110 results sorted by ID
Coral: Maliciously Secure Computation Framework for Packed and Mixed Circuits
Zhicong Huang, Wen-jie Lu, Yuchen Wang, Cheng Hong, Tao Wei, WenGuang Chen
Cryptographic protocols
Achieving malicious security with high efficiency in dishonest-majority secure multiparty computation is a formidable challenge. The milestone works SPDZ and TinyOT have spawn a large family of protocols in this direction. For boolean circuits, state-of-the-art works (Cascudo et. al, TCC 2020 and Escudero et. al, CRYPTO 2022) have proposed schemes based on reverse multiplication-friendly embedding (RMFE) to reduce the amortized cost. However, these protocols are theoretically described and...
Efficient Zero-Knowledge Arguments for Paillier Cryptosystem
Borui GONG, Wang Fat Lau, Man Ho Au, Rupeng Yang, Haiyang Xue, Lichun Li
Cryptographic protocols
We present an efficient zero-knowledge argument of knowledge system customized for the Paillier cryptosystem. Our system enjoys sublinear proof size, low verification cost, and acceptable proof generation effort, while also supporting batch proof generation/verification. Existing works specialized for Paillier cryptosystem feature linear proof size and verification time. Using existing sublinear argument systems for generic statements (e.g., zk-SNARK) results in unaffordable proof generation...
Batching-Efficient RAM using Updatable Lookup Arguments
Moumita Dutta, Chaya Ganesh, Sikhar Patranabis, Shubh Prakash, Nitin Singh
Cryptographic protocols
RAM (random access memory) is an important primitive in verifiable computation. In this paper, we focus on realizing RAM with efficient batching property, i.e, proving a batch of $m$ updates on a RAM of size $N$ while incurring a cost that is sublinear in $N$. Classical approaches based on Merkle-trees or address ordered transcripts to model RAM correctness are either concretely inefficient, or incur linear overhead in the size of the RAM. Recent works explore cryptographic accumulators...
On amortization techniques for FRI-based SNARKs
Albert Garreta, Hayk Hovhanissyan, Aram Jivanyan, Ignacio Manzur, Isaac Villalobos, Michał Zając
Cryptographic protocols
We present two techniques to improve the computational and/or communication costs of STARK proofs: packing and modular split-and-pack.
Packing allows to generate a single proof of the satisfiability of several constraints. We achieve this by packing the evaluations of all relevant polynomials in the same Merkle leaves, and combining all DEEP FRI functions into a single randomized validity function. Our benchmarks show that packing reduces the verification time and proof size compared...
BPDTE: Batch Private Decision Tree Evaluation via Amortized Efficient Private Comparison
Huiqiang Liang, Haining Lu, Geng Wang
Applications
Machine learning as a service requires the client to trust the server and provide its own private information to use this service. Usually, clients may worry that their private data is being collected by server without effective supervision, and the server also aims to ensure proper management of the user data to foster the advancement of its services. In this work, we focus on private decision tree evaluation (PDTE) which can alleviates such privacy concerns associated with classification...
Efficient Linkable Ring Signatures: New Framework and Post-Quantum Instantiations
Yuxi Xue, Xingye Lu, Man Ho Au, Chengru Zhang
Public-key cryptography
In this paper, we introduce a new framework for constructing linkable ring signatures (LRS). Our framework is based purely on signatures of knowledge (SoK) which allows one to issue signatures on behalf of any NP-statement using the corresponding witness. Our framework enjoys the following advantages: (1) the security of the resulting LRS depends only on the security of the underlying SoK; (2) the resulting LRS naturally supports online/offline signing (resp. verification), where the output...
Perfectly-Secure Multiparty Computation with Linear Communication Complexity over Any Modulus
Daniel Escudero, Yifan Song, Wenhao Wang
Cryptographic protocols
Consider the task of secure multiparty computation (MPC) among $n$ parties with perfect security and guaranteed output delivery, supporting $t<n/3$ active corruptions. Suppose the arithmetic circuit $C$ to be computed is defined over a finite ring $\mathbb{Z}/q\mathbb{Z}$, for an arbitrary $q\in\mathbb{Z}$. It is known that this type of MPC over such ring is possible, with communication that scales as $O(n|C|)$, assuming that $q$ scales as $\Omega(n)$. However, for constant-size rings...
Haven++: Batched and Packed Dual-Threshold Asynchronous Complete Secret Sharing with Applications
Nicolas Alhaddad, Mayank Varia, Ziling Yang
Cryptographic protocols
Asynchronous complete secret sharing (ACSS) is a foundational primitive in the design of distributed algorithms and cryptosystems that require secrecy. Dual-threshold ACSS permits a dealer to distribute a secret to a collection of $n$ servers so that everyone holds shares of a polynomial containing the dealer's secret.
This work contributes a new ACSS protocol, called Haven++, that uses packing and batching to make asymptotic and concrete advances in the design and application of ACSS for...
HARTS: High-Threshold, Adaptively Secure, and Robust Threshold Schnorr Signatures
Renas Bacho, Julian Loss, Gilad Stern, Benedikt Wagner
Cryptographic protocols
Threshold variants of the Schnorr signature scheme have recently been at the center of attention due to their applications to Bitcoin, Ethereum, and other cryptocurrencies. However, existing constructions for threshold Schnorr signatures among a set of $n$ parties with corruption threshold $t_c$ suffer from at least one of the following drawbacks: (i) security only against static (i.e., non-adaptive) adversaries, (ii) cubic or higher communication cost to generate a single signature, (iii)...
Secure Transformer Inference Made Non-interactive
Jiawen Zhang, Jian Liu, Lipeng He, Xinpeng Yang, Wen-jie Lu, Yinghao Wang, Kejia Chen, Xiaoyang Hou, Kui Ren, Xiaohu Yang
Cryptographic protocols
Secure transformer inference has emerged as a prominent research topic following the proliferation of ChatGPT. Existing solutions are typically interactive, involving substantial communication load and numerous interaction rounds between the client and the server.
