## CryptoDB

### Elaine Shi

#### Publications

**Year**

**Venue**

**Title**

2022

EUROCRYPT

A Complete Characterization of Game-Theoretically Fair, Multi-Party Coin Toss
Abstract

Cleve's celebrated lower bound (STOC'86) showed that a de facto strong fairness notion is impossible in 2-party coin toss, i.e., the corrupt party always has a strategy of biasing the honest party's outcome by a noticeable amount. Nonetheless, Blum's famous coin-tossing protocol (CRYPTO'81) achieves a strictly weaker "game-theoretic'' notion of fairness — specifically, it is a 2-party coin toss protocol in which neither party can bias the outcome towards its own preference; and thus the honest protocol forms a Nash equilibrium in which neither party would want to deviate. Surprisingly, an n-party analog of Blum's famous coin toss protocol was not studied till recently. The work by Chung et al.~(TCC'18) was the first to explore the feasibility of game-theoretically fair n-party coin toss in the presence of corrupt majority. We may assume that each party has a publicly stated preference for either the bit 0 or 0, and if the outcome agrees with the party's preference, it obtains utility 1; else it obtains nothing.
A natural game-theoretic formulation is to require that the honest protocol form a coalition-resistant Nash equilibrium, i.e., no coalition should have incentive to deviate from the honest behavior. Chung et al. phrased this game-theoretic notion as “cooperative-strategy-proofness'' or ”CSP-fairness'' for short. Unfortunately, Chung et al.~showed that under (n-1)-sized coalitions,
it is impossible to design such a CSP-fair coin toss protocol, unless all parties except one prefer the same bit. In this paper, we show that the impossibility of Chung et al.~is in fact not as broad as it may seem. When coalitions are majority but not $n-1$ in size, we can indeed get feasibility results in some meaningful parameter regimes. We give a complete characterization of the regime in which CSP-fair coin toss is possible, by providing a matching upper- and lower-bound. Our complete characterization theorem also shows that the mathematical structure of game-theoretic fairness is starkly different from the de facto strong fairness notion in the multi-party computation literature.

2021

EUROCRYPT

Non-Interactive Anonymous Router
📺
Abstract

Anonymous routing is one of the most fundamental online
privacy problems and has been studied extensively for decades. Almost
all known approaches that achieve anonymous routing (e.g., mix-nets,
DC-nets, and numerous other systems) rely on multiple servers or routers
to engage in some interactive protocol; and anonymity is guaranteed in
the threshold model, i.e., if one or more of the servers/routers behave
honestly.
Departing from all prior approaches, we propose a novel non-interactive
abstraction called a Non-Interactive Anonymous Router (NIAR), that
works even with a single untrusted router. In a NIAR scheme, suppose
that n senders each want to talk to a distinct receiver. A one-time trusted
setup is performed such that each sender obtains a sending key, each
receiver obtains a receiving key, and the router receives a token that
“encrypts” the permutation mapping the senders to receivers. In every
time step, the senders can each encrypt its message using its sender key,
and the router can use its token to convert the n ciphertexts received from
the senders to n transformed ciphertexts. Each transformed ciphertext is
delivered to the corresponding receiver, and the receiver can decrypt the
message using its receiver key. Imprecisely speaking, security requires
that the untrusted router, even when colluding with a subset of corrupt
senders and/or receivers, should not be able to break the privacy of
honest parties, including who is talking to who, and the messages they
exchange.
We show how to construct a communication-efficient NIAR scheme with
provable security guarantees based on the SXDH assumption in suitable
bilinear groups and assuming Random Oracles (RO); further, the RO
assumption can be removed if we allow a public key that is as large
as the number of time steps supported. We also define a paranoid
notion of security that achieves full insider protection, and show that
if we additionally assume sub-exponentially secure Indistinguishability
Obfuscation and as sub-exponentially secure one-way functions, one can
construct a NIAR scheme with paranoid security. We show that a com-
pelling application of NIAR is to realize a Non-Interactive Anonymous
Shuffler (NIAS), where an untrusted server or data analyst can only de-
crypt a shuffled version of the messages coming from n senders where
the permutation is hidden. NIAS can be adopted to construct privacy-
preserving surveys, differentially private protocols in the shuffle model,
and pseudonymous bulletin boards.

