Cryptographic reverse firewalls for interactive proof systems

We study interactive proof systems (IPSes) in a strong adversarial setting where the machines of *honest parties* might be corrupted and under control of the adversary. Our aim is to answer the following, seemingly paradoxical, questions: - Can Peggy convince Vic of the veracity of an NP statement, without leaking any information about the witness even in case Vic is malicious and Peggy does not trust her computer? - Can we avoid that Peggy fools Vic into accepting false statements, even if Peggy is malicious and Vic does not trust her computer? At EUROCRYPT 2015, Mironov and Stephens-Davidowitz introduced cryptographic reverse firewalls (RFs) as an attractive approach to tackling such questions. Intuitively, a RF for Peggy/Vic is an external party that sits between Peggy/Vic and the outside world and whose scope is to sanitize Peggy's/Vic's incoming and outgoing messages in the face of subversion of her/his computer, e.g. in order to destroy subliminal channels. In this paper, we put forward several natural security properties for RFs in the concrete setting of IPSes. As our main contribution, we construct efficient RFs for different IPSes derived from a large class of Sigma protocols that we call malleable. A nice feature of our design is that it is completely transparent, in the sense that our RFs can be directly applied to already deployed IPSes, without the need to re-implement them

Optimal Extension Protocols for Byzantine Broadcast and Agreement

The problems of Byzantine Broadcast (BB) and Byzantine Agreement (BA) are of interest to both distributed computing and cryptography community. Extension protocols for these primitives have been introduced to handle long messages efficiently at the cost of small number of single-bit broadcasts, referred to as seed broadcasts. While the communication optimality has remained the most sought-after property of an extension protocol in the literature, we prioritize both communication and round optimality in this work. In a setting with $n$ parties and an adversary controlling at most $t$ parties in Byzantine fashion, we present BB and BA extension protocols with $t<n$, $t < n/2$ and $t<n/3$ that are simultaneously optimal in terms of communication and round complexity. The best communication that an extension protocol can achieve in any setting is $O(\ell n)$ bits for a message of length $\ell$ bits. The best achievable round complexity is $O(n)$ for the setting $t< n$ and $O(1)$ in the other two settings $t < n/2$ and $t<n/3$. The existing constructions are either optimal only in terms of communication complexity, or require more rounds than our protocols, or achieve optimal round complexity at the cost of sub-optimal communication. Specifically, we construct communication-optimal protocols in the three corruption scenarios with the following round complexities: 1. $t<n/3$: $3$ rounds, improving over $O(\sqrt{\ell} + n^2)$ 2. $t<n/2$: $5$ rounds, improving over $6$ 3. $t<n$: $O(n)$ rounds, improving over $O(n^2)$ A concrete protocol from an extension protocol is obtained by replacing the seed broadcasts with a BB protocol for a single bit. Our extension protocols minimize the seed-round complexity and seed-communication complexity. The former refers to the number of rounds in an extension protocol in which seed broadcasts are invoked and impacts the round complexity of a concrete protocol due to a number of sequential calls to bit broadcast. The latter refers to the number of bits communicated through the seed broadcasts and impacts the round and communication complexity due to parallel instances of single-bit broadcast. In the settings of $t<n/3$, $t<n/2$ and $t<n$, our protocols improve the seed-round complexity from $O(\sqrt{\ell} + n^2)$ to $1$, from $3$ to $2$ and from $O(n^2)$ to $O(n)$ respectively. Our protocols keep the seed-communication complexity independent of the message length $\ell$ and, either improve or keep the complexity almost in the same order compared to the existing protocols

Hashing Garbled Circuits for Free

We introduce {\em Free Hash}, a new approach to generating Garbled Circuit (GC) hash at no extra cost during GC generation. This is in contrast with state-of-the-art approaches, which hash GCs at computational cost of up to $6\times$ of GC generation. GC hashing is at the core of the cut-and-choose technique of GC-based secure function evaluation (SFE). Our main idea is to intertwine hash generation/verification with GC generation and evaluation. While we {\em allow} an adversary to generate a GC \widehat{\GC} whose hash collides with an honestly generated \GC, such a \widehat{\GC} w.h.p. will fail evaluation and cheating will be discovered. Our GC hash is simply a (slightly modified) XOR of all the gate table rows of GC. It is compatible with Free XOR and half-gates garbling, and can be made to work with many cut-and-choose SFE protocols. With today\u27s network speeds being not far behind hardware-assisted fixed-key garbling throughput, eliminating the GC hashing cost will significantly improve SFE performance. Our estimates show substantial cost reduction in typical settings, and up to factor $6$ in specialized applications relying on GC hashes. We implemented GC hashing algorithm and report on its performance