In this paper, we propose NEXUS, the first non-interactive protocol for secure transformer inference, using which the client is only required to perform one round of communication with the server throughout the evaluation...
Memory adds no cost to lattice sieving for computers in 3 or more spatial dimensions
Samuel Jaques
Attacks and cryptanalysis
The security of lattice-based crytography (LWE, NTRU, and FHE) depends on the hardness of the shortest-vector problem (SVP). Sieving algorithms give the lowest asymptotic runtime to solve SVP, but depend on exponential memory. Memory access costs much more in reality than in the RAM model, so we consider a computational model where processors, memory, and meters of wire are in constant proportions to each other. While this adds substantial costs to route data during lattice sieving, we...
Unconditionally secure MPC for Boolean circuits with constant online communication
Zhenkai Hu, Kang Yang, Yu Yu
Cryptographic protocols
Through tremendous efforts, the communication cost of secure multi-party computation (MPC) in the honest-majority setting has been significantly improved.
In particular, the state-of-the-art honest-majority MPC protocol by Escudero et al. (CCS'22) takes 12 field elements in total per multiplication gate for arithmetic circuits in the online phase. However, it still requires $12 \log(5n/4)$ bits of online communication per AND gate for Boolean circuits. That is, for Boolean circuits, no...
Efficient Pre-processing PIR Without Public-Key Cryptography
Ashrujit Ghoshal, Mingxun Zhou, Elaine Shi
Cryptographic protocols
Classically, Private Information Retrieval (PIR) was studied in a setting without any pre-processing. In this setting, it is well-known that 1) public-key cryptography is necessary to achieve
non-trivial (i.e., sublinear) communication efficiency in the single-server setting, and 2) the total server computation
per query must be linear in the size of the database, no matter in the single-server or multi-server setting. Recent works have shown that both of these barriers can be overcome...
Pay Less for Your Privacy: Towards Cost-Effective On-Chain Mixers
Zhipeng Wang, Marko Cirkovic, Duc V. Le, William Knottenbelt, Christian Cachin
Applications
On-chain mixers, such as Tornado Cash (TC), have become a popular privacy solution for many non-privacy-preserving blockchain users. These mixers enable users to deposit a fixed amount of coins and withdraw them to another address, while effectively reducing the linkability between these addresses and securely obscuring their transaction history. However, the high cost of interacting with existing on-chain mixer smart contracts prohibits standard users from using the mixer, mainly due to the...
Securing Lattice-Based KEMs with Code-Based Masking: A Theoretical Approach
Pierre-Augustin Berthet, Yoan Rougeolle, Cédric Tavernier, Jean-Luc Danger, Laurent Sauvage
The recent technological advances in Post-Quantum Cryptography (PQC) raise the questions of robust implementations of new asymmetric cryptographic primitives in today’s technology. This is the case for the lattice-based Module Lattice-Key Encapsulation Mechanism (ML-KEM) algorithm which is proposed by the NIST as the first standard for Key Encapsulation Mechanism (KEM), taking inspiration from CRYSTALS-Kyber. We have notably to make sure the ML-KEM implementation is resilient against...
Fast batched asynchronous distributed key generation
Jens Groth, Victor Shoup
Cryptographic protocols
We present new protocols for threshold Schnorr signatures that work in an asynchronous communication setting, providing robustness and optimal resilience. These protocols provide unprecedented performance in terms of communication and computational complexity. In terms of communication complexity, for each signature, a single party must transmit a few dozen group elements and scalars across the network (independent of the size of the signing committee). In terms of computational...
Amortized Functional Bootstrapping in less than 7ms, with $\tilde{O}(1)$ polynomial multiplications
Zeyu Liu, Yunhao Wang
Cryptographic protocols
Amortized bootstrapping offers a way to refresh multiple ciphertexts of a fully homomorphic encryption scheme in parallel more efficiently than refreshing a single ciphertext at a time. Micciancio and Sorrell (ICALP 2018) first proposed the technique to bootstrap $n$ LWE ciphertexts simultaneously, reducing the total cost from $\tilde{O}(n^2)$ to $\tilde{O}(3^\epsilon n^{1+\frac{1}{\epsilon}})$ for arbitrary $\epsilon > 0$. Several recent works have further improved the asymptotic cost....
Efficient 3PC for Binary Circuits with Application to Maliciously-Secure DNN Inference
Yun Li, Yufei Duan, Zhicong Huang, Cheng Hong, Chao Zhang, Yifan Song
Cryptographic protocols
In this work, we focus on maliciously secure 3PC for binary circuits with honest majority. While the state-of-the-art (Boyle et al. CCS 2019) has already achieved the same amortized communication as the best-known semi-honest protocol (Araki et al. CCS 2016), they suffer from a large computation overhead: when comparing with the best-known implementation result (Furukawa et al. Eurocrypt 2017) which requires $9\times$ communication cost of Araki et al., the protocol by Boyle et al. is around...
High-Throughput Deep Convolutional Neural Networks on Fully Homomorphic Encryption Using Channel-By-Channel Packing
Jung Hee Cheon, Minsik Kang, Taeseong Kim, Junyoung Jung, Yongdong Yeo
Applications
Secure Machine Learning as a Service is a viable solution where clients seek secure delegation of the ML computation while protecting their sensitive data. We propose an efficient method to securely evaluate deep standard convolutional neural networks based on CKKS fully homomorphic encryption, in the manner of batch inference. In this paper, we introduce a packing method called Channel-by-Channel Packing that maximizes the slot compactness and single-instruction-multipledata capabilities in...
Detect, Pack and Batch: Perfectly-Secure MPC with Linear Communication and Constant Expected Time
Ittai Abraham, Gilad Asharov, Shravani Patil, Arpita Patra
Cryptographic protocols
We prove that perfectly-secure optimally-resilient secure Multi-Party Computation (MPC) for a circuit with $C$ gates and depth $D$ can be obtained in $O((Cn+n^4 + Dn^2)\log n)$ communication complexity and $O(D)$ expected time. For $D \ll n$ and $C\geq n^3$, this is the first perfectly-secure optimal-resilient MPC protocol with linear communication complexity per gate and constant expected time complexity per layer.
