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Abstract
Introduction
Overview of Protocols
Related Work
Claim. The Protocol
Claim. The Protocol a S [H],
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Outsourcing multi-party computation

Profile image of Seny KamaraSeny Kamara

2011

Abstract

Abstract We initiate the study of secure multi-party computation (MPC) in a server-aided setting, where the parties have access to a single server that (1) does not have any input to the computation;(2) does not receive any output from the computation; but (3) has a vast (but bounded) amount of computational resources. In this setting, we are concerned with designing protocols that minimize the computation of the parties at the expense of the server.

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Secure Outsourced Computation in a Multi-tenant Cloud
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Abstract We present a general-purpose protocol that enables a client to delegate the computation of any function to a cluster of n machines in such a way that no adversary that corrupts at most n− 1 machines can recover any information about the client's input or output. The protocol makes black-box use of multi-party computation (MPC) and secret sharing and inherits the security properties of the underlying MPC protocol (ie, passive vs. adaptive security and security in the presence of a semi-honest vs. malicious adversary).

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On the practical importance of communication complexity for secure multi-party computation protocols
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Many advancements in the area of Secure Multi-Party Computation (SMC) protocols use improvements in communication complexity as a justification. We conducted an experimental study of a specific protocol for a real-world sized problem under realistic conditions and it suggests that the practical performance of the protocol is almost independent of the network performance. We argue that our result can be generalized to a whole class of SMC protocols.

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Efficient and verifiable algorithms for secure outsourcing of cryptographic computations
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Reducing computational cost of cryptographic computations for resource-constrained devices is an active research area. One of the practical solutions is to securely outsource the computations to an external and more powerful cloud server. Modular exponentiations are the most expensive computation from the cryptographic point of view. Therefore, outsourcing modular exponentiations to a single, external and potentially untrusted cloud server while ensuring the security and privacy provide an efficient solution. In this paper, we propose new efficient outsourcing algorithms for modular exponentiations using only one untrusted cloud server. These algorithms cover public-base & private-exponent, private-base & public-exponent, private-base & privateexponent, and more generally private-base & private-exponents simultaneous modular exponentiations. Our algorithms are the most efficient solutions utilizing only one single untrusted server with best checkability probabilities. Furthermore, unlike existing schemes, which have fixed checkability probability, our algorithms provide adjustable predetermined checkability parameters. Finally, we apply our algorithms to outsource Oblivious Transfer Protocols and Blind Signatures which are expensive primitives in modern cryptography.

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Semi-trusted Collaborative Framework for Multi-party Computation
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Data sharing is an essential process for collaborative works particularly in the banking, finance and healthcare industries. These industries require many collaborative works with their internal and external parties such as branches, clients, and service providers. When data are shared among collaborators, security and privacy concerns becoming crucial issues and cannot be avoided. Privacy is an important issue that is frequently discussed during the development of collaborative systems. It is closely related with the security issues because each of them can affect the other. The tradeoff between privacy and security is an interesting topic that we are going to address in this paper. In view of the practical problems in the existing approaches, we propose a collaborative framework which can be used to facilitate concurrent operations, single point failure problem, and overcome constraints for two-party computation. Two secure computation protocols will be discussed to demonstrate our collaborative framework.

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Secure multi-party computation (MPC) allows multiple parties to compute a known function over inputs held by each party, without any party having to reveal its private input. Unfortunately, traditional MPC algorithms do not scale well to large numbers of parties. In this paper, we describe several recent MPC algorithms that are designed to handle large networks. All of these algorithms rely on recent techniques from the Byzantine agreement literature on forming and using quorums. Informally, a quorum is a small set of parties, most of which are trust-worthy. We describe the advantages and disadvantages of these scalable algorithms, and we propose new ideas for improving practicality of current techniques. Finally, we conduct simulations to measure bandwidth cost for several current MPC algorithms.

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The Price of Low Communication in Secure Multi-party Computation
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Traditional protocols for secure multi-party computation among n parties communicate at least a linear (in n) number of bits, even when computing very simple functions. In this work we investigate the feasibility of protocols with sublinear communication complexity. Concretely, we consider two clients, one of which may be corrupted, who wish to perform some “small” joint computation using n servers but without any trusted setup. We show that enforcing sublinear communication complexity drastically affects the feasibility bounds on the number of corrupted parties that can be tolerated in the setting of information-theoretic security.

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Multi-Client Verifiable Computation with Stronger Security Guarantees
Jonathan Katz

Lecture Notes in Computer Science, 2015

introduced the notion of multiclient verifiable computation (MVC) in which a set of clients outsource to an untrusted server the computation of a function f over their collective inputs in a sequence of time periods. In that work, the authors defined and realized multi-client verifiable computation satisfying soundness against a malicious server and privacy against the semi-honest corruption of a single client. Very recently, Goldwasser et al. (Eurocrypt 2014) provided an alternative solution relying on multi-input functional encryption. Here we conduct a systematic study of MVC, with the goal of satisfying stronger security requirements. We begin by introducing a simulationbased notion of security that provides a unified way of defining soundness and privacy, and automatically captures several attacks not addressed in previous work. We then explore the feasibility of achieving this notion of security. Assuming no collusion between the server and the clients, we demonstrate a protocol for multi-client verifiable computation that achieves stronger security than the protocol of Choi et al. in several respects. When server-client collusion is possible, we show (somewhat surprisingly) that simulation-based security cannot be achieved, even assuming only semi-honest behavior.

