Biblio

Symbolic methods have been used extensively for proving security of cryptographic protocols in the Dolev-Yao model, and more recently for proving security of cryptographic primitives and constructions in the computational model. However, existing methods for proving security of cryptographic constructions in the computational model often require significant expertise and interaction, or are fairly limited in scope and expressivity. This paper introduces a symbolic approach for proving security of cryptographic constructions based on the Learning With Errors assumption (Regev, STOC 2005). Such constructions are instances of lattice-based cryptography and are extremely important due to their potential role in post-quantum cryptography. Following (Barthe, Grégoire and Schmidt, CCS 2015), our approach combines a computational logic and deducibility problems—a standard tool for representing the adversary's knowledge, the Dolev-Yao model. The computational logic is used to capture (indistinguishability-based) security notions and drive the security proofs whereas deducibility problems are used as side-conditions to control that rules of the logic are applied correctly. We then use AutoLWE, an implementation of the logic, to deliver very short or even automatic proofs of several emblematic constructions, including CPA-PKE (Gentry et al., STOC 2008), (Hierarchical) Identity-Based Encryption (Agrawal et al. Eurocrypt 2010), Inner Product Encryption (Agrawal et al. Asiacrypt 2011), CCA-PKE (Micciancio et al., Eurocrypt 2012). The main technical novelty beyond AutoLWE is a set of (semi-)decision procedures for deducibility problems, using extensions of Gröbner basis computations for subalgebras in the (non-)commutative setting (instead of ideals in the commutative setting). Our procedures cover the theory of matrices, which is required for lattice-based assumption, as well as the theory of non-commutative rings, fields, and Diffie-Hellman exponentiation, in its standard, bilinear and multilinear forms. Additionally, AutoLWE supports oracle-relative assumptions, which are used specifically to apply (advanced forms of) the Leftover Hash Lemma, an information-theoretical tool widely used in lattice-based proofs.

Nakamoto's famous blockchain protocol enables achieving consensus in a so-called permissionless setting—anyone can join (or leave) the protocol execution, and the protocol instructions do not depend on the identities of the players. His ingenious protocol prevents "sybil attacks" (where an adversary spawns any number of new players) by relying on computational puzzles (a.k.a. "moderately hard functions") introduced by Dwork and Naor (Crypto'92). Recent work by Garay et al (EuroCrypt'15) and Pass et al (manuscript, 2016) demonstrate that this protocol provably achieves consistency and liveness assuming a) honest players control a majority of the computational power in the network, b) the puzzle-hardness is appropriately set as a function of the maximum network delay and the total computational power of the network, and c) the computational puzzle is modeled as a random oracle. Assuming honest participation, however, is a strong assumption, especially in a setting where honest players are expected to perform a lot of work (to solve the computational puzzles). In Nakamoto's Bitcoin application of the blockchain protocol, players are incentivized to solve these puzzles by receiving rewards for every "block" (of transactions) they contribute to the blockchain. An elegant work by Eyal and Sirer (FinancialCrypt'14), strengthening and formalizing an earlier attack discussed on the Bitcoin forum, demonstrates that a coalition controlling even a minority fraction of the computational power in the network can gain (close to) 2 times its "fair share" of the rewards (and transaction fees) by deviating from the protocol instructions. In contrast, in a fair protocol, one would expect that players controlling a φ fraction of the computational resources to reap a φ fraction of the rewards. We present a new blockchain protocol—the FruitChain protocol—which satisfies the same consistency and liveness properties as Nakamoto's protocol (assuming an honest majority of the computing power), and additionally is δ-approximately fair: with overwhelming probability, any honest set of players controlling a φ fraction of computational power is guaranteed to get at least a fraction (1-δ)φ of the blocks (and thus rewards) in any Ω(κ/δ) length segment of the chain (where κ is the security parameter). Consequently, if this blockchain protocol is used as the ledger underlying a cryptocurrency system, where rewards and transaction fees are evenly distributed among the miners of blocks in a length κ segment of the chain, no coalition controlling less than a majority of the computing power can gain more than a factor (1+3δ) by deviating from the protocol (i.e., honest participation is an n/2-coalition-safe 3δ-Nash equilibrium). Finally, the FruitChain protocol enables decreasing the variance of mining rewards and as such significantly lessens (or even obliterates) the need for mining pools.

Thanks to their anonymity (pseudonymity) and elimination of trusted intermediaries, cryptocurrencies such as Bitcoin have created or stimulated growth in many businesses and communities. Unfortunately, some of these are criminal, e.g., money laundering, illicit marketplaces, and ransomware. Next-generation cryptocurrencies such as Ethereum will include rich scripting languages in support of smart contracts, programs that autonomously intermediate transactions. In this paper, we explore the risk of smart contracts fueling new criminal ecosystems. Specifically, we show how what we call criminal smart contracts (CSCs) can facilitate leakage of confidential information, theft of cryptographic keys, and various real-world crimes (murder, arson, terrorism). We show that CSCs for leakage of secrets (a la Wikileaks) are efficiently realizable in existing scripting languages such as that in Ethereum. We show that CSCs for theft of cryptographic keys can be achieved using primitives, such as Succinct Non-interactive ARguments of Knowledge (SNARKs), that are already expressible in these languages and for which efficient supporting language extensions are anticipated. We show similarly that authenticated data feeds, an emerging feature of smart contract systems, can facilitate CSCs for real-world crimes (e.g., property crimes). Our results highlight the urgency of creating policy and technical safeguards against CSCs in order to realize the promise of smart contracts for beneficial goals.