Compared to state-of-the-art MPC protocols in the player elimination...
Group Oblivious Message Retrieval
Zeyu Liu, Eran Tromer, Yunhao Wang
Cryptographic protocols
Anonymous message delivery, as in private communication and privacy-preserving blockchain applications, ought to protect recipient metadata: a message should not be inadvertently linkable to its destination. But how can messages then be delivered to each recipient, without each recipient scanning all messages? Recent work constructed Oblivious Message Retrieval (OMR) protocols that outsource this job to untrusted servers in a privacy-preserving manner.
We consider the case of group...
Quasi-linear masking to protect against both SCA and FIA
Claude Carlet, Abderrahman Daif, Sylvain Guilley, Cédric Tavernier
Applications
The implementation of cryptographic algorithms must be protected against physical attacks. Side-channel and fault injection analyses are two prominent such implem\-entation-level attacks. Protections against either do exist; they are characterized by security orders: the higher the order, the more difficult the attack.
In this paper, we leverage fast discrete Fourier transform to reduce the complexity of high-order masking, and extend it to allow for fault detection and/or correction. The...
Panacea: Non-interactive and Stateless Oblivious RAM
Kelong Cong, Debajyoti Das, Georgio Nicolas, Jeongeun Park
Cryptographic protocols
Oblivious RAM (ORAM) allows a client to outsource storage to a
remote server while hiding the data access pattern from the server. Many ORAM designs have been proposed to reduce the computational overhead and bandwidth blowup for the client. A recent work, Onion Ring ORAM (CCS'19), is able to achieve $O(1)$ bandwidth blowup in the online phase using fully homomorphic encryption (FHE) techniques, at the cost of a computationally expensive client-side offline phase. Furthermore, such a scheme...
Actively Secure Arithmetic Computation and VOLE with Constant Computational Overhead
Benny Applebaum, Niv Konstantini
Foundations
We study the complexity of two-party secure arithmetic computation where the goal is to evaluate an arithmetic circuit over a finite field $F$ in the presence of an active (aka malicious) adversary. In the passive setting, Applebaum et al. (Crypto 2017) constructed a protocol that only makes a *constant* (amortized) number of field operations per gate. This protocol uses the underlying field $F$ as a black box, makes black-box use of (standard) oblivious transfer, and its security is based...
Faster Amortized FHEW bootstrapping using Ring Automorphisms
Gabrielle De Micheli, Duhyeong Kim, Daniele Micciancio, Adam Suhl
Public-key cryptography
Amortized bootstrapping offers a way to simultaneously refresh many ciphertexts of a fully homomorphic encryption scheme, at a total cost comparable to that of refreshing a single ciphertext. An amortization method for FHEW-style cryptosystems was first proposed by (Micciancio and Sorrell, ICALP 2018), who showed that the amortized cost of bootstrapping n FHEW-style ciphertexts can be reduced from $O(n)$ basic cryptographic operations to just $O(n^{\epsilon})$, for any constant...
On the Amortized Communication Complexity of Byzantine Broadcast
Atsuki Momose, Ling Ren, Elaine Shi, Jun Wan, Zhuolun Xiang
Applications
Designing an efficient solution for Byzantine broadcast is an important problem for many distributed computing and cryptographic tasks. There have been many attempts to achieve sub-quadratic communication complexity in several directions, both in theory and practice, all with pros and cons. This paper initiates the study of another attempt: improving the amortized communication complexity of multi-shot Byzantine broadcast. Namely, we try to improve the average cost when we have sequential...
Amortized Bootstrapping Revisited: Simpler, Asymptotically-faster, Implemented
Antonio Guimarães, Hilder V. L. Pereira, Barry van Leeuwen
Public-key cryptography
Micciancio and Sorrel (ICALP 2018) proposed a bootstrapping algorithm that can refresh many messages at once with sublinearly many homomorphic operations per message. However, despite the attractive asymptotic cost, it is unclear if their algorithm could ever be practical, which reduces the impact of their results. In this work, we follow their general framework, but propose an amortized bootstrapping that is conceptually simpler and asymptotically cheaper. We reduce the number of...
Fully Succinct Batch Arguments for NP from Indistinguishability Obfuscation
Rachit Garg, Kristin Sheridan, Brent Waters, David J. Wu
Cryptographic protocols
Non-interactive batch arguments for $\mathsf{NP}$ provide a way to amortize the cost of $\mathsf{NP}$ verification across multiple instances. In particular, they allow a prover to convince a verifier of multiple $\mathsf{NP}$ statements with communication that scales sublinearly in the number of instances.
In this work, we study fully succinct batch arguments for $\mathsf{NP}$ in the common reference string (CRS) model where the length of the proof scales not only sublinearly in the...
Private Access Control for Function Secret Sharing
Sacha Servan-Schreiber, Simon Beyzerov, Eli Yablon, Hyojae Park
Cryptographic protocols
Function Secret Sharing (FSS; Eurocrypt 2015) allows a dealer to share a function f with two or more evaluators. Given secret shares of a function f, the evaluators can locally compute secret shares of f(x) on an input x, without learning information about f.
In this paper, we initiate the study of access control for FSS. Given the shares of f, the evaluators can ensure that the dealer is authorized to share the provided function. For a function family F and an access control list defined...
The Parallel Reversible Pebbling Game: Analyzing the Post-Quantum Security of iMHFs
Jeremiah Blocki, Blake Holman, Seunghoon Lee
Attacks and cryptanalysis
The classical (parallel) black pebbling game is a useful abstraction which allows us to analyze the resources (space, space-time, cumulative space) necessary to evaluate a function $f$ with a static data-dependency graph $G$. Of particular interest in the field of cryptography are data-independent memory-hard functions $f_{G,H}$ which are defined by a directed acyclic graph (DAG) $G$ and a cryptographic hash function $H$. The pebbling complexity of the graph $G$ characterizes the amortized...
