Conference Paper

Simplified VSS and Fact-Track Multiparty Computations with Applications to Threshold Cryptography.

Source: DBLP
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    • "Because SSS is linear, addition of two shared secrets can be computed by having each player locally add his shares of the two values. Multiplication of two shared secrets requires an extra round of communication to guarantee randomness and to correct the degree of the new polynomial [11]. Thus, a distributed multiplication requires a synchronization round with n 2 total messages. "
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    ABSTRACT: Privacy-preserving techniques for distributed computation have been proposed recently as a promising framework in collaborative inter-domain network monitoring. Several different approaches exist to solve such class of problems, e.g., Homomorphic Encryption (HE) and Secure Multiparty Computation (SMC) based on Shamir’s Secret Sharing algorithm (SSS). Such techniques are complete from a computation-theoretic perspective: given a set of private inputs, it is possible to perform arbitrary computation tasks without revealing any of the intermediate results. In this paper we advocate the use of “elementary” (as opposite to “complete“) Secure Multiparty Computation (E-SMC) procedures for traffic monitoring. E-SMC supports only simple computations with private input and public output, i.e., they can not handle secret input nor secret (intermediate) output. The proposed simplification brings a dramatic reduction in complexity and enables massive-scale implementation with acceptable delay and overhead. Notwithstanding their simplicity, we claim that a simple additive E-SMC scheme is sufficient to perform many computation tasks of practical relevance to collaborative network monitoring, such as anonymous publishing and set operations.
    Traffic Monitoring and Analysis - Third International Workshop, TMA 2011, Vienna, Austria, April 27, 2011. Proceedings; 01/2011
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    • "., Pn, operations [x] + [y], [x] + c, and c[x] are performed by each Pi locally on its shares of x and y, while computation of [x][y] is interactive. The most common way of implementing multiplication is by sending the total of O(n 2 ) messages (where each Pi sends n − 1 messages, one to each other participant ) using, for instance, the techniques of [30], but recent results [37] [5] lower the communication to O(n) messages per multiplication at the cost of preprocessing. We assume complexity O(n 2 ) in our analysis. "
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    ABSTRACT: Privacy-preserving set operations and set intersection in particular are a popular research topic. Despite a large body of literature, the great majority of the available solutions are two-party protocols and are not composable. In this work we design a comprehensive suite of secure multi-party protocols for set and multiset operations that are composable, do not assume any knowledge of the sets by the parties carrying out the secure computation, and can be used for secure outsourcing. All of our protocols have communication and computation complexity of O(m log m) for sets or multisets of size m, which compares favorably with prior work. Furthermore, we are not aware of any results that realize composable operations. Our protocols are secure in the information theoretic sense and are designed to minimize the round complexity.
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    • "leading to m/2 product values shared among m players . A collaborative multiplication [10] [11] [13] of s 1 × s 2 takes the shares of s 1 and s 2 as input, and results in each party X i receiving its respective share of the computed product: (s 1 × s 2 ) i . "
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    ABSTRACT: Secure multiparty computation (SMC) has gained tremendous importance with the growth of the Internet and e-commerce, where mutually untrusted parties need to jointly compute a function of their private inputs. However, SMC protocols usually have very high computational complexities, rendering them practically unusable. In this paper, we tackle the problem of comparing two input values in a secure distributed fashion. We propose efficient secure comparison protocols for both the homomorphic encryption and secret sharing schemes. We also give experimental results to show their practical relevance.
    Database and Expert Systems Application, 2009. DEXA '09. 20th International Workshop on; 10/2009
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