Smart contracts are programs that execute autonomously on blockchains. Their key envisioned uses (e.g. financial instruments) require them to consume data from outside the blockchain (e.g. stock quotes). Trustworthy data feeds that support a broad range of data requests will thus be critical to smart contract ecosystems. We present an authenticated data feed system called Town Crier (TC). TC acts as a bridge between smart contracts and existing web sites, which are already commonly trusted for non-blockchain applications. It combines a blockchain front end with a trusted hardware back end to scrape HTTPS-enabled websites and serve source-authenticated data to relying smart contracts. TC also supports confidentiality. It enables private data requests with encrypted parameters. Additionally, in a generalization that executes smart-contract logic within TC, the system permits secure use of user credentials to scrape access-controlled online data sources. We describe TC's design principles and architecture and report on an implementation that uses Intel's recently introduced Software Guard Extensions (SGX) to furnish data to the Ethereum smart contract system. We formally model TC and define and prove its basic security properties in the Universal Composibility (UC) framework. Our results include definitions and techniques of general interest relating to resource consumption (Ethereum's "gas" fee system) and TCB minimization. We also report on experiments with three example applications. We plan to launch TC soon as an online public service.

The surprising success of cryptocurrencies has led to a surge of interest in deploying large scale, highly robust, Byzantine fault tolerant (BFT) protocols for mission-critical applications, such as financial transactions. Although the conventional wisdom is to build atop a (weakly) synchronous protocol such as PBFT (or a variation thereof), such protocols rely critically on network timing assumptions, and only guarantee liveness when the network behaves as expected. We argue these protocols are ill-suited for this deployment scenario. We present an alternative, HoneyBadgerBFT, the first practical asynchronous BFT protocol, which guarantees liveness without making any timing assumptions. We base our solution on a novel atomic broadcast protocol that achieves optimal asymptotic efficiency. We present an implementation and experimental results to show our system can achieve throughput of tens of thousands of transactions per second, and scales to over a hundred nodes on a wide area network. We even conduct BFT experiments over Tor, without needing to tune any parameters. Unlike the alternatives, HoneyBadgerBFT simply does not care about the underlying network.

An authenticated data structure (ADS) is a data structure whose operations can be carried out by an untrusted prover, the results of which a verifier can efficiently check as authentic. This is done by having the prover produce a compact proof that the verifier can check along with each operation's result. ADSs thus support outsourcing data maintenance and processing tasks to untrusted servers without loss of integrity. Past work on ADSs has focused on particular data structures (or limited classes of data structures), one at a time, often with support only for particular operations.

This paper presents a generic method, using a simple extension to a ML-like functional programming language we call λ• (lambda-auth), with which one can program authenticated operations over any data structure defined by standard type constructors, including recursive types, sums, and products. The programmer writes the data structure largely as usual and it is compiled to code to be run by the prover and verifier. Using a formalization of λ• we prove that all well-typed λ• programs result in code that is secure under the standard cryptographic assumption of collision-resistant hash functions. We have implemented λ• as an extension to the OCaml compiler, and have used it to produce authenticated versions of many interesting data structures including binary search trees, red-black+ trees, skip lists, and more. Performance experiments show that our approach is efficient, giving up little compared to the hand-optimized data structures developed previously.

Proofs of Retrievability (PoR), proposed by Juels and Kaliski in 2007, enable a client to store n file blocks with a cloud server so that later the server can prove possession of all the data in a very efficient manner (i.e., with constant computation and bandwidth). Although many efficient PoR schemes for static data have been constructed, only two dynamic PoR schemes exist. The scheme by Stefanov et. al. (ACSAC 2012) uses a large of amount of client storage and has a large audit cost. The scheme by Cash (EUROCRYPT 2013) is mostly of theoretical interest, as it employs Oblivious RAM (ORAM) as a black box, leading to increased practical overhead (e.g., it requires about 300 times more bandwidth than our construction). We propose a dynamic PoR scheme with constant client storage whose bandwidth cost is comparable to a Merkle hash tree, thus being very practical. Our construction outperforms the constructions of Stefanov et. al. and Cash et. al., both in theory and in practice. Specifically, for n outsourced blocks of beta bits each, writing a block requires beta+O(lambdalog n) bandwidth and O(betalog n) server computation (lambda is the security parameter). Audits are also very efficient, requiring beta+O(lambda^2log n) bandwidth. We also show how to make our scheme publicly verifiable, providing the first dynamic PoR scheme with such a property. We finally provide a very efficient implementation of our scheme.