2021

CRYPTO

Puncturable Pseudorandom Sets and Private Information Retrieval with Near-Optimal Online Bandwidth and Time
📺
Abstract

Imagine one or more non-colluding servers each holding a large
public database, e.g., the repository of DNS entries. Clients would
like to access entries in this database without disclosing their
queries to the servers. Classical private information retrieval (PIR)
schemes achieve polylogarithmic bandwidth per query, but require the
server to perform linear computation per query, which is a
significant barrier towards deployment.
Several recent works showed, however, that by introducing a
one-time, per-client, off-line preprocessing phase, an
\emph{unbounded} number of client queries can be subsequently served
with sublinear online computation time per query (and the cost of the
preprocessing can be amortized over the unboundedly many queries).
Existing preprocessing PIR schemes (supporting unbounded queries), unfortunately, make undesirable tradeoffs to achieve sublinear online computation:
they are either significantly non-optimal in online time or bandwidth,
or require the servers to store
a linear amount of state per client or even per query, or require
polylogarithmically many non-colluding servers.
We propose a novel 2-server preprocessing PIR scheme that achieves
$\widetilde{O}(\sqrt{n})$ online computation per query and
$\widetilde{O}(\sqrt{n})$ client storage, while
preserving the polylogarithmic online bandwidth of classical PIR
schemes. Both the online bandwidth and computation
are optimal up to a poly-logarithmic factor.
In our construction, each server stores only the original
database and nothing extra, and each online query is served within a
single round trip. Our construction relies on the standard LWE
assumption. As an important stepping stone, we propose new, more
generalized definitions for a cryptographic object called a Privately
Puncturable Pseudorandom Set, and give novel constructions that depart
significantly from prior approaches.

2021

CRYPTO

Game-Theoretic Fairness Meets Multi-Party Protocols: The Case of Leader Election
📺
Abstract

Suppose that $n$ players
want to elect a random leader and they communicate by posting
messages to a common broadcast channel.
This problem is called leader election, and it is
fundamental to the distributed systems and cryptography literature.
Recently, it has attracted renewed interests
due to its promised applications in decentralized environments.
In a game theoretically fair leader election protocol, roughly speaking,
we want that even a majority coalition
cannot increase its own chance of getting
elected, nor hurt the chance of any honest individual.
The folklore tournament-tree
protocol, which completes in logarithmically many rounds,
can easily be shown to satisfy game theoretic security. To the best of our knowledge,
no sub-logarithmic round protocol was known in the setting that we consider.
We show that
by adopting an appropriate notion of approximate game-theoretic fairness,
and under standard cryptographic assumption,
we can achieve
$(1-1/2^{\Theta(r)})$-fairness in $r$ rounds for $\Theta(\log \log n) \leq r \leq \Theta(\log n)$,
where $n$ denotes the number of players. In particular, this means that we can approximately match the fairness of the tournament tree protocol using as few as $O(\log \log n)$ rounds.
We also prove a lower bound showing that
logarithmically many rounds are necessary if we restrict ourselves
to ``perfect'' game-theoretic fairness
and protocols that are
``very similar in structure'' to the tournament-tree protocol.
Although leader election is a well-studied problem in other contexts in distributed
computing,
our work is the first exploration of the round complexity
of {\it game-theoretically
fair} leader election in the presence of a possibly majority coalition.
As a by-product of our exploration,
we suggest a new, approximate game-theoretic fairness
notion, called ``approximate sequential fairness'',
which provides a more desirable solution concept than some previously
studied approximate fairness notions.

2021

CRYPTO

Oblivious RAM with Worst-Case Logarithmic Overhead
📺
Abstract

We present the first Oblivious RAM (ORAM) construction that for $N$ memory blocks supports accesses with \emph{worst-case} $O(\log N)$ overhead for any block size $\Omega(\log N)$ while requiring a client memory of only a constant number of memory blocks. We rely on the existence of one-way functions and guarantee computational security. Our result closes a long line of research on fundamental feasibility results for ORAM constructions as logarithmic overhead is necessary.
The previous best logarithmic overhead construction only guarantees it in an \emph{amortized} sense, i.e., logarithmic overhead is achieved only for long enough access sequences, where some of the individual accesses incur $\Theta(N)$ overhead. The previously best ORAM in terms of \emph{worst-case} overhead achieves $O(\log^2 N/\log\log N)$ overhead.
Technically, we design a novel de-amortization framework for modern ORAM constructions that use the ``shuffled inputs'' assumption. Our framework significantly departs from all previous de-amortization frameworks, originating from Ostrovsky and Shoup (STOC~'97), that seem to be fundamentally too weak to be applied on modern ORAM constructions.

