for Coded Databases

Obead

Lin

Rosnes

et al. 2018

2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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We consider the problem of private linear computation (PLC) in a distributed storage system. In PLC, a user wishes to compute a linear combination of f messages stored in noncolluding databases while revealing no information about the coefficients of the desired linear combination to the databases. In extension of our previous work we employ linear codes to encode the information on the databases. We show that the PLC capacity, which is the ratio of the desired linear function size and the total amount of downloaded information, matches the maximum distance separable (MDS) coded capacity of private information retrieval for a large class of linear codes that includes MDS codes. In particular, the proposed converse is valid for any number of messages and linear combinations, and the capacity expression depends on the rank of the coefficient matrix obtained from all linear combinations.

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Achievable Rate of Private Function Retrieval from MDS Coded Databases

Cited by 32 publications

References 13 publications

Private Polynomial Computation From Lagrange Encoding

Private Polynomial Computation From Lagrange Encoding

Private Polynomial Computation for Noncolluding Coded Databases

Capacity of Private Linear Computation for Coded Databases

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