Threshold Linear Secret Sharing to the Rescue of MPC-in-the-Head
Thibauld Feneuil, Matthieu Rivain
Cryptographic protocols
The MPC-in-the-Head paradigm is a popular framework to build zero-knowledge proof systems using techniques from secure multi-party computation (MPC). While this paradigm is not restricted to a particular secret sharing scheme, all the efficient instantiations for small circuits proposed so far rely on additive secret sharing.
In this work, we show how applying a threshold linear secret sharing scheme (threshold LSSS) can be beneficial to the MPC-in-the-Head paradigm. For a general...
Vectorized Batch Private Information Retrieval
Muhammad Haris Mughees, Ling Ren
Cryptographic protocols
This paper studies Batch Private Information Retrieval (BatchPIR), a variant of private information retrieval (PIR) where the client wants to retrieve multiple entries from the server in one batch.
BatchPIR matches the use case of many practical applications and holds the potential for substantial efficiency improvements over PIR in terms of amortized cost per query.
Existing BatchPIR schemes have achieved decent computation efficiency but have not been able to improve communication...
Sustained Space and Cumulative Complexity Trade-offs for Data-Dependent Memory-Hard Functions
Jeremiah Blocki, Blake Holman
Foundations
Memory-hard functions (MHFs) are a useful cryptographic primitive which can be used to design egalitarian proof of work puzzles and to protect low entropy secrets like passwords against brute-force attackers. Intuitively, a memory-hard function is a function whose evaluation costs are dominated by memory costs even if the attacker uses specialized hardware (FPGAs/ASICs), and several cost metrics have been proposed to quantify this intuition. For example, space-time cost looks at the product...
More Efficient Dishonest Majority Secure Computation over $\mathbb{Z}_{2^k}$ via Galois Rings
Daniel Escudero, Chaoping Xing, Chen Yuan
Cryptographic protocols
In this work we present a novel actively secure multiparty computation protocol in the dishonest majority setting, where the computation domain is a ring of the type $\mathbb{Z}_{2^k}$. Instead of considering an "extension ring" of the form $\mathbb{Z}_{2^{k+\kappa}}$ as in SPD$\mathbb{Z}_{2^k}$ (Cramer et al, CRYPTO 2018) and its derivatives, we make use of an actual ring extension, or more precisely, a Galois ring extension $\mathbb{Z}_{p^k}[\mathtt{X}]/(h(\mathtt{X}))$ of large enough...
Linear Communication in Malicious Majority MPC
S. Dov Gordon, Phi Hung Le, Daniel McVicker
Cryptographic protocols
The SPDZ multiparty computation protocol allows $n$ parties to securely compute arithmetic circuits over a finite field, while tolerating up to $n − 1$ active corruptions. A line of work building upon SPDZ have made considerable improvements to the protocol’s performance, typically focusing on concrete efficiency. However, the communication complexity of each of these protocols is $\Omega(n^2 |C|)$.
In this paper, we present a protocol that achieves $O(n|C|)$ communication. Our...
Fast Fully Secure Multi-Party Computation over Any Ring with Two-Thirds Honest Majority
Anders Dalskov, Daniel Escudero, Ariel Nof
Cryptographic protocols
We introduce a new MPC protocol to securely compute any functionality over an arbitrary black-box finite ring (which may not be commutative), tolerating $t<n/3$ active corruptions while \textit{guaranteeing output delivery} (G.O.D.).
Our protocol is based on replicated secret-sharing, whose share size is known to grow exponentially with the number of parties $n$.
However, even though the internal storage and computation in our protocol remains exponential, the communication complexity of our...
PQ-HPKE: Post-Quantum Hybrid Public Key Encryption
Mila Anastasova, Panos Kampanakis, Jake Massimo
Public-key cryptography
Public key cryptography is used to asymmetrically establish keys, authenticate or encrypt data between communicating parties at a relatively high performance cost. To reduce computational overhead, modern network protocols combine asymmetric primitives for key establishment and authentication with symmetric ones. Similarly, Hybrid Public Key Encryption, a relatively new scheme, uses public key cryptography for key derivation and symmetric key cryptography for data encryption. In this paper,...
Batch Arguments for NP and More from Standard Bilinear Group Assumptions
Brent Waters, David J. Wu
Cryptographic protocols
Non-interactive batch arguments for NP provide a way to amortize the cost of NP verification across multiple instances. They enable a prover to convince a verifier of multiple NP statements with communication much smaller than the total witness length and verification time much smaller than individually checking each instance.
In this work, we give the first construction of a non-interactive batch argument for NP from standard assumptions on groups with bilinear maps (specifically, from...
Efficient Proof of RAM Programs from Any Public-Coin Zero-Knowledge System
Cyprien Delpech de Saint Guilhem, Emmanuela Orsini, Titouan Tanguy, Michiel Verbauwhede
Public-key cryptography
We show a compiler that allows to prove the correct execution of RAM programs using any zero-knowledge system for circuit satisfiability. At the core of this work is an arithmetic circuit which verifies the consistency of a list of memory access tuples in zero-knowledge.
Using such a circuit, we obtain the first constant-round and concretely efficient zero-knowledge proof protocol for RAM programs using any stateless zero-knowledge proof system for Boolean or arithmetic circuits. Both the...
NanoGRAM: Garbled RAM with $\widetilde{O}(\log N)$ Overhead
Andrew Park, Wei-Kai Lin, Elaine Shi
Cryptographic protocols
We propose a new garbled RAM construction called NanoGRAM, which achieves an amortized cost of $\widetilde{O}(\lambda \cdot (W \log N + \log^3 N))$ bits per memory access, where $\lambda$ is the security parameter, $W$ is the block size, and $N$ is the total number of blocks, and $\widetilde{O}(\cdot)$ hides $poly\log\log$ factors. For sufficiently large blocks where $W = \Omega(\log^2 N)$, our scheme achieves $\widetilde{O}(\lambda \cdot W \log N)$ cost per memory access, where the...
