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.
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.
We first study the problem of doing Verifiable Secret Sharing (VSS) information theoretically secure for a general access structure.We do it in the model where private channels between players and a broadcast channel is given, and where an active, adaptive adversary can corrupt any set of players not in the access structure.In particular, we consider the complexity of protocols for this problem, as a function of the access structure and the number of players.For all access 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 an impossibility result indicating that a similar equivalence does hot hold for Multiparty Computation (MPC): we show that even if protocols are given black-box access for free to an idealized secret sharing scheme secure for the access structure in question, it is not possible to handle all relevant access structures efficiently, not even if the adversary is passive and static.In other words, general MPC can only be black-box reduced efficiently to secret sharing if extra properties of the secret sharing scheme used (such as linearity) are assumed.
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
We first study the problem of doing Verifiable Secret Sharing (VSS) information theoretically secure for a general access structure. We do it in the model where private channels between players and a broadcast channel is given, and where an active, adaptive adversary can corrupt any set of players not in the access structure. In particular, we consider the complexity of protocols for this problem, as a function of the access structure and the number of players. For all access 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 an impossibility result indicating that a similar equivalence does not hold for Multiparty Computation (MPC): we show that even if protocols are given blac...
In this work we focus on two basic secure distributed computation tasks- Probabilistic Weak Secret Sharing (PWSS) and Probabilistic Verifiable Secret Sharing (PVSS). PVSS allows a dealer to share a secret among several players in a way that would later allow a unique reconstruction of the secret with negligible error probability. PWSS is slightly weaker version of PVSS where the dealer can choose not to disclose his secret later. Both of them are well-studied problems. While PVSS is used as a building block in every general probabilistic secure multiparty computation, PWSS can be used as a building block for PVSS protocols. Both these problems can be parameterized by the number of players (n) and the fault tolerance threshold (t) which bounds the total number of malicious (Byzantine) players having unbounded computing power. We focus on the standard secure channel model, where all players have access to secure point-topoint channels and a common broadcast medium. We show the following for PVSS: (a) 1-round PVSS is possible iff t = 1 and n> 3 (b) 2-round PVSS is possible if n> 3t (c) 4-round PVSS is possible if n> 2t. For the PWSS we show the following: (a) 1-round PWSS is possible iff n> 3t and (b) 3-round PWSS is possible if n> 2t. All our protocols are efficient. Comparing our results with the existing trade-off results for perfect (zero error probability) VSS and WSS, we find that probabilistically relaxing the conditions of VSS/WSS helps to increase fault tolerance significantly.
Broadcast and verifiable secret sharing (VSS) are central building blocks for secure multi-party computation. These protocols are required to be resilient against a Byzantine adversary who controls at most t out of the n parties running the protocol. In this dissertation, we consider the design of fault-tolerant protocols for broadcast and verifiable secret sharing with stronger security guarantees and improved round complexity. Broadcast allows a party to send the same message to all parties, and all parties are assured they have received identical messages. Given a public-key infrastructure (PKI) and digital signatures, it is possible to construct broadcast protocols tolerating any number of corrupted parties. We address two important issues related to broadcast: (1) Almost all existing protocols do not distinguish between corrupted parties (who do not follow the protocol) and honest parties whose secret (signing) keys have been compromised (but who continue to behave honestly); (2) all existing protocols for broadcast are insecure against an adaptive adversary who can choose which parties to corrupt as the protocol progresses. We propose new security models that capture these issues, and present tight feasibility and impossibility results. In the problem of verifiable secret sharing, there is a designated player who shares a secret during an initial sharing phase such that the secret is hidden from an adversary that corrupts at most t parties. In a subsequent reconstruction phase of the protocol, a unique secret, well-defined by the view of honest players in the sharing phase, is reconstructed. The round complexity of VSS protocols is a very important metric of their efficiency. We show two improvements regarding the round complexity of information-theoretic VSS. First, we construct an efficient perfectly secure VSS protocol tolerating t < n/3 corrupted parties that is simultaneously optimal in both the number of rounds and the number of invocations of broadcast. Second, we construct a statistically secure VSS protocol tolerating t < n/2 corrupted parties that has optimal round complexity, and an efficient statistical VSS protocol tolerating t < n/2 corrupted parties that requires one additional round.
Verifiable secret sharing (VSS) is a fundamental cryptographic primitive, lying at the core of secure multi-party computation (MPC) and, as the distributed analogue of a commitment functionality, used in numerous applications. In this paper we focus on unconditionally secure VSS protocols with honest majority. In this setting it is typically assumed that parties are connected pairwise by authenticated, private channels, and that in addition they have access to a “broadcast ” channel. Because broadcast cannot be simulated on a point-to-point network when a third or more of the parties are corrupt, it is impossible to construct VSS (and more generally, MPC) protocols in this setting without using a broadcast channel (or some equivalent addition to the model). A great deal of research has focused on increasing the efficiency of VSS, primarily in terms of round complexity. In this work we consider a refinement of the round complexity of VSS, by adding a measure we term broadcast complexity. We view the broadcast channel as an expensive resource and seek to minimize the number of rounds in which it is invoked as well. We construct a (linear) VSS protocol which uses the broadcast channel only twice in the sharing phase, while running in an overall constant number of rounds. 1