2020

JOFC

Locally Decodable and Updatable Non-malleable Codes and Their Applications
Abstract

Non-malleable codes, introduced as a relaxation of error-correcting codes by Dziembowski, Pietrzak, and Wichs (ICS ’10), provide the security guarantee that the message contained in a tampered codeword is either the same as the original message or is set to an unrelated value. Various applications of non-malleable codes have been discovered, and one of the most significant applications among these is the connection with tamper-resilient cryptography. There is a large body of work considering security against various classes of tampering functions, as well as non-malleable codes with enhanced features such as leakage resilience . In this work, we propose combining the concepts of non-malleability , leakage resilience , and locality in a coding scheme. The contribution of this work is threefold: 1. As a conceptual contribution, we define a new notion of locally decodable and updatable non-malleable code that combines the above properties. 2. We present two simple and efficient constructions achieving our new notion with different levels of security. 3. We present an important application of our new tool—securing RAM computation against memory tampering and leakage attacks. This is analogous to the usage of traditional non-malleable codes to secure implementations in the circuit model against memory tampering and leakage attacks.

2020

EUROCRYPT

OptORAMa: Optimal Oblivious RAM
📺
Abstract

Oblivious RAM (ORAM), first introduced in the ground-breaking work of Goldreich and Ostrovsky (STOC '87 and J. ACM '96) is a technique for provably obfuscating programs' access patterns, such that the access patterns leak no information about the programs' secret inputs. To compile a general program to an oblivious counterpart, it is well-known that $\Omega(\log N)$ amortized blowup is necessary, where $N$ is the size of the logical memory. This was shown in Goldreich and Ostrovksy's original ORAM work for statistical security and in a somewhat restricted model (the so called \emph{balls-and-bins} model), and recently by Larsen and Nielsen (CRYPTO '18) for computational security.
A long standing open question is whether there exists an optimal ORAM construction that matches the aforementioned logarithmic lower bounds (without making large memory word assumptions, and assuming a constant number of CPU registers). In this paper, we resolve this problem and present the first secure ORAM with $O(\log N)$ amortized blowup, assuming one-way functions. Our result is inspired by and non-trivially improves on the recent beautiful work of Patel et al. (FOCS '18) who gave a construction with $O(\log N\cdot \log\log N)$ amortized blowup, assuming one-way functions.
One of our building blocks of independent interest is a linear-time deterministic oblivious algorithm for tight compaction: Given an array of $n$ elements where some elements are marked, we permute the elements in the array so that all marked elements end up in the front of the array. Our $O(n)$ algorithm improves the previously best known deterministic or randomized algorithms whose running time is $O(n \cdot\log n)$ or $O(n \cdot\log \log n)$, respectively.

2020

PKC

Sublinear-Round Byzantine Agreement Under Corrupt Majority
📺
Abstract

Although Byzantine Agreement (BA) has been studied for three decades, perhaps somewhat surprisingly, there still exist significant gaps in our understanding regarding its round complexity. A long-standing open question is the following: can we achieve BA with sublinear round complexity under corrupt majority? Due to the beautiful works by Garay et al. (FOCS’07) and Fitzi and Nielsen (DISC’09), we have partial and affirmative answers to this question albeit for the narrow regime $$f = n/2 + o(n)$$ where f is the number of corrupt nodes and n is the total number of nodes. So far, no positive result is known about the setting $$f > 0.51n$$ even for static corruption! In this paper, we make progress along this somewhat stagnant front. We show that there exists a corrupt-majority BA protocol that terminates in $$O(frac{1}{epsilon } log frac{1}{delta })$$ rounds in the worst case, satisfies consistency with probability at least $$1 - delta $$ , and tolerates $$(1-epsilon )$$ fraction of corrupt nodes. Our protocol secures against an adversary that can corrupt nodes adaptively during the protocol execution but cannot perform “after-the-fact” removal of honest messages that have already been sent prior to corruption. Our upper bound is optimal up to a logarithmic factor in light of the elegant $$varOmega (1/epsilon )$$ lower bound by Garay et al. (FOCS’07).

