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Lecture notes in computer science

Efficient Multiparty Computations Secure Against an Adaptive Adversary

Ronald Cramer, Ivan Damgård, Stefan Dziembowski, Martin Hirt, Tal Rabin

Published Jan 1, 1999• 223 citations
Publisher
DOI
10.1007/3-540-48910-x_22

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Multiparty Computations Information-Theoretically Secure Against an Adaptive Adversary

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In this thesis we study a problem of doing Verifiable Secret Sharing (VSS) and Multiparty Computations (MPC) in a model where private channels between the players and a broadcast channel is available. The adversary is active, adaptive and has an unbounded computing power. The thesis is based on two papers [CDD00, CDD 99]. In [CDD00] we assume that the adversary can corrupt any set from a given adversary structure. In this setting we study a problem of doing efficient VSS and MPC given an access to a secret sharing scheme (SS). For all adversary structures where VSS is possible at all, we show that, up to a polynomial time black-box reduction, the complexity of adaptively secure VSS is the same as that of ordinary secret sharing (SS), where security is only required against a passive, static adversary. Previously, such a connection was only known for linear secret sharing and VSS schemes. We then show

•Jan 1, 2002•0 citations
We consider verifiable secret sharing (VSS) and multiparty computation (MPC) in the secure channels model, where a broadcast channel is given and a non-zero error probability is allowed. In this model Rabin and Ben-Or proposed VSS and MPC protocols, secure against an adversary that can corrupt any minority of the players. In this paper, we rst observe that a subprotocol of theirs, known as weak secret sharing (WSS), is not secure against an adaptive adversary, contrary to what was believed earlier. We then propose new and adaptively secure protocols for WSS, VSS and MPC that are substantially more efficient than the original ones. Our protocols generalize easily to provide security against general Q2 adversaries.
In this thesis we study a problem of doing Verifiable Secret Sharing (VSS) and Multiparty Computations (MPC) in a model where private channels between the players and a broadcast channel is available. The adversary is active, adaptive and has an unbounded computing power. The thesis is based on two papers [CDD00, CDD 99]. In [CDD00] we assume that the adversary can corrupt any set from a given adversary structure. In this setting we study a problem of doing efficient VSS and MPC given an access to a secret sharing scheme (SS). For all adversary structures where VSS is possible at all, we show that, up to a polynomial time black-box reduction, the complexity of adaptively secure VSS is the same as that of ordinary secret sharing (SS), where security is only required against a passive, static adversary. Previously, such a connection was only known for linear secret sharing and VSS schemes. We then show