Secure Multi-Party Computation is a hot topic in recent years. However, though Secure Multi-Party Computation allows each participant to calculate without making their information known to other nodes, the underlying topology of their network is prone to exposure. Inspired by Tal Moran, Bo Mi et al. designed a broadcast protocol based on NTRUEcrypt, which realized topology-hiding but relying on a third party. In view of this shortcoming, we proposed a topology-hiding broadcast protocol based on Shamir's Secret Sharing scheme with self-adaptive paradigm. Security and performance analyses demonstrated that our scheme is unconditional secure and computationally light-weighted.
Secure Multi-Party Computation is a hot topic in recent years. However, though Secure Multi-Party Computation allows each participant to calculate without making their information known to other nodes, the underlying topology of their network is prone to exposure. Inspired by Tal Moran, Bo Mi et al. designed a broadcast protocol based on NTRUEcrypt, which realized topology-hiding but relying on a third party. In view of this shortcoming, we proposed a topology-hiding broadcast protocol based on Shamir's Secret Sharing scheme with self-adaptive paradigm. Security and performance analyses demonstrated that our scheme is unconditional secure and computationally light-weighted.
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
Abstract. Rational secret sharing protocols in both the two-party and multi-party settings are proposed. These protocols are built in standard communication networks and with unconditional security. Namely, the protocols run over standard point-to-point networks without requiring physical assumptions or simultaneous channels, and even a computationally unbounded player cannot gain more than ɛ by deviating from the protocol. More precisely, for the 2-out-of-2 protocol the ɛ is a negligible function in the size of the secret, which is caused by the informationtheoretic MACs used for authentication. The t-out-of-n protocol is (t−1)resilient and the ɛ is exponentially small in the number of participants. Although secret recovery cannot be guaranteed in this setting, a participant can at least reduce the Shannon entropy of the secret to less than 1 after the protocol. When the secret-domain is large, every rational player has great incentive to participate in the protocol.
Secure multiparty computation (MPC) is perhaps the most popular paradigm in the area of cryptographic protocols. It allows several mutually untrustworthy parties to jointly compute a function of their private inputs, without revealing to each other information about those inputs. In the case of unconditional (information-theoretic) security, protocols are known which tolerate a dishonest minority of players, who may coordinate their attack and deviate arbitrarily from the protocol specification. It is typically assumed in these results that parties are connected pairwise by authenticated, private channels, and that in addition they have access to a “broadcast ” channel. Broadcast allows one party to send a consistent message to all other parties, guaranteeing consistency even if the broadcaster is corrupted. Because broadcast cannot be simulated on the point-to-point network when more than a third of the parties are corrupt, it is impossible to construct general 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 MPC, primarily in terms of round complexity and communication complexity. In this work we propose a refinement of the round complexity which we term broadcast complexity. We view the broadcast channel as an expensive resource
We show that some problems in information security can be solved without using one-way functions. The latter are usually regarded as a central concept of cryptography, but the very existence of one-way functions depends on difficult conjectures in complexity theory, most notably on the notorious “” conjecture. This is why cryptographic primitives that do not employ one-way functions are often called “unconditionally secure”. In this paper, we suggest protocols for secure computation of the sum, product, and some other functions of two or more elements of an arbitrary constructible ring, without using any one-way functions. A new input that we offer here is that, in contrast with other proposals, we conceal “intermediate results” of a computation. For example, when we compute the sum of k numbers, only the final result is known to the parties; partial sums are not known to anybody. Other applications of our method include voting/rating over insecure channels and a rather elegant and efficient solution of the “two millionaires problem”. Then, while it is fairly obvious that a secure (bit) commitment between two parties is impossible without a one-way function, we show that it is possible if the number of parties is at least 3. We also show how our unconditionally secure (bit) commitment scheme for three parties can be used to arrange an unconditionally secure (bit) commitment between just two parties if they use a “dummy” (e.g., a computer) as the third party. We explain how our concept of a “dummy” is different from the well-known concept of a “trusted third party”. Based on a similar idea, we also offer an unconditionally secure k - n oblivious transfer protocol between two parties who use a “dummy”. We also suggest a protocol, without using a one-way function, for the so-called “mental poker”, i.e., a fair card dealing (and playing) over distance. Finally, we propose a secret sharing scheme where an advantage over Shamir's and other known secret sharing schemes is that nobody, including the dealer, ends up knowing the shares (of the secret) owned by any particular player. It should be mentioned that computational cost of our protocols is negligible to the point that all of them can be executed without a computer.