2020

TCC

Expected Constant Round Byzantine Broadcast under Dishonest Majority
📺
Abstract

Byzantine Broadcast (BB) is a central question in distributed systems, and an important challenge is to understand its round complexity. Under the honest majority setting, it is long known that there exist randomized protocols that can achieve BB in expected constant rounds, regardless of the number of nodes $n$. However, whether we can match the expected constant round complexity in the corrupt majority setting --- or more precisely, when $f \geq n/2 + \omega(1)$ --- remains unknown, where $f$ denotes the number of corrupt nodes.
In this paper, we are the first to resolve this long-standing question. We show how to achieve BB in expected $O((n/(n-f))^2)$ rounds. In particular, even when 99\% of the nodes are corrupt we can achieve expected constant rounds. Our results hold under both a static adversary and a weakly adaptive adversary who cannot perform ``after-the-fact removal'' of messages already sent by a node before it becomes corrupt.

2020

TCC

Round-Efficient Byzantine Broadcast under Strongly Adaptive and Majority Corruptions
📺
Abstract

The round complexity of Byzantine Broadcast (BB) has been a central question
in distributed systems and cryptography. In the honest majority setting, expected constant round protocols have been known for decades even in the presence of a strongly adaptive adversary. In the corrupt majority setting, however, no protocol with sublinear round complexity is known, even when the adversary is allowed to {\it strongly adaptively} corrupt only 51\% of the players, and even under reasonable setup or cryptographic assumptions. Recall that a strongly adaptive adversary can examine what original message an honest player would have wanted to send in some round, adaptively corrupt the player in the same round and make it send a completely different message instead.
In this paper, we are the first to construct a BB protocol with sublinear round complexity in the corrupt majority setting. Specifically, assuming the existence of time-lock puzzles with suitable hardness parameters and other standard cryptographic assumptions, we show how to achieve BB in $(\frac{n}{n-f})^2 \cdot \poly\log \lambda$ rounds with $1-\negl(\lambda)$ probability, where $n$ denotes the total number of players, $f$ denotes the maximum number of corrupt players, and $\lambda$ is the security parameter. Our protocol completes in polylogarithmically many rounds even when 99\% of the players can be corrupt.

2020

TCC

Secure Massively Parallel Computation for Dishonest Majority
📺
Abstract

This work concerns secure protocols in the massively parallel computation (MPC) model, which is one of the most widely-accepted models for capturing the challenges of writing protocols for the types of parallel computing clusters which have become commonplace today (MapReduce, Hadoop, Spark, etc.). Recently, the work of Chan et al. (ITCS ’20) initiated this study, giving a way to compile any MPC protocol into a secure one in the common random string model, achieving the standard secure multi-party computation definition of security with up to 1/3 of the parties being corrupt.
We are interested in achieving security for much more than 1/3 corruptions. To that end, we give two compilers for MPC protocols, which assume a simple public-key infrastructure, and achieve semi-honest security for all-but-one corruptions. Our first compiler assumes hardness of the learning-with-errors
(LWE) problem, and works for any MPC protocol with “short” output—that is, where the output of the protocol can fit into the storage space of one machine, for instance protocols that output a trained machine learning model. Our second compiler works for any MPC protocol (even ones with a long output, such as sorting) but assumes, in addition to LWE, indistinguishability obfuscation and a circular secure variant of threshold FHE.

2020

ASIACRYPT

On the Adaptive Security of MACs and PRFs
📺
Abstract

We consider the security of two of the most commonly used cryptographic primitives--message authentication codes (MACs) and pseudorandom functions (PRFs)--in a multi-user setting with adaptive corruption. Whereas is it well known that any secure MAC or PRF is also multi-user secure under adaptive corruption, the trivial reduction induces a security loss that is linear in the number of users.
Our main result shows that black-box reductions from "standard" assumptions cannot be used to provide a tight, or even a linear-preserving, security reduction for adaptive multi-user secure deterministic stateless MACs and thus also PRFs. In other words, a security loss that grows with the number of users is necessary for any such black-box reduction.