Single-Server Private Information Retrieval with Sublinear Amortized Time
Henry Corrigan-Gibbs, Alexandra Henzinger, Dmitry Kogan
Cryptographic protocols
We construct new private-information-retrieval protocols in the single-server setting. Our schemes allow a client to privately fetch a sequence of database records from a server, while the server answers each query in average time sublinear in the database size. Specifically, we introduce the first single-server private-information-retrieval schemes that have sublinear amortized server time, require sublinear additional storage, and allow the client to make her queries adaptively. Our...
Verifiable Decryption for BGV
Tjerand Silde
Cryptographic protocols
In this work we present a direct construction for verifiable decryption for the BGV encryption scheme by combining existing zero-knowledge proofs for linear relations and bounded values. This is one of the first constructions of verifiable decryption protocols for lattice-based cryptography, and we give a protocol that is simpler and at least as efficient as the state of the art when amortizing over many ciphertexts.
To prove its practicality we provide concrete parameters, resulting in...
On the Download Rate of Homomorphic Secret Sharing
Ingerid Fosli, Yuval Ishai, Victor I. Kolobov, Mary Wootters
Cryptographic protocols
A homomorphic secret sharing (HSS) scheme is a secret sharing scheme that supports evaluating functions on shared secrets by means of a local mapping from input shares to output shares. We initiate the study of the download rate of HSS, namely, the achievable ratio between the length of the output shares and the output length when amortized over $\ell$ function evaluations. We obtain the following results.
* In the case of linear information-theoretic HSS schemes for degree-$d$...
Amortizing Rate-1 OT and Applications to PIR and PSI
Melissa Chase, Sanjam Garg, Mohammad Hajiabadi, Jialin Li, Peihan Miao
Cryptographic protocols
Recent new constructions of rate-1 OT [Döttling, Garg, Ishai, Malavolta, Mour, and Ostrovsky, CRYPTO 2019] have brought this primitive under the spotlight and the techniques have led to new feasibility results for private-information retrieval, and homomorphic encryption for branching programs. The receiver communication of this construction consists of a quadratic (in the sender's input size) number of group elements for a single instance of rate-1 OT. Recently [Garg, Hajiabadi, Ostrovsky,...
Practical Garbled RAM: GRAM with $O(\log^2 n)$ Overhead
David Heath, Vladimir Kolesnikov, Rafail Ostrovsky
Cryptographic protocols
Garbled RAM (GRAM) is a powerful technique introduced by Lu and Ostrovsky that equips Garbled Circuit (GC) with a sublinear cost RAM without adding rounds of interaction. While multiple GRAM constructions are known, none are suitable for practice, due to costs that have high constants and poor scaling.
We present the first GRAM suitable for practice. For computational security parameter $\kappa$ and for a size-$n$ RAM that stores blocks of size $w = \Omega(\log^2 n)$ bits, our GRAM incurs...
Stateful KEM: Towards Optimal Robust Combiner for Key Encapsulation Mechanism
Jia Xu, Yiwen Gao, Hoon Wei Lim, Hongbing Wang, Ee-Chien Chang
Public-key cryptography
A $(1,n)$-robust combiner combines $n$ cryptography primitives to construct a new primitive of the same type, and guarantees that if any of the ingredient primitive is secure, then the resulting primitive is secure. In recent two decades, robust combiners for various crypto primitives (e.g. public key encryption, oblivious transfer) have been proposed. Very recently, more works on robust combiners for post-quantum key encapsulation mechanism appear to achieve multi-layer of defence, to...
Legendre PRF (Multiple) Key Attacks and the Power of Preprocessing
Alexander May, Floyd Zweydinger
Public-key cryptography
Due to its amazing speed and multiplicative properties the Legendre PRF recently finds widespread applications e.g. in Ethereum 2.0, multiparty computation and in the quantum-secure signature proposal LegRoast. However, its security is not yet extensively studied.
The Legendre PRF computes for a key $k$ on input $x$ the Legendre symbol $L_k(x) = \left( \frac {x+k} {p} \right)$ in some finite field $\F_p$. As standard notion, PRF security is analysed by giving an attacker oracle access to...
Over 100x Faster Bootstrapping in Fully Homomorphic Encryption through Memory-centric Optimization with GPUs
Wonkyung Jung, Sangpyo Kim, Jung Ho Ahn, Jung Hee Cheon, Younho Lee
Implementation
Fully Homomorphic encryption (FHE) has been gaining popularity as an emerging way of enabling an unlimited number of operations on the encrypted message without decryption. A major drawback of FHE is its high computational cost. Especially, a bootstrapping that refreshes the noise accumulated through consequent FHE operations on the ciphertext is even taking minutes. This significantly limits the practical use of FHE in numerous real applications.
By exploiting massive parallelism available...
HashSplit: Exploiting Bitcoin Asynchrony to Violate Common Prefix and Chain Quality
Muhammad Saad, Afsah Anwar, Srivatsan Ravi, David Mohaisen
Applications
The safety of the Bitcoin blockchain relies on strong network synchrony. Therefore, violating the blockchain safety requires strong adversaries who control a mining pool with 51% hash rate. In this paper, we show that the network synchrony does not hold in the real world Bitcoin network, which can be exploited to amortize the cost of various attacks. Towards that, first we construct the Bitcoin ideal world functionality to formally specify its ideal execution model in a synchronous network....
SPURT: Scalable Distributed Randomness Beacon with Transparent Setup
Sourav Das, Vinith Krishnan, Irene Miriam Isaac, Ling Ren
Cryptographic protocols
Having shared access to high-quality random numbers is essential in many important applications. Yet, existing constructions of distributed random beacons still have limitations such as imperfect security guarantees, strong setup or network assumptions, or high costs. In this paper, we present SPURT, an efficient distributed randomness beacon protocol that does not require any trusted or expensive setup and is secure against a malicious adversary that controls up to one-third of the nodes in...
