Two shannon-type problems on secure multi-party computations

Lee, Eun Jee; Abbé, Emmanuel

doi:10.1109/allerton.2014.7028604

Cited by 17 publications

(24 citation statements)

References 17 publications

(20 reference statements)

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“…In the encryption stage, suppose the random numbers are 10 and 7, then the resulting of Equation 1 is 68 × 33 + 10 = 2254 and 78 × 33 + 7 = 2581. After encryption, the plain data x becomes encrypt(x) = { [12,8,26], [15,21,1], [8,19,22]}, and the plain data y becomes encrypt(y) = { [16,26,20], [14,0,9], [6,13,8]}, the client sends encrypt(x) and encrypt(y) to the server.…”

Section: Algorithm 4 Decryptionmentioning

confidence: 99%

Confused-Modulo-Projection-Based Somewhat Homomorphic Encryption—Cryptosystem, Library, and Applications on Secure Smart Cities

Jin

Zhang

et al. 2021

IEEE Internet Things J.

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With the development of cloud computing, the storage and processing of massive visual media data has gradually transferred to the cloud server. For example, if the intelligent video monitoring system cannot process a large amount of data locally, the data will be uploaded to the cloud. Therefore, how to process data in the cloud without exposing the original data has become an important research topic. We propose a single-server version of somewhat homomorphic encryption cryptosystem based on confused modulo projection theorem named CMP-SWHE, which allows the server to complete blind data processing without seeing the effective information of user data. On the client side, the original data is encrypted by amplification, randomization, and setting confusing redundancy. Operating on the encrypted data on the server side is equivalent to operating on the original data. As an extension, we designed and implemented a blind computing scheme of accelerated version based on batch processing technology to improve efficiency. To make this algorithm easy to use, we also designed and implemented an efficient general blind computing library based on CMP-SWHE. We have applied this library to foreground extraction, optical flow tracking and object detection with satisfactory results, which are helpful for building smart cities. We also discuss how to extend the algorithm to deep learning applications. Compared with other homomorphic encryption cryptosystems and libraries, the results show that our method has obvious advantages in computing efficiency. Although our algorithm has some tiny errors (10 −6) when the data is too large, it is very efficient and practical, especially suitable for blind image and video processing.

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Section: Algorithm 4 Decryptionmentioning

confidence: 99%

Confused-Modulo-Projection-Based Somewhat Homomorphic Encryption—Cryptosystem, Library, and Applications on Secure Smart Cities

Jin

Zhang

et al. 2021

IEEE Internet Things J.

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“…Within the standard secure multi-party computation model of [9], Lee and Abbe determine in [10] the least amount of randomness needed for securely computing a given function. This provides a novel notion of the complexity of a function for its secure computation.…”

Section: A Related Workmentioning

confidence: 99%

“…In [11], Data et al take a distributed source coding approach to the problem of securely computing the modulo-2 sum of two distributed binary sources. Similarly to [10], they assume the data to be drawn from some joint memoryless source and derive bounds on the amount of randomness and communication needed to asymptotically achieve secrecy. In [12], the results are extended to arbitrary functions.…”

Section: A Related Workmentioning

confidence: 99%

On secure computation over the binary modulo-2 adder multiple-access wiretap channel

