Iddo Bentov

How to Use Bitcoin to Design Fair Protocols

We study a model of fairness in secure computation in which an adversarial party that aborts on receiving output is forced to pay a mutually predefined monetary penalty. We then show how the Bitcoin network can be used to achieve the above notion of fairness in the two-party as well as the multiparty setting (with a dishonest majority). In particular, we propose new ideal functionalities and protocols for fair secure computation and fair lottery in this model.

Cryptocurrencies Without Proof of Work

We study decentralized cryptocurrency protocols in which the participants do not deplete physical scarce resources. Such protocols commonly rely on Proof of Stake, i.e., on mechanisms that extend voting power to the stakeholders of the system. We offer analysis of existing protocols that have a substantial amount of popularity. We then present our novel pure Proof of Stake protocols, and argue that they help in mitigating problems that the existing protocols exhibit.

How to Use Bitcoin to Incentivize Correct Computations

We study a model of incentivizing correct computations in a variety of cryptographic tasks. For each of these tasks we propose a formal model and design protocols satisfying our models constraints in a hybrid model where parties have access to special ideal functionalities that enable monetary transactions. We summarize our results: Verifiable computation. We consider a setting where a delegator outsources computation to a worker who expects to get paid in return for delivering correct outputs. We design protocols that compile both public and private verification schemes to support incentivizations described above. Secure computation with restricted leakage. Building on the recent work of Huang et al. (Security and Privacy 2012), we show an efficient secure computation protocol that monetarily penalizes an adversary that attempts to learn one bit of information but gets detected in the process. Fair secure computation. Inspired by recent work, we consider a model of secure computation where a party that aborts after learning the output is monetarily penalized. We then propose an ideal transaction functionality FML and show a constant-round realization on the Bitcoin network. Then, in the FML-hybrid world we design a constant round protocol for secure computation in this model. Noninteractive bounties. We provide formal definitions and candidate realizations of noninteractive bounty mechanisms on the Bitcoin network which (1) allow a bounty maker to place a bounty for the solution of a hard problem by sending a single message, and (2) allow a bounty collector (unknown at the time of bounty creation) with the solution to claim the bounty, while (3) ensuring that the bounty maker can learn the solution whenever its bounty is collected, and (4) preventing malicious eavesdropping parties from both claiming the bounty as well as learning the solution. All our protocol realizations (except those realizing fair secure computation) rely on a special ideal functionality that is not currently supported in Bitcoin due to limitations imposed on Bitcoin scripts. Motivated by this, we propose validation complexity of a protocol, a formal complexity measure that captures the amount of computational effort required to validate Bitcoin transactions required to implement it in Bitcoin. Our protocols are also designed to take advantage of optimistic scenarios where participating parties behave honestly.

Proof of Activity: Extending Bitcoin's Proof of Work via Proof of Stake [Extended Abstract]y

We propose a new protocol for a cryptocurrency, that builds upon the Bitcoin protocol by combining its Proof of Work component with a Proof of Stake type of system. Our Proof of Activity protocol offers good security against possibly practical attacks on Bitcoin, and has a relatively low penalty in terms of network communication and storage space.

How to Use Bitcoin to Play Decentralized Poker

Back and Bentov (arXiv 2014) and Andrychowicz et al. (Security and Privacy 2014) introduced techniques to perform secure multiparty computations on Bitcoin. Among other things, these works constructed lottery protocols that ensure that any party that aborts after learning the outcome pays a monetary penalty to all other parties. Following this, Andrychowicz et al. (Bitcoin Workshop 2014) and concurrently Bentov and Kumaresan (Crypto 2014) extended the solution to arbitrary secure function evaluation while guaranteeing fairness in the following sense: any party that aborts after learning the output pays a monetary penalty to all parties that did not learn the output. Andrychowicz et al. (Bitcoin Workshop 2014) also suggested extending to scenarios where parties receive a payoff according to the output of a secure function evaluation, and outlined a 2-party protocol for the same that in addition satisfies the notion of fairness described above. In this work, we formalize, generalize, and construct multiparty protocols for the primitive suggested by Andrychowicz et al. We call this primitive secure cash distribution with penalties. Our formulation of secure cash distribution with penalties poses it as a multistage reactive functionality (i.e., more general than secure function evaluation) that provides a way to securely implement smart contracts in a decentralized setting, and consequently suffices to capture a wide variety of stateful computations involving data and/or money, such as decentralized auctions, market, and games such as poker, etc. Our protocol realizing secure cash distribution with penalties works in a hybrid model where parties have access to a claim-or-refund transaction functionality FCR}* which can be efficiently realized in (a variant of) Bitcoin, and is otherwise independent of the Bitcoin ecosystem. We emphasize that our protocol is dropout-tolerant in the sense that any party that drops out during the protocol is forced to pay a monetary penalty to all other parties. Our formalization and construction generalize both secure computation with penalties of Bentov and Kumaresan (Crypto 2014), and secure lottery with penalties of Andrychowicz et al. (Security and Privacy 2014).

Computational Integrity with a Public Random String from Quasi-Linear PCPs

A party executing a computation on behalf of others may benefit from misreporting its output. Cryptographic protocols that detect this can facilitate decentralized systems with stringent computational integrity requirements. For the computation’s result to be publicly trustworthy, it is moreover imperative to usepublicly verifiable protocols that have no “backdoors” or secret keys that enable forgery.

Instantaneous Decentralized Poker

We present efficient protocols for amortized secure multiparty computation with penalties and secure cash distribution, of which poker is a prime example. Our protocols have an initial phase where the parties interact with a cryptocurrency network, that then enables them to interact only among themselves over the course of playing many poker games in which money changes hands.

Decentralized Prediction Market Without Arbiters

We consider a prediction market in which all aspects are controlled by market forces, in particular the correct outcomes of events are decided by the market itself rather than by trusted arbiters. This kind of a decentralized prediction market can sustain betting on events whose outcome may remain unresolved for a long or even unlimited time period, and can facilitate trades among participants who are spread across diverse geographical locations, may wish to remain anonymous and/or avoid burdensome identification procedures, and are distrustful of each other. We describe how a cryptocurrency such as Bitcoin can be enhanced to accommodate a truly decentralized prediction market, by employing an innovative variant of the Colored Coins concept. We examine the game-theoretic properties of our design, and offer extensions that enable other financial instruments as well as real-time exchange.