Reverse Firewalls for Oblivious Transfer Extension and Applications to Zero-Knowledge

In the setting of subversion, an adversary tampers with the machines of the honest parties thus leaking the honest parties\u27 secrets through the protocol transcript. The work of Mironov and Stephens-Davidowitz (EUROCRYPT’15) introduced the idea of reverse firewalls (RF) to protect against tampering of honest parties\u27 machines. All known constructions in the RF framework rely on the malleability of the underlying operations in order for the RF to rerandomize/sanitize the transcript. RFs are thus limited to protocols that offer some structure, and hence based on public-key operations. In this work, we initiate the study of $efficient$ Multiparty Computation (MPC) protocols in the presence of tampering. In this regard, - We construct the $first$ Oblivious Transfer (OT) extension protocol in the RF setting. We obtain $poly(\kappa)$ maliciously-secure OTs using $O(\kappa)$ public key operations and $O(1)$ inexpensive symmetric key operations, where $\kappa$ is the security parameter. - We construct the $first$ Zero-knowledge protocol in the RF setting where each multiplication gate can be proven using $O(1)$ symmetric key operations. We achieve this using our OT extension protocol and by extending the ZK protocol of Quicksilver (Yang, Sarkar, Weng and Wang, CCS\u2721) to the RF setting. - Along the way, we introduce new ideas for malleable interactive proofs that could be of independent interest. We define a notion of $full$ $malleability$ for Sigma protocols that unlike prior notions allow modifying the instance as well, in addition to the transcript. We construct new protocols that satisfy this notion, construct RFs for such protocols and use them in constructing our OT extension. The key idea of our work is to demonstrate that correlated randomness may be obtained in an RF-friendly way $without$ having to rerandomize the entire transcript. This enables us to avoid expensive public-key operations that grow with the circuit-size

Efficient Zero-Knowledge Proof of Algebraic and Non-Algebraic Statements with Applications to Privacy Preserving Credentials

Practical anonymous credential systems are generally built around sigma-protocol ZK proofs. This requires that credentials be based on specially formed signatures. Here we ask whether we can instead use a standard (say, RSA, or (EC)DSA) signature that includes formatting and hashing messages, as a credential, and still provide privacy. Existing techniques do not provide efficient solutions for proving knowledge of such a signature: On the one hand, ZK proofs based on garbled circuits (Jawurek et al. 2013) give efficient proofs for checking formatting of messages and evaluating hash functions. On the other hand they are expensive for checking algebraic relations such as RSA or discrete-log, which can be done efficiently with sigma protocols. We design new constructions obtaining the best of both worlds: combining the efficiency of the garbled circuit approach for non-algebraic statements and that of sigma protocols for algebraic ones. We then discuss how to use these as building-blocks to construct privacy-preserving credential systems based on standard RSA and (EC)DSA signatures. Other applications of our techniques include anonymous credentials with more complex policies, the ability to efficiently switch between commitments (and signatures) in different groups, and secure two-party computation on committed/signed inputs

How to Make Rational Arguments Practical and Extractable

We investigate proof systems where security holds against rational parties instead of malicious ones. Our starting point is the notion of rational arguments, a variant of rational proofs (Azar and Micali, STOC 2012) where security holds against rational adversaries that are also computationally bounded. Rational arguments are an interesting primitive because they generally allow for very efficient protocols, and in particular sublinear verification (i.e. where the Verifier does not have to read the entire input). In this paper we aim at narrowing the gap between literature on rational schemes and real world applications. Our contribution is two-fold. We provide the first construction of rational arguments for the class of polynomial computations that is practical (i.e., it can be applied to real-world computations on reasonably common hardware) and with logarithmic communication. Techniques-wise, we obtain this result through a compiler from information-theoretic protocols and rational proofs for polynomial evaluation. The latter could be of independent interest. As a second contribution, we propose a new notion of extractability for rational arguments. Through this notion we can obtain arguments where knowledge of a witness is incentivized (rather than incentivizing mere soundness). We show how our aforementioned compiler can also be applied to obtain efficient extractable rational arguments for $\mathsf{NP}$