An Incentive-Compatible Smart Contract for Decentralized Commerce
Nikolaj I. Schwartzbach
Applications
We propose a smart contract that allows two mutually distrusting parties to transact any non-digital good or service on a blockchain. The contract acts as an escrow and settles disputes by letting parties wager that they can convince an arbiter they were the honest party. We analyze the contract as an extensive-form game and prove that the contract is secure in a strong game-theoretic sense if and only if the arbiter is biased in favor of honest parties. We show this is inherent to any...
Banquet: Short and Fast Signatures from AES
Carsten Baum, Cyprien Delpech de Saint Guilhem, Daniel Kales, Emmanuela Orsini, Peter Scholl, Greg Zaverucha
Public-key cryptography
In this work we introduce Banquet, a digital signature scheme with post-quantum security, constructed using only symmetric-key primitives. The design is based on the MPC-in-head paradigm also used by Picnic (CCS 2017) and BBQ (SAC 2019).
Like BBQ, Banquet uses only standardized primitives, namely AES and SHA-3, but signatures are more than 50% shorter, making them competitive with Picnic (which uses a non-standard block cipher to improve performance).
The MPC protocol in Banquet uses a new...
Puncturable Pseudorandom Sets and Private Information Retrieval with Near-Optimal Online Bandwidth and Time
Elaine Shi, Waqar Aqeel, Balakrishnan Chandrasekaran, Bruce Maggs
Cryptographic protocols
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...
MOTIF: (Almost) Free Branching in GMW via Vector-Scalar Multiplication
David Heath, Vladimir Kolesnikov, Stanislav Peceny
Cryptographic protocols
MPC functionalities are increasingly specified in high-level languages, where control-flow constructions such as conditional statements are extensively used. Today, concretely efficient MPC protocols are circuit-based and must evaluate all conditional branches at high cost to hide the taken branch.
The Goldreich-Micali-Wigderson, or GMW, protocol is a foundational circuit-based technique that realizes MPC for p players and is secure against up to p - 1 semi-honest corruptions. While GMW...
Packed Multiplication: How to Amortize the Cost of Side-channel Masking ?
Weijia Wang, Chun Guo, François-Xavier Standaert, Yu Yu, Gaëtan Cassiers
Implementation
Higher-order masking countermeasures provide strong provable security against side-channel attacks at the cost of incurring significant overheads, which largely hinders its applicability. Previous works towards remedying cost mostly concentrated on ``local'' calculations, i.e., optimizing the cost of computation units such as a single AND gate or a field multiplication. This paper explores a complementary ``global'' approach, i.e., considering multiple operations in the masked domain as a...
Circuit Amortization Friendly Encodings and their Application to Statistically Secure Multiparty Computation
Anders Dalskov, Eysa Lee, Eduardo Soria-Vazquez
Cryptographic protocols
At CRYPTO 2018, Cascudo et al. introduced Reverse Multiplication Friendly Embeddings (RMFEs). These are a mechanism to compute $\delta$ parallel evaluations of the same arithmetic circuit over a field $\mathbb{F}_q$ at the cost of a single evaluation of that circuit in $\mathbb{F}_{q^d}$, where $\delta < d$. Due to this inequality, RMFEs are a useful tool when protocols require to work over $\mathbb{F}_{q^d}$ but one is only interested in computing over $\mathbb{F}_q$. In this work we...
Private Join and Compute from PIR with Default
Tancrède Lepoint, Sarvar Patel, Mariana Raykova, Karn Seth, Ni Trieu
Cryptographic protocols
The private join and compute (PJC) functionality enables secure computation over data distributed across different databases, which is a functionality with a wide range of applications, many of which address settings where the input databases are of significantly different sizes.
We introduce the notion of private information retrieval (PIR) with default, which enables two-party PJC functionalities in a way that hides the size of the intersection of the two databases and incurs sublinear...
ALBATROSS: publicly AttestabLe BATched Randomness based On Secret Sharing
Ignacio Cascudo, Bernardo David
Cryptographic protocols
In this paper we present ALBATROSS, a family of multiparty randomness generation protocols with guaranteed output delivery and public verification that allows to trade off corruption tolerance for a much improved amortized computational complexity. Our basic stand alone protocol is based on publicly verifiable secret sharing (PVSS) and is secure under in the random oracle model under the decisional Diffie-Hellman (DDH) hardness assumption.
We also address the important issue of constructing...
Private Identity Agreement for Private Set Functionalities
Ben Kreuter, Sarvar Patel, Ben Terner
Applications
Private set intersection and related functionalities are among the most prominent real-world applications of secure multiparty computation. While such protocols have attracted significant attention from the research community, other functionalities are often required to support a PSI application in practice. For example, in order for two parties to run a PSI over the unique users contained in their databases, they might first invoke on a support functionality to agree on the primary keys to...
Practical MPC+FHE with Applications in Secure Multi-PartyNeural Network Evaluation
Ruiyu Zhu, Changchang Ding, Yan Huang
The theoretical idea of using FHE to realize MPC has been therefor over a decade. Existing threshold (and multi-key) FHE schemes were constructed by modifying and analyzing a traditional single-keyFHE in a case-by-case manner, thus technically highly-demanding.This work explores a new approach to build threshold FHE (therebyMPC schemes) through tailoring generic MPC protocols to the base FHE scheme while requiring no effort in FHE redesign. We applied our approach to two representative...
Diogenes: Lightweight Scalable RSA Modulus Generation with a Dishonest Majority
Megan Chen, Carmit Hazay, Yuval Ishai, Yuriy Kashnikov, Daniele Micciancio, Tarik Riviere, abhi shelat, Muthu Venkitasubramaniam, Ruihan Wang
Implementation
In this work, we design and implement the first protocol for RSA modulus construction that can support thousands of parties and offers security against an arbitrary number of corrupted parties.
