Secure Numerical and Logical Multi Party Operations

We derive algorithms for efficient secure numerical and logical operations using a recently introduced scheme for secure multi-party computation~\cite{sch15} in the semi-honest model ensuring statistical or perfect security. To derive our algorithms for trigonometric functions, we use basic mathematical laws in combination with properties of the additive encryption scheme in a novel way. For division and logarithm we use a new approach to compute a Taylor series at a fixed point for all numbers. All our logical operations such as comparisons and large fan-in AND gates are perfectly secure. Our empirical evaluation yields speed-ups of more than a factor of 100 for the evaluated operations compared to the state-of-the-art

Finding Safety in Numbers with Secure Allegation Escrows

For fear of retribution, the victim of a crime may be willing to report it only if other victims of the same perpetrator also step forward. Common examples include 1) identifying oneself as the victim of sexual harassment, especially by a person in a position of authority or 2) accusing an influential politician, an authoritarian government, or ones own employer of corruption. To handle such situations, legal literature has proposed the concept of an allegation escrow: a neutral third-party that collects allegations anonymously, matches them against each other, and de-anonymizes allegers only after de-anonymity thresholds (in terms of number of co-allegers), pre-specified by the allegers, are reached. An allegation escrow can be realized as a single trusted third party; however, this party must be trusted to keep the identity of the alleger and content of the allegation private. To address this problem, this paper introduces Secure Allegation Escrows (SAE, pronounced "say"). A SAE is a group of parties with independent interests and motives, acting jointly as an escrow for collecting allegations from individuals, matching the allegations, and de-anonymizing the allegations when designated thresholds are reached. By design, SAEs provide a very strong property: No less than a majority of parties constituting a SAE can de-anonymize or disclose the content of an allegation without a sufficient number of matching allegations (even in collusion with any number of other allegers). Once a sufficient number of matching allegations exist, the join escrow discloses the allegation with the allegers' identities. We describe how SAEs can be constructed using a novel authentication protocol and a novel allegation matching and bucketing algorithm, provide formal proofs of the security of our constructions, and evaluate a prototype implementation, demonstrating feasibility in practice.Comment: To appear in NDSS 2020. New version includes improvements to writing and proof. The protocol is unchange

Novel Secret Sharing and Commitment Schemes for Cryptographic Applications

In the second chapter, the notion of a social secret sharing (SSS) scheme is introduced in which shares are allocated based on a player's reputation and the way she interacts with other parties. In other words, this scheme renews shares at each cycle without changing the secret, and it allows the trusted parties to gain more authority. Our motivation is that, in real-world applications, components of a secure scheme have different levels of importance (i.e., the number of shares a player has) and reputation (i.e., cooperation with other parties). Therefore, a good construction should balance these two factors accordingly. In the third chapter, a novel socio-rational secret sharing (SRS) scheme is introduced in which rational foresighted players have long-term interactions in a social context, i.e., players run secret sharing while founding and sustaining a public trust network. To motivate this, consider a repeated secret sharing game such as sealed-bid auctions. If we assume each party has a reputation value, we can then penalize (or reward) the players who are selfish (or unselfish) from game to game. This social reinforcement stimulates the players to be cooperative in the secret recovery phase. Unlike the existing protocols in the literature, the proposed solution is stable and it only has a single reconstruction round. In the fourth chapter, a comprehensive analysis of the existing dynamic secret sharing (DSS) schemes is first provided. In a threshold scheme, the sensitivity of the secret and the number of players may fluctuate due to various reasons. Moreover, a common problem with almost all secret sharing schemes is that they are ``one-time'', meaning that the secret and shares are known to everyone after secret recovery. We therefore provide new techniques where the threshold and/or the secret can be changed multiple times to arbitrary values after the initialization. In addition, we introduce a new application of dynamic threshold schemes, named sequential secret sharing (SQS), in which several secrets with increasing thresholds are shared among the players who have different levels of authority. In the fifth chapter, a cryptographic primitive, named multicomponent commitment scheme (MCS) is proposed where we have multiple committers and verifiers. This new scheme is used to construct different sealed-bid auction protocols (SAP) where the auction outcomes are defined without revealing the losing bids. The main reason for constructing secure auctions is the fact that the values of the losing bids can be exploited in future auctions and negotiations if they are not kept private. In our auctioneer-free protocols, bidders first commit to their bids before the auction starts. They then apply a decreasing price mechanism to define the winner and selling price in an unconditionally secure setting

Asymmetric Multi-Party Computation

Current protocols for Multi-Party Computation (MPC) consider the setting where all parties have access to similar resources. For example, all parties have access to channels bounded by the same worst-case delay upper bound ?, and all channels have the same cost of communication. As a consequence, the overall protocol performance (resp. the communication cost) may be heavily affected by the slowest (resp. the most expensive) channel, even when most channels are fast (resp. cheap). Given the state of affairs, we initiate a systematic study of asymmetric MPC. In asymmetric MPC, the parties are divided into two categories: fast and slow parties, depending on whether they have access to high-end or low-end resources. We investigate two different models. In the first, we consider asymmetric communication delays: Fast parties are connected via channels with small delay ? among themselves, while channels connected to (at least) one slow party have a large delay ? ? ?. In the second model, we consider asymmetric communication costs: Fast parties benefit from channels with cheap communication, while channels connected to a slow party have an expensive communication. We provide a wide range of positive and negative results exploring the trade-offs between the achievable number of tolerated corruptions t and slow parties s, versus the round complexity and communication cost in each of the models. Among others, we achieve the following results. In the model with asymmetric communication delays, focusing on the information-theoretic (i-t) setting: - An i-t asymmetric MPC protocol with security with abort as long as t+s < n and t < n/2, in a constant number of slow rounds. - We show that achieving an i-t asymmetric MPC protocol for t+s = n and with number of slow rounds independent of the circuit size implies an i-t synchronous MPC protocol with round complexity independent of the circuit size, which is a major problem in the field of round-complexity of MPC. - We identify a new primitive, asymmetric broadcast, that allows to consistently distribute a value among the fast parties, and at a later time the same value to slow parties. We completely characterize the feasibility of asymmetric broadcast by showing that it is possible if and only if 2t + s < n. - An i-t asymmetric MPC protocol with guaranteed output delivery as long as t+s < n and t < n/2, in a number of slow rounds independent of the circuit size. In the model with asymmetric communication cost, we achieve an asymmetric MPC protocol for security with abort for t+s < n and t < n/2, based on one-way functions (OWF). The protocol communicates a number of bits over expensive channels that is independent of the circuit size. We conjecture that assuming OWF is needed and further provide a partial result in this direction