2019

EUROCRYPT

Consensus Through Herding
📺
Abstract

State Machine Replication (SMR) is an important abstraction for a set of nodes to agree on an ever-growing, linearly-ordered log of transactions. In decentralized cryptocurrency applications, we would like to design SMR protocols that (1) resist adaptive corruptions; and (2) achieve small bandwidth and small confirmation time. All past approaches towards constructing SMR fail to achieve either small confirmation time or small bandwidth under adaptive corruptions (without resorting to strong assumptions such as the erasure model or proof-of-work).We propose a novel paradigm for reaching consensus that departs significantly from classical approaches. Our protocol is inspired by a social phenomenon called herding, where people tend to make choices considered as the social norm. In our consensus protocol, leader election and voting are coalesced into a single (randomized) process: in every round, every node tries to cast a vote for what it views as the most popular item so far: such a voting attempt is not always successful, but rather, successful with a certain probability. Importantly, the probability that the node is elected to vote for v is independent from the probability it is elected to vote for $$v' \ne v$$v′≠v. We will show how to realize such a distributed, randomized election process using appropriate, adaptively secure cryptographic building blocks.We show that amazingly, not only can this new paradigm achieve consensus (e.g., on a batch of unconfirmed transactions in a cryptocurrency system), but it also allows us to derive the first SMR protocol which, even under adaptive corruptions, requires only polylogarithmically many rounds and polylogarithmically many honest messages to be multicast to confirm each batch of transactions; and importantly, we attain these guarantees under standard cryptographic assumptions.

2019

EUROCRYPT

Locality-Preserving Oblivious RAM
📺
Abstract

Oblivious RAMs, introduced by Goldreich and Ostrovsky [JACM’96], compile any RAM program into one that is “memory oblivious”, i.e., the access pattern to the memory is independent of the input. All previous ORAM schemes, however, completely break the locality of data accesses (for instance, by shuffling the data to pseudorandom positions in memory).In this work, we initiate the study of locality-preserving ORAMs—ORAMs that preserve locality of the accessed memory regions, while leaking only the lengths of contiguous memory regions accessed. Our main results demonstrate the existence of a locality-preserving ORAM with poly-logarithmic overhead both in terms of bandwidth and locality. We also study the tradeoff between locality, bandwidth and leakage, and show that any scheme that preserves locality and does not leak the lengths of the contiguous memory regions accessed, suffers from prohibitive bandwidth.To the best of our knowledge, before our work, the only works combining locality and obliviousness were for symmetric searchable encryption [e.g., Cash and Tessaro (EUROCRYPT’14), Asharov et al. (STOC’16)]. Symmetric search encryption ensures obliviousness if each keyword is searched only once, whereas ORAM provides obliviousness to any input program. Thus, our work generalizes that line of work to the much more challenging task of preserving locality in ORAMs.

2019

CRYPTO

Synchronous, with a Chance of Partition Tolerance
📺
Abstract

Murphy, Murky, Mopey, Moody, and Morose decide to write a paper together over the Internet and submit it to the prestigious CRYPTO’19 conference that has the most amazing PC. They encounter a few problems. First, not everyone is online every day: some are lazy and go skiing on Mondays; others cannot use git correctly and they are completely unaware that they are losing messages. Second, a small subset of the co-authors may be secretly plotting to disrupt the project (e.g., because they are writing a competing paper in stealth).Suppose that each day, sufficiently many honest co-authors are online (and use git correctly); moreover, suppose that messages checked into git on Monday can be correctly received by honest and online co-authors on Tuesday or any future day. Can the honest co-authors successfully finish the paper in a small number of days such that they make the CRYPTO deadline; and perhaps importantly, can all the honest co-authors, including even those who are lazy and those who sometimes use git incorrectly, agree on the final theorem?

2019

ASIACRYPT

Streamlined Blockchains: A Simple and Elegant Approach (A Tutorial and Survey)
Abstract

A blockchain protocol (also called state machine replication) allows a set of nodes to agree on an ever-growing, linearly ordered log of transactions. The classical consensus literature suggests two approaches for constructing a blockchain protocol: (1) through composition of single-shot consensus instances often called Byzantine Agreement; and (2) through direct construction of a blockchain where there is no clear-cut boundary between single-shot consensus instances. While conceptually simple, the former approach precludes cross-instance optimizations in a practical implementation. This perhaps explains why the latter approach has gained more traction in practice: specifically, well-known protocols such as Paxos and PBFT all follow the direct-construction approach.In this tutorial, we present a new paradigm called “streamlined blockchains” for directly constructing blockchain protocols. This paradigm enables a new family of protocols that are extremely simple and natural: every epoch, a proposer proposes a block extending from a notarized parent chain, and nodes vote if the proposal’s parent chain is not
. Whenever a block gains
votes, it becomes notarized. Whenever a node observes a notarized chain with
blocks of consecutive epochs at the end, then the entire chain chopping off
blocks at the end is final.By varying the parameters highlighted in
, we illustrate two variants for the partially synchronous and synchronous settings respectively. We present very simple proofs of consistency and liveness. We hope that this tutorial provides a compelling argument why this new family of protocols should be used in lieu of classical candidates (e.g., PBFT, Paxos, and their variants), both in practical implementation and for pedagogical purposes.