In a nutshell, we design the ``best'' protocol for this scale that is secure against passive corruption, then amplify it to obtain active security using efficient non-interactive zero-knowledge arguments. Our protocol satisfies a stronger security guarantee where a deviating party can be identified...
A Secret-Sharing Based MPC Protocol for Boolean Circuits with Good Amortized Complexity
Ignacio Cascudo, Jaron Skovsted Gundersen
Cryptographic protocols
We present a new secure multiparty computation protocol in the preprocessing model that allows for the evaluation of a number of instances of a boolean circuit in parallel, with a small online communication complexity per instance of 10 bits per party and multiplication gate. Our protocol is secure against an active dishonest majority, and can be also transformed, via known techniques, into a protocol for the evaluation of a single “well-formed” boolean circuit with the same complexity per...
Breaking the $O(\sqrt n)$-Bit Barrier: Byzantine Agreement with Polylog Bits Per Party
Elette Boyle, Ran Cohen, Aarushi Goel
Cryptographic protocols
Byzantine agreement (BA), the task of $n$ parties to agree on one of their input bits in the face of malicious agents, is a powerful primitive that lies at the core of a vast range of distributed protocols. Interestingly, in protocols with the best overall communication, the demands of the parties are highly unbalanced: the amortized cost is $\tilde O(1)$ bits per party, but some parties must send $\Omega(n)$ bits. In best known balanced protocols, the overall communication is sub-optimal,...
Commodity-Based 2PC for Arithmetic Circuits
Ivan Damgård, Helene Haagh, Michael Nielsen, Claudio Orlandi
Cryptographic protocols
We revisit the framework of Commodity-based Cryptography presented by Beaver (STOC'97) with a focus on updating the framework to fit with modern multiparty computation (MPC) protocols. We study the possibility of replacing the well-known preprocessing model with a commodity-based setting, where a set of independent servers (some of which may be corrupt) provide clients with correlated randomness. From this, the clients then distill correct and secure correlated randomness that they can use...
Fully Homomorphic Encryption with k-bit Arithmetic Operations
Benjamin M. Case, Shuhong Gao, Gengran Hu, Qiuxia Xu
Public-key cryptography
We present a fully homomorphic encryption scheme continuing the line of works
of Ducas and Micciancio (2015, [DM15]), Chillotti et al. (2016, [CGGI16a]; 2017,
[CGGI17]; 2018, [CGGI18a]), and Gao (2018,[Gao18]). Ducas and Micciancio (2015)
show that homomorphic computation of one bit operation on LWE ciphers can be done
in less than a second, which is then reduced by Chillotti et al. (2016, 2017, 2018) to
13ms. According to Chillotti et al. (2018, [CGGI18b]), the cipher expansion for TFHE
is...
Efficient Private Comparison Queries over Encrypted Databases using Fully Homomorphic Encryption with Finite Fields
Benjamin Hong Meng Tan, Hyung Tae Lee, Huaxiong Wang, Shu Qin Ren, Khin Mi Mi Aung
Applications
To achieve security and privacy for data stored on the cloud, we need the ability to secure data in compute. Equality comparisons, ``$x=y, x\neq y$'', have been widely studied with many proposals but there is much room for improvement for order comparisons, ``$x < y,~x \leq y, x > y$ and $x \geq y$''. Most protocols for order comparisons have some limitation, either leaking some information about the data or requiring several rounds of communication between client and server. In addition,...
Compressing Vector OLE
Elette Boyle, Geoffroy Couteau, Niv Gilboa, Yuval Ishai
Cryptographic protocols
Oblivious linear-function evaluation (OLE) is a secure two-party protocol allowing a receiver to learn a secret linear combination of a pair of field elements held by a sender. OLE serves as a common building block for secure computation of arithmetic circuits, analogously to the role of oblivious transfer (OT) for boolean circuits.
A useful extension of OLE is vector OLE (VOLE), allowing the receiver to learn a linear combination of two vectors held by the sender. In several applications of...
Efficient Circuit-based PSI with Linear Communication
Benny Pinkas, Thomas Schneider, Oleksandr Tkachenko, Avishay Yanai
Cryptographic protocols
We present a new protocol for computing a circuit which implements the private set intersection functionality (PSI). Using circuits for this task is advantageous over the usage of specific protocols for PSI, since many applications of PSI do not need to compute the intersection itself but rather functions based on the items in the intersection.
Our protocol is the first circuit-based PSI protocol to achieve linear communication complexity. It is also concretely more efficient than all...
Zero-Knowledge Proofs on Secret-Shared Data via Fully Linear PCPs
Dan Boneh, Elette Boyle, Henry Corrigan-Gibbs, Niv Gilboa, Yuval Ishai
Foundations
We introduce and study the notion of fully linear probabilistically checkable proof systems. In such a proof system, the verifier can make a small number of linear queries that apply jointly to the input and a proof vector.
Our new type of proof system is motivated by applications in which the input statement is not fully available to any single verifier, but can still be efficiently accessed via linear queries. This situation arises in scenarios where the input is partitioned or...
Efficient UC Commitment Extension with Homomorphism for Free (and Applications)
Ignacio Cascudo, Ivan Damgård, Bernardo David, Nico Döttling, Rafael Dowsley, Irene Giacomelli
Cryptographic protocols
Homomorphic universally composable (UC) commitments allow for the sender to reveal the result of additions and multiplications of values contained in commitments without revealing the values themselves while assuring the receiver of the correctness of such computation on committed values.
In this work, we construct essentially optimal additively homomorphic UC commitments from any (not necessarily UC or homomorphic) extractable commitment. We obtain amortized linear computational complexity...
Data-Independent Memory Hard Functions: New Attacks and Stronger Constructions
Jeremiah Blocki, Ben Harsha, Siteng Kang, Seunghoon Lee, Lu Xing, Samson Zhou
Memory-hard functions (MHFs) are a key cryptographic primitive underlying the design of moderately expensive password hashing algorithms and egalitarian proofs of work. Over the past few years several increasingly stringent goals for an MHF have been proposed including the requirement that the MHF have high sequential space-time (ST) complexity, parallel space-time complexity, amortized area-time (aAT) complexity and sustained space complexity.
