Private Sequential Function Computation

Tahmasebi, Behrooz; Maddah-Ali, Mohammad Ali

doi:10.48550/arxiv.1908.01204

Cited by 4 publications

(6 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this work, we take a Shannon theoretic perspective at the canonical conditional disclosure of secrets problem to seek capacity characterizations where the secret size is allowed to approach infinity while most cryptography work focuses on the scaling of communication cost with the input size 7 [1,[5][6][7][8][9]. This Shannon theoretic perspective follows the footsteps of recent attempts in the information theory community on other cryptographic primitives [14][15][16][17][18][19][20][21][22][23]. Towards this end, we further develop the noise and signal alignment approach, which is a variation of interference alignment originally studied in wireless communication networks [24][25][26] and is introduced in [4], to characterize the linear capacity of a class of CDS instances, which go beyond the highest capacity scenarios found in [4].…”

Section: Discussionmentioning

confidence: 99%

On the Linear Capacity of Conditional Disclosure of Secrets

Li¹,

Sun²

2021

Preprint

View full text Add to dashboard Cite

Conditional disclosure of secrets (CDS) is the problem of disclosing as efficiently as possible, one secret from Alice and Bob to Carol if and only if the inputs at Alice and Bob satisfy some function f . The information theoretic capacity of CDS is the maximum number of bits of the secret that can be securely disclosed per bit of total communication. All CDS instances, where the capacity is the highest and is equal to 1/2, are recently characterized through a noise and signal alignment approach and are described using a graph representation of the function f . In this work, we go beyond the best case scenarios and further develop the alignment approach to characterize the linear capacity of a class of CDS instances to be (ρ − 1)/(2ρ), where ρ is a covering parameter of the graph representation of f .

show abstract

Section: Discussionmentioning

confidence: 99%

On the Linear Capacity of Conditional Disclosure of Secrets

Li¹,

Sun²

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…The problem in Fig. 2 is related to private information retrieval (PIR), introduced in [29] and widely studied in recent years, e.g., [30]- [39]. In the PIR problem, the master server wishes to retrieve a message within some library from a set of distributed databases, each of which stores all the messages.…”

Section: B Related Workmentioning

confidence: 99%

“…, P , respectively. Since each undesired matrix is evaluated at an identical random point for all workers the second term in (39), i.e., r∈[1,L]\κ F B (r) (z r ), can be considered as a constant term.…”

Section: A Secure and Private Generalized Polydot Codesmentioning

confidence: 99%

Private and Secure Distributed Matrix Multiplication With Flexible Communication Load

Aliasgari

Simeone

Kliewer

2020

IEEE Trans.Inform.Forensic Secur.

View full text Add to dashboard Cite

Large matrix multiplications are central to largescale machine learning applications. These operations are often carried out on a distributed computing platform with a master server and multiple workers in the cloud operating in parallel. For such distributed platforms, it has been recently shown that coding over the input data matrices can reduce the computational delay, yielding a trade-off between recovery threshold, i.e., the number of workers required to recover the matrix product, and communication load, i.e., the total amount of data to be downloaded from the workers. In this paper, in addition to exact recovery requirements, we impose security and privacy constraints on the data matrices, and study the recovery threshold as a function of the communication load. We first assume that both matrices contain private information and that workers can collude to eavesdrop on the content of these data matrices. For this problem, we introduce a novel class of secure codes, referred to as secure generalized PolyDot (SGPD) codes, that generalize state-of-the-art non-secure codes for matrix multiplication. SGPD codes allow a flexible trade-off between recovery threshold and communication load for a fixed maximum number of colluding workers while providing perfect secrecy for the two data matrices. We then assume that one of the data matrices is taken from a public set known to all the workers. In this setup, the identity of the matrix of interest should be kept private from the workers. For this model, we present a variant of generalized PolyDot codes that can guarantee both secrecy of one matrix and privacy for the identity of the other matrix for the case of no colluding servers.

show abstract

“…It is thus imperative to understand the fundamental limits of perfect security in multi-user networks, which has been studied in the cryptography and theoretical computer science communities [4], although typically not using information theoretic tools. Due to the increasing importance of security in modern communication systems, it has also recently become one of the focuses for the information theory community [5][6][7], where both classical cryptography formulations are studied [8][9][10][11][12][13] and new models are introduced [14][15][16][17][18]. The goal of this paper is to use information theoretic tools to study a canonical theoretical computer science problem (i.e., a cryptographic primitive) -conditional disclosure of secrets (CDS) [19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Conditional Disclosure of Secrets: A Noise and Signal Alignment Approach

Li¹,

Sun²

2020

Preprint

View full text Add to dashboard Cite

In the conditional disclosure of secrets (CDS) problem, Alice and Bob (each holds an input and a common secret) wish to disclose, as efficiently as possible, the secret to Carol if and only if their inputs satisfy some function. The capacity of CDS is the maximum number of bits of the secret that can be securely disclosed per bit of total communication. We characterize the necessary and sufficient condition for the extreme case where the capacity of CDS is the highest and is equal to 1/2. For the simplest instance where the capacity is smaller than 1/2, we show that the linear capacity is 2/5.

show abstract

Private Sequential Function Computation

Cited by 4 publications

References 0 publications

On the Linear Capacity of Conditional Disclosure of Secrets

On the Linear Capacity of Conditional Disclosure of Secrets

Private and Secure Distributed Matrix Multiplication With Flexible Communication Load

Conditional Disclosure of Secrets: A Noise and Signal Alignment Approach

Contact Info

Product

Resources

About