2019

ASIACRYPT

Towards Attribute-Based Encryption for RAMs from LWE: Sub-linear Decryption, and More
Abstract

Attribute based encryption (ABE) is an advanced encryption system with a built-in mechanism to generate keys associated with functions which in turn provide restricted access to encrypted data. Most of the known candidates of attribute based encryption model the functions as circuits. This results in significant efficiency bottlenecks, especially in the setting where the function associated with the ABE key is represented by a random access machine (RAM) and a database, with the runtime of the RAM program being sublinear in the database size. In this work we study the notion of attribute based encryption for random access machines (RAMs), introduced in the work of Goldwasser, Kalai, Popa, Vaikuntanathan and Zeldovich (Crypto 2013). We present a construction of attribute based encryption for RAMs satisfying sublinear decryption complexity assuming learning with errors; this is the first construction based on standard assumptions. Previously, Goldwasser et al. achieved this result based on non-falsifiable knowledge assumptions. We also consider a dual notion of ABE for RAMs, where the database is in the ciphertext and we show how to achieve this dual notion, albeit with large attribute keys, also based on learning with errors.

2019

ASIACRYPT

Streamlined blockchains: A simple and elegant approach (tutorial)
★
Abstract

A blockchain protocol (also called state machine replication) allows a set of nodes to agree on an ever-growing, linearly ordered log of transactions. In this tutorial, we present a new paradigm called “streamlined blockchains”. This paradigm enables a new family of protocols that are extremely simple and natural: every epoch, a proposer proposes a block extending from a notarized parent chain, and nodes vote if the proposal’s parent chain is not too old. Whenever a block gains enough votes, it becomes notarized. Whenever a node observes a notarized chain with several blocks of consecutive epochs at the end, then the entire chain chopping off a few blocks at the end is final. By varying the parameters highlighted in blue, we illustrate two variants for the partially synchronous and synchronous settings respectively. We present very simple proofs of consistency and liveness. We hope that this tutorial provides a compelling argument why this new family of protocols should be used in lieu of classical candidates (e.g., PBFT, Paxos, and their variants), both in practical implementation and for pedagogical purposes.

2019

JOFC

Oblivious Network RAM and Leveraging Parallelism to Achieve Obliviousness
Abstract

Oblivious RAM (ORAM) is a cryptographic primitive that allows a trusted CPU to securely access untrusted memory, such that the access patterns reveal nothing about sensitive data. ORAM is known to have broad applications in secure processor design and secure multiparty computation for big data. Unfortunately, due to a logarithmic lower bound by Goldreich and Ostrovsky (J ACM 43(3):431–473, 1996 ), ORAM is bound to incur a moderate cost in practice. In particular, with the latest developments in ORAM constructions, we are quickly approaching this limit, and the room for performance improvement is small. In this paper, we consider new models of computation in which the cost of obliviousness can be fundamentally reduced in comparison with the standard ORAM model. We propose the oblivious network RAM model of computation, where a CPU communicates with multiple memory banks, such that the adversary observes only which bank the CPU is communicating with, but not the address offset within each memory bank. In other words, obliviousness within each bank comes for free—either because the architecture prevents a malicious party from observing the address accessed within a bank, or because another solution is used to obfuscate memory accesses within each bank—and hence we only need to obfuscate communication patterns between the CPU and the memory banks. We present new constructions for obliviously simulating general or parallel programs in the network RAM model. We describe applications of our new model in distributed storage applications with a network adversary.