NIWI and New Notions of Extraction for Algebraic Languages

We give an efficient construction of a computational non-interactive witness indistinguishable (NIWI) proof in the plain model, and investigate notions of extraction for NIZKs for algebraic languages. Our starting point is the recent work of Couteau and Hartmann (CRYPTO 2020) who developed a new framework (CH framework) for constructing non-interactive zero-knowledge proofs and arguments under falsifiable assumptions for a large class of languages called algebraic languages. In this paper, we construct an efficient NIWI proof in the plain model for algebraic languages based on the CH framework. In the plain model, our NIWI construction is more efficient for algebraic languages than state-of-the-art Groth-Ostrovsky-Sahai (GOS) NIWI (JACM 2012). Next, we explore knowledge soundness of NIZK systems in the CH framework. We define a notion of strong f-extractability, and show that the CH proof system satisfies this notion. We then put forth a new definition of knowledge soundness called semantic extraction. We explore the relationship of semantic extraction with existing knowledge soundness definitions and show that it is a general definition that recovers black-box and non-black-box definitions as special cases. Finally, we show that NIZKs for algebraic languages in the CH framework cannot satisfy semantic extraction. We extend this impossibility to a class of NIZK arguments over algebraic languages, namely quasi-adaptive NIZK arguments that are constructed from smooth projective hash functions

Proof-of-Stake Protocols for Privacy-Aware Blockchains

Proof-of-stake (PoS) protocols are emerging as one of the most promising alternative to the wasteful proof-of-work (PoW) protocols for consensus in Blockchains (or distributed ledgers). However, current PoS protocols inherently disclose both the identity and the wealth of the stakeholders, and thus seem incompatible with privacy-preserving cryptocurrencies (such as ZCash, Monero, etc.). In this paper we initiate the formal study for PoS protocols with privacy properties. Our results include: - A (theoretical) feasibility result showing that it is possible to construct a general class of private PoS (PPoS) protocols; and to add privacy to a wide class of PoS protocols, - A privacy-preserving version of a popular PoS protocol, Ouroboros Praos. Towards our result, we define the notion of anonymous verifiable random function, which we believe is of independent interest

Secure Auctions in the Presence of Rational Adversaries

Sealed bid auctions are used to allocate a resource among a set of interested parties. Traditionally, auctions need the presence of a trusted auctioneer to whom the bidders provide their private bid values. Existence of such a trusted party is not an assumption easily realized in practice. Generic secure computation protocols can be used to remove a trusted party. However, generic techniques result in inefficient protocols, and typically do not provide fairness - that is, a corrupt party can learn the output and abort the protocol thereby preventing other parties from learning the output. At CRYPTO 2009, Miltersen, Nielsen and Triandopoulos [MNT09], introduced the problem of building auctions that are secure against rational bidders. Such parties are modeled as self-interested agents who care more about maximizing their utility than about learning information about bids of other agents. To realize this, they put forth a novel notion of information utility and introduce a game-theoretic framework that helps analyse protocols while taking into account both information utility as well as monetary utility. Unfortunately, their construction makes use a of generic MPC protocol and, consequently, the authors do not analyze the concrete efficiency of their protocol. In this work, we construct the first concretely efficient and provably secure protocol for First Price Auctions in the rational setting. Our protocol guarantees privacy and fairness. Inspired by [MNT09], we put forth a solution concept that we call Privacy Enhanced Computational Weakly Dominant Strategy Equilibrium that captures parties\u27 privacy and monetary concerns in the game theoretic context, and show that our protocol realizes this. We believe this notion to be of independent interest. Our protocol is crafted specifically for the use case of auctions, is simple, using off-the-shelf cryptographic components. Executing our auction protocol on commodity hardware with 10 bidders, with bids of length 10, our protocol runs to completion in 0.141s and has total communication of 30KB

Succinct Verification of Compressed Sigma Protocols in the Updatable SRS setting

We propose protocols in the Compressed Sigma Protocol framework that achieve a succinct verifier. Towards this, we construct a new inner product argument and cast it in the Compressed Sigma Protocol (CSP) framework as a protocol for opening a committed linear form, achieving logarithmic verification. We then use our succinct-verifier CSP to construct a zero-knowledge argument for circuit satisfiability (under the discrete logarithm assumption in bilinear groups) in the updatable Structured Reference String (SRS) setting that achieves $O(\log n)$ proof size and $O(\log n)$ verification complexity. Our circuit zero-knowledge protocol has concretely better proof/prover/verifier complexity compared to the the state-of-the-art protocol in the updatable setting under the same assumption. Our techniques of achieving verifier-succinctness in the compression framework is of independent interest. We then show a commitment scheme for committing to group elements using a structured commitment key. We construct protocols to open a committed homomorphism on a committed vector with verifier succinctness in the designated verifier setting. This has applications in making the verifier in compressed sigma protocols for bilinear group arithmetic circuits, succinct