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Secure Multi-party Computation Minimizing Online Rounds
Seung Geol Choi

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Multi-party secure computations are general important procedures to compute any function while keeping the security of private inputs. In this work we ask whether preprocessing can allow low latency (that is, small round) secure multi-party protocols that are universally-composable (UC). In particular, we allow any polynomial time preprocessing as long as it is independent of the exact circuit and actual inputs of the specific instance problem to solve, with only a bound k on the number of gates in the circuits known. To address the question, we first define the model of "Multi-Party Computation on Encrypted Data" (MP-CED), implicitly described in [FH96, JJ00, CDN01, DN03]. In this model, computing parties establish a threshold public key in a preprocessing stage, and only then private data, encrypted under the shared public key, is revealed. The computing parties then get the computational circuit they agree upon and evaluate the circuit on the encrypted data. The MP-CED model is interesting since it is well suited for modern computing environments, where many repeated computations on overlapping data are performed. We present two different round-efficient protocols in this model:-The first protocol generates k garbled gates in the preprocessing stage and requires only two (online) rounds.-The second protocol generates a garbled universal circuit of size O(k log k) in the preprocessing stage, and requires only one (online) round (i.e., an obvious lower bound), and therefore it can run asynchronously. Both protocols are secure against an active, static adversary controlling any number of parties. When the fraction of parties the adversary can corrupt is less than half, the adversary cannot force the protocols to abort. The MP-CED model is closely related to the general Multi-Party Computation (MPC) model and, in fact, both can be reduced to each other. The first (resp. second) protocol above naturally gives protocols for three-round (resp. two-round) universally composable MPC secure against active, static adversary controlling any number of parties (with preprocessing).

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References (60)

  1. Let m and n be the sizes of the inputs sets for parties P 1 and P 2 with elements in the domain R. Let G and F be pseudo-random permutation. Let t be a security parameter. Let com be a commitment scheme. Inputs: P 1 has input set X; P 2 has input set Y Outputs: P 1 and P 2 receive X Y Protocol:
  2. P 1 and P 2 run a coin tossing protocol to choose two key K 1 and K 2 .
  3. P 1 computes X = {G K1 (x) | x ∈ X}.
  4. P 1 computes Y = {G K1 (y) | y ∈ Y }.
  5. For each x i ∈ X , 1 ≤ i ≤ m P 1 computes a i,j = F K2 (x i |j) for 1 ≤ j ≤ t. P 1 sends the set A = {a i,j } to S.
  6. For each y i ∈ Y , 1 ≤ i ≤ n P 2 computes b i,j = F K2 (y i |j) for 1 ≤ j ≤ t. P 2 sends the set B = {b i,j } to S.
  7. S computes the set A B and sends a commitment com(A B) to both P 1 and P 2 .
  8. P 1 sends the set X and K 2 to S and P 2 sends Y and K 2 to S.
  9. S verified that he received the same key from both parties and that the sets A and B have been computed correctly, namely contain exactly t PRF values for each input element. If the verification fails, S aborts the protocol.
  10. S opens the the commitment com(A B) and sends the intersection set A B to P 1 and P 2 .
  11. Both P 1 and P 2 verify the open commitment. If the verification fails, they abort the protocol.
  12. P 1 checks that the PRP values corresponding to d are present in A B and e 1 is not. He also checks that A B contains t corresponding PRP values for each element of X in the intersection A B. If either of these checks fails, P 1 aborts the protocol.
  13. Using K 1 and K 2 P 1 and P 2 recover the values in X ∩ Y . References
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  54. the challenger computes (σ x , τ x ) ← ProbGen sk (x),
  55. given σ x , the adversary A outputs an encoding σ , 6. if Verify sk (τ, σ )
  56. ∈ {⊥, f (x)} then output 1 else output 0. We say that Del is verifiable if for all ppt adversaries A, Pr [ Ver Del,A (k) = 1 ] ≤ negl(k) where the probability is over the coins of Gen, O, A and ProbGen. Informally, a delegated computation scheme is private if its public encodings reveal no useful information about the input x.
  57. Definition B.3 (Privacy). Let Del = (Gen, ProbGen, Compute, Verify) be a delegated computation scheme, A be a stateful adversary and consider the following probabilistic experiment Priv Del,A (k): 1. the challenger computes (pk, sk) ← Gen(1 k , f ),
  58. let O(sk, •) be a probabilistic oracle that takes as input an element x in the domain of f , computes (σ, τ ) ← ProbGen sk (x) and outputs σ,
  59. given pk and oracle access to O(sk, •), A outputs two inputs x 0 and x 1 , 4. the challenger samples a bit b at random and computes (σ b , τ b ) ← ProbGen sk (x b ),
  60. A, Pr [ Priv Del,A (k) = 1 ] ≤ negl(k) where the probability is over the coins of Gen, O, A and ProbGen.

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Two-Cloud-Servers-Assisted Secure Outsourcing Multiparty Computation
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Assisting Server for Secure Multi-Party Computation
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Distributed threats like botnets are among the most serious threats in the Internet. Due to their distributed nature, these attacks are difficult to detect in an early stage without the collaboration of several network operators. However, the exchange of monitoring data between different parties turns out to be difficult in practice, due to the desire of operators not to disclose network internals and legal data protection requirements. Secure Multi-Party Computation (SMC) for privacypreserving sharing of network monitoring data can be a solution to the problem. As real-time performance of SMC is important for this application, we investigate ways to speed up SMC. The focus and contribution of our work is a new model for SMC that enables to increase the performance of certain SMC primitives significantly. We introduce an assisting server which operates on dedicated, intermediate data values in plaintext. The overall rationale behind our approach is that the performance gains outweigh the slight decrease in security introduced by revealing intermediate computation results to the assisting server. We propose a new primitive for checking the equality between two values, equal + , based on our new model. Through prototypical implementation we compare equal + with existing algorithms. Further, we evaluate equal + in the context of a cooperative network monitoring application, link-counting. Our results demonstrate that certain SMC applications can be computed much faster with our approach. Finally, we discuss the security implications of the new model.

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