2018

TCC

Game Theoretic Notions of Fairness in Multi-party Coin Toss
Abstract

Coin toss has been extensively studied in the cryptography literature, and the well-accepted notion of fairness (henceforth called strong fairness) requires that a corrupt coalition cannot cause non-negligible bias. It is well-understood that two-party coin toss is impossible if one of the parties can prematurely abort; further, this impossibility generalizes to multiple parties with a corrupt majority (even if the adversary is computationally bounded and fail-stop only).Interestingly, the original proposal of (two-party) coin toss protocols by Blum in fact considered a weaker notion of fairness: imagine that the (randomized) transcript of the coin toss protocol defines a winner among the two parties. Now Blum’s notion requires that a corrupt party cannot bias the outcome in its favor (but self-sacrificing bias is allowed). Blum showed that this weak notion is indeed attainable for two parties assuming the existence of one-way functions.In this paper, we ask a very natural question which, surprisingly, has been overlooked by the cryptography literature: can we achieve Blum’s weak fairness notion in multi-party coin toss? What is particularly interesting is whether this relaxation allows us to circumvent the corrupt majority impossibility that pertains to strong fairness. Even more surprisingly, in answering this question, we realize that it is not even understood how to define weak fairness for multi-party coin toss. We propose several natural notions drawing inspirations from game theory, all of which equate to Blum’s notion for the special case of two parties. We show, however, that for multiple parties, these notions vary in strength and lead to different feasibility and infeasibility results.

2018

TCC

Perfectly Secure Oblivious Parallel RAM
Abstract

We show that PRAMs can be obliviously simulated with perfect security, incurring only $$O(\log N \log \log N)$$ blowup in parallel runtime, $$O(\log ^3 N)$$ blowup in total work, and O(1) blowup in space relative to the original PRAM. Our results advance the theoretical understanding of Oblivious (Parallel) RAM in several respects. First, prior to our work, no perfectly secure Oblivious Parallel RAM (OPRAM) construction was known; and we are the first in this respect. Second, even for the sequential special case of our algorithm (i.e., perfectly secure ORAM), we not only achieve logarithmic improvement in terms of space consumption relative to the state-of-the-art, but also significantly simplify perfectly secure ORAM constructions. Third, our perfectly secure OPRAM scheme matches the parallel runtime of earlier statistically secure schemes with negligible failure probability. Since we remove the dependence (in performance) on the security parameter, our perfectly secure OPRAM scheme in fact asymptotically outperforms known statistically secure ones if (sub-)exponentially small failure probability is desired. Our techniques for achieving small parallel runtime are novel and we employ special expander graphs to derandomize earlier statistically secure OPRAM techniques—this is the first time such techniques are used in the constructions of ORAMs/OPRAMs.

2018

ASIACRYPT

More is Less: Perfectly Secure Oblivious Algorithms in the Multi-server Setting
Abstract

The problem of Oblivious RAM (ORAM) has traditionally been studied in the single-server setting, but more recently the multi-server setting has also been considered. Yet it is still unclear whether the multi-server setting has any inherent advantages, e.g., whether the multi-server setting can be used to achieve stronger security goals or provably better efficiency than is possible in the single-server case.In this work, we construct a perfectly secure 3-server ORAM scheme that outperforms the best known single-server scheme by a logarithmic factor. In the process we also show, for the first time, that there exist specific algorithms for which multiple servers can overcome known lower bounds in the single-server setting.

2017

ASIACRYPT

2012

PKC

#### Program Committees

- Eurocrypt 2017
- TCC 2017
- Crypto 2014

#### Coauthors

- Prabhanjan Ananth (1)
- Daniel Apon (1)
- Waqar Aqeel (1)
- Gilad Asharov (4)
- T-H. Hubert Chan (1)
- T.-H. Hubert Chan (9)
- Balakrishnan Chandrasekaran (1)
- Kai-Min Chung (3)
- Dana Dachman-Soled (4)
- Srini Devadas (1)
- Srinivas Devadas (2)
- Xiong Fan (1)
- Rex Fernando (1)
- Christopher W. Fletcher (1)
- Shafi Goldwasser (1)
- S. Dov Gordon (3)
- Vipul Goyal (1)
- Yue Guo (3)
- Abhishek Jain (1)
- Jonathan Katz (4)
- Ilan Komargodski (3)
- Mingfei Li (1)
- Wei-Kai Lin (4)
- Feng-Hao Liu (5)
- Yanyi Liu (1)
- Chang Liu (2)
- Bruce Maggs (1)
- Andrew Morgan (1)
- Kartik Nayak (4)
- Charalampos Papamanthou (4)
- Rafael Pass (9)
- Enoch Peserico (1)
- Antigoni Polychroniadou (1)
- Ling Ren (2)
- Amit Sahai (1)
- Emily Shen (1)
- Dawn Song (1)
- Emil Stefanov (2)
- Roberto Tamassia (2)
- Aishwarya Thiruvengadam (1)
- Florian Tramèr (1)
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