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Lecture notes in computer science

Group-Based Secure Computation: Optimizing Rounds, Communication, and Computation

Elette Boyle, Niv Gilboa, Yuval Ishai

Published Jan 1, 2017• 80 citations
Publisher
DOI
10.1007/978-3-319-56614-6_6

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VSS is an important generalized secure multi-party computation protocol,the round complexity and communication complexity are two of its most important complexity measures.Some existing VSS protocols with constant round under standard model that requires secure channel and broadcast channel are efficient theoretically,however,they can' t be applied to real point-to-point networks.Because secure group communication has significant influence on security and performance for secure multi-party computation protocols,an architecture—SMPC over SM was proposed.A two-level decentralized group key management scheme that shared a group key among all members was designed.By assembling those messages needed to be unicast respectively in the scheme,and then multicasting the assembled message,constant order communication complexity was achieved,better scalability and ability of fault tolerance were also obtained.Based on the proposed architecture—SMPC over SM and group key management,VSS with constant round under standard model in Katz et al was optimized,its communication complexity was reduced from O(n3) to O(n2),optimum round complexity was inherited and processing delay of nodes was lowered to 1/n as well.
Oblivious transfer is one of the most important cryptographic primitives, both for theoretical and practical reasons and several protocols were proposed during the years. We provide the first oblivious transfer protocol which is simultaneously optimal on the following list of parameters: Security: it has universal composition. Trust in setup assumptions: only one of the parties needs to trust the setup (and some setup is needed for UC security). Trust in computational assumptions: only one of the parties needs to trust a computational assumption. Round complexity: it uses only two rounds. Communication complexity: it communicates O(1) group elements to transfer one out of two group elements. The Big-O notation hides 32, meaning that the communication is probably not optimal, but is essentially optimal in that the overhead is at least constant. Our construction is based on pairings, and we assume the presence of a key registration authority.
A group key agreement protocol provides a set of users with a shared secret key to achieve cryptographic goal. When membership changes, group session key should be updated efficiently and securely. Hence, dynamic group key agreement protocols are of practical significance. Identity-based group key agreement protocols are preferred to certificate-based ones since identity-based protocols can simplify public key management procedure. Most of previous dynamic group key agreement protocols need at least two rounds to establish or refresh group session keys. In this paper, an identity-based dynamic authenticated group key agreement (DAGKA) protocol is presented. It is round-optimal, since: 1) in setup and join algorithms, only one round of communication is required; 2) in leave algorithm, there is no message exchange among group members. Joining members cannot compute previous session keys and leaving members cannot compute subsequent session keys. The protocol is provably secure. Its AKE-security is proved under decisional bilinear Diffie-Hellman (DBDH) assumption. In addition, the protocol resists key control attack and achieves forward security.