[Paper Review] Multiparty Cloud Computation

Qingji Zheng, Xinwen Zhang|arXiv (Cornell University)|Jun 17, 2012

Cryptography and Data Security8 references3 citations

TL;DR

This paper introduces multiparty cloud computation (MCC), a novel framework enabling multiple clients to securely outsource both data and computation to the cloud while preserving privacy. It proposes a homomorphic threshold proxy re-encryption scheme that supports proxy re-encryption, threshold decryption, and homomorphic evaluation of arbitrary additions and one multiplication on encrypted data, enabling secure joint computation without data decryption in the cloud.

ABSTRACT

With the increasing popularity of the cloud, clients oursource their data to clouds in order to take advantage of unlimited virtualized storage space and the low management cost. Such trend prompts the privately oursourcing computation, called \emph{multiparty cloud computation} (\MCC): Given $k$ clients storing their data in the cloud, how can they perform the joint functionality by contributing their private data as inputs, and making use of cloud's powerful computation capability. Namely, the clients wish to oursource computation to the cloud together with their private data stored in the cloud, which naturally happens when the computation is involved with large datasets, e.g., to analyze malicious URLs. We note that the \MCC\ problem is different from widely considered concepts, e.g., secure multiparty computation and multiparty computation with server aid. To address this problem, we introduce the notion of \emph{homomorphic threshold proxy re-encryption} schemes, which are encryption schemes that enjoy three promising properties: proxy re-encryption -- transforming encrypted data of one user to encrypted data of target user, threshold decryption -- decrypting encrypted data by combining secret key shares obtained by a set of users, and homomorphic computation -- evaluating functions on the encrypted data. To demonstrate the feasibility of the proposed approach, we present an encryption scheme which allows anyone to compute arbitrary many additions and at most one multiplications.

Motivation & Objective

• To address the challenge of enabling multiple clients to securely outsource both data and computation to the cloud while preserving data privacy.
• To design a cryptographic primitive that supports proxy re-encryption, threshold decryption, and homomorphic evaluation on encrypted data.
• To enable efficient and secure joint computation on large-scale datasets stored in the cloud without revealing inputs to the cloud or individual clients beyond the final result.
• To demonstrate feasibility through a concrete construction based on bilinear pairings that supports arbitrary additions and one multiplication.

Proposed method

• Introduces a homomorphic threshold proxy re-encryption (HTPRE) scheme combining proxy re-encryption, threshold decryption, and homomorphic evaluation.
• Uses bilinear groups of prime order p with generator g and pairing e: G × G → G_T to construct the scheme.
• Each client encrypts data using their public key, and proxy re-encryption keys allow transformation of ciphertexts to a common target key.
• Homomorphic evaluation is performed by combining ciphertexts via component-wise multiplication: (C'11·C''11, C'12·C''12) for multiplication of messages.
• Threshold decryption uses secret shares s(i) of a shared secret key, where clients jointly compute the result using Lagrange interpolation with coefficients λ_i.
• The final decryption combines all clients' contributions via ∏(w_i)^λ_i to recover the plaintext result.

Experimental results

Research questions

• RQ1 How can multiple clients securely outsource both data and computation to the cloud while preserving data confidentiality?
• RQ2 What cryptographic primitive enables secure transformation of encrypted data across clients and supports homomorphic evaluation in the cloud?
• RQ3 Can a scheme be constructed that supports proxy re-encryption, threshold decryption, and homomorphic evaluation simultaneously?
• RQ4 What is the feasibility of enabling joint computation on encrypted data with minimal communication and strong privacy guarantees?

Key findings

• The proposed HTPRE scheme supports arbitrary additions and at most one multiplication on encrypted data, enabling practical joint computation.
• Proxy re-encryption allows secure transformation of ciphertexts from one client’s key to a common target key without revealing plaintexts.
• Threshold decryption ensures that only a qualified subset of clients can jointly recover the result, preserving privacy from the cloud and individual clients.
• The scheme is secure under the decisional Diffie-Hellman assumption in the context of bilinear groups.
• The protocol minimizes communication overhead by avoiding data downloads from the cloud, preserving the efficiency advantage of cloud computation.
• The construction demonstrates feasibility of secure multiparty cloud computation for real-world applications like malicious URL detection and healthcare data analysis.