Goldenbaum

Boche

Poor

2016

2016 IEEE Information Theory Workshop (ITW)

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In this paper, the problem of securely computing a function over the binary modulo-2 adder multiple-access wiretap channel is considered. The problem involves a legitimate receiver that wishes to reliably and efficiently compute a function of distributed binary sources while an eavesdropper has to be kept ignorant of them. In order to characterize the corresponding fundamental limit, the notion of secrecy computation-capacity is introduced. Although determining the secrecy computation-capacity is challenging for arbitrary functions, it surprisingly turns out that if the function perfectly matches the algebraic structure of the channel and the joint source distribution fulfills certain conditions, the secrecy computation-capacity equals the computation capacity, which is the supremum of all achievable computation rates without secrecy constraints. Unlike the case of securely transmitting messages, no additional randomness is needed at the encoders nor does the legitimate receiver need any advantage over the eavesdropper. The results therefore show that the problem of securely computing a function over a multiple-access wiretap channel may significantly differ from the one of securely communicating messages. Index TermsSecure distributed computation, computation coding, multiple-access wiretap channel, physical-layer security I. INTRODUCTION In their seminal work [1], Nazer and Gastpar lay the information-theoretic foundation of distributed computation over unreliable channels. The big difference between this approach and the standard theory dealing with reliable message transfer is that, in [1], the intended receiver decodes function values immediately from the channel output. In other words, the receiver does not care about individual messages and penalizes itself only when the function is incorrectly decoded.In this regard, Nazer and Gastpar show that in many cases, the performance gain over separation-based computation strategies is proportional to the number of source terminals. In a separation-based strategy, the receiver first reliably decodes all individual messages and subsequently computes the sought function value. It is remarkable that the gains over separation-based strategies stem from a match between the desired function and the algebraic structure of the channel. Since the publication of [1], the results and ideas have been extended in many different ways [2]-[6].Due to the trend towards large-scale decentralized networks consisting of many mutually distrusting terminals, security and integrity of computation results are of high priority in order to guarantee trustworthy operation. In this work, we therefore make a first attempt to extend the concept of computation coding [1] by taking information theoretic security aspects into account. In particular, we consider the problem of computing a function over the binary modulo-2 adder multiple-access wiretap channel (MAWC). The problem involves a legitimate receiver that wishes to reliably compute a function of distributed binary sources in the ...

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“…Specifically, we will assume a probability distribution for the data (discrete memoryless distributed source), and seek the averagecase performance under asymptotically vanishing error and vanishing privacy leakage. We would like to point out that [15] already considered a similar setting, but for a much weaker notion of security than what we consider below. For concreteness and simplicity, we focus on the famous example of Körner and Marton [12].…”

Section: Introductionmentioning

confidence: 99%

“…As already pointed out above, another related work is [15]. It studies the randomness required for secure sum computation under two different settings: (i) in the zero-error, perfect privacy, worst-case setting, and (ii) average case, asymptotically correct setting under a much weaker notion of privacy that users are unable to asymptotically correctly guess the entire data of another user, but when no private randomness is available to the users.…”

Section: Introductionmentioning

confidence: 99%

How to securely compute the modulo-two sum of binary sources

Data¹,

Dey²,

Mishra³

et al. 2014

2014 IEEE Information Theory Workshop (ITW 2014)

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Abstract-In secure multiparty computation, mutually distrusting users in a network want to collaborate to compute functions of data which is distributed among the users. The users should not learn any additional information about the data of others than what they may infer from their own data and the functions they are computing. Previous works have mostly considered the worst case context (i.e., without assuming any distribution for the data); Lee and Abbe (2014) is a notable exception. Here, we study the average case (i.e., we work with a distribution on the data) where correctness and privacy is only desired asymptotically.For concreteness and simplicity, we consider a secure version of the function computation problem of Körner and Marton (1979) where two users observe a doubly symmetric binary source with parameter p and the third user wants to compute the XOR. We show that the amount of communication and randomness resources required depends on the level of correctness desired. When zero-error and perfect privacy are required, the results of Data et al. (2014) show that it can be achieved if and only if a total rate of 1 bit is communicated between every pair of users and private randomness at the rate of 1 is used up. In contrast, we show here that, if we only want the probability of error to vanish asymptotically in blocklength, it can be achieved by a lower rate (binary entropy of p) for all the links and for private randomness; this also guarantees perfect privacy. We also show that no smaller rates are possible even if privacy is only required asymptotically.

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Two shannon-type problems on secure multi-party computations

Cited by 17 publications

References 17 publications

Confused-Modulo-Projection-Based Somewhat Homomorphic Encryption—Cryptosystem, Library, and Applications on Secure Smart Cities

Confused-Modulo-Projection-Based Somewhat Homomorphic Encryption—Cryptosystem, Library, and Applications on Secure Smart Cities

On secure computation over the binary modulo-2 adder multiple-access wiretap channel

How to securely compute the modulo-two sum of binary sources

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