Data-Independent Memory Hard Functions (iMHFs)...
Homomorphic Evaluation of Lattice-Based Symmetric Encryption Schemes
Pierre-Alain Fouque, Benjamin Hadjibeyli, Paul Kirchner
Secret-key cryptography
Optimizing performance of Fully Homomorphic Encryption (FHE) is nowadays an active trend of research in cryptography. One way of improvement is to use a hybrid construction with a classical symmetric encryption scheme to transfer encrypted data to the Cloud. This allows to reduce the bandwidth since the expansion factor of symmetric schemes (the ratio between the ciphertext and the plaintext length) is close to one, whereas for FHE schemes it is in the order of 1,000 to 1,000,000. However,...
Ring packing and amortized FHEW bootstrapping
Daniele Micciancio, Jessica Sorrell
Public-key cryptography
The FHEW fully homomorphic encryption scheme (Ducas and Micciancio, Eurocrypt 2015) offers very fast homomorphic NAND-gate computations (on encrypted data) and a relatively fast refreshing procedure that allows to homomorphically evaluate arbitrary NAND boolean circuits. Unfortunately, the refreshing procedure needs to be executed after every single NAND computation, and each refreshing operates on a single encrypted bit, greatly decreasing the overall throughput of the scheme. We give a new...
Amortized Complexity of Information-Theoretically Secure MPC Revisited
Ignacio Cascudo, Ronald Cramer, Chaoping Xing, Chen Yuan
Cryptographic protocols
A fundamental and widely-applied paradigm due to Franklin and Yung (STOC 1992) on Shamir-secret-sharing based general $n$-player MPC shows how one may trade the adversary threshold $t$ against amortized communication complexity, by using a so-called packed version of Shamir's scheme. For e.g.~the BGW-protocol (with active security), this trade-off means that if $t + 2k -2 < n/3$, then $k$ parallel evaluations of the same arithmetic circuit on different inputs can be performed at the...
PanORAMa: Oblivious RAM with Logarithmic Overhead
Sarvar Patel, Giuseppe Persiano, Mariana Raykova, Kevin Yeo
We present PanORAMa, the first Oblivious RAM construction that achieves communication overhead $O(\log N \cdot \log \log N)$ for a database of $N$ blocks and for any block size $B=\Omega(\log N)$ while requiring client memory of only a constant number of memory blocks. Our scheme can be instantiated in the ``balls and bins" model in which Goldreich and Ostrovsky [JACM 96] showed an $\Omega(\log N)$ lower bound for ORAM communication.
Our construction follows the hierarchical approach to...
Perfectly Secure Oblivious RAM with Sublinear Bandwidth Overhead
Michael Raskin, Mark Simkin
Cryptographic protocols
Oblivious RAM (ORAM) has established itself as a fundamental cryptographic building block.
Understanding which bandwidth overheads are possible under which assumptions has been the topic of a vast amount of previous works.
In this work, we focus on perfectly secure ORAM and we present the first construction with sublinear bandwidth overhead in the worst-case.
All prior constructions with perfect security require linear communication overhead in the worst-case and only achieve sublinear...
Bandwidth-Hard Functions: Reductions and Lower Bounds
Jeremiah Blocki, Peiyuan Liu, Ling Ren, Samson Zhou
Foundations
Memory Hard Functions (MHFs) have been proposed as an answer to the growing inequality between the computational speed of general purpose CPUs and Application Specific Integrated Circuits (ASICs).
MHFs have seen widespread applications including password hashing, key stretching and proofs of work.
Several metrics have been proposed to quantify the ``memory hardness'' of a function. Cumulative memory complexity (CMC) (Alwen and Serbinenko, STOC 2015) (or amortized Area $\times$ Time...
Bootstrapping for Approximate Homomorphic Encryption
Jung Hee Cheon, Kyoohyung Han, Andrey Kim, Miran Kim, Yongsoo Song
Public-key cryptography
This paper extends the leveled homomorphic encryption scheme for an approximate arithmetic of Cheon et al. (ASIACRYPT 2017) to a fully homomorphic encryption, i.e., we propose a new technique to refresh low-level ciphertexts based on Gentry's bootstrapping procedure.
The modular reduction operation is the main bottleneck in the homomorphic evaluation of the decryption circuit. We exploit a scaled sine function as an approximation of the modular reduction operation and present an efficient...
Sustained Space Complexity
Joel Alwen, Jeremiah Blocki, Krzysztof Pietrzak
Cryptographic protocols
Memory-hard functions (MHF) are functions whose evaluation cost is dominated by memory cost. MHFs are egalitarian, in the sense that evaluating them on dedicated hardware (like FPGAs or ASICs) is not much cheaper than on off-the-shelf hardware (like x86 CPUs). MHFs have interesting cryptographic applications, most notably to password hashing and securing blockchains.
Alwen and Serbinenko [STOC'15] define the cumulative memory complexity (cmc) of a function as the sum (over all time-steps)...
Fast and Universally-Composable Oblivious Transfer and Commitment Scheme with Adaptive Security
Megha Byali, Arpita Patra, Divya Ravi, Pratik Sarkar
Cryptographic protocols
Adaptive security embodies one of the strongest notions of security that allows an adversary to corrupt parties at any point during protocol execution and gain access to its internal state. Since it models real-life situations such as ``hacking", efficient adaptively-secure multiparty computation (MPC) protocols are desirable. Such protocols demand primitives such as oblivious transfer (OT) and commitment schemes that are adaptively-secure as building blocks. Efficient realizations of these...
PIR with compressed queries and amortized query processing
Sebastian Angel, Hao Chen, Kim Laine, Srinath Setty
Private information retrieval (PIR) is a key building block in many privacy-preserving systems. Unfortunately, existing constructions remain very expensive. This paper introduces two techniques that make the computational variant of PIR (CPIR) more efficient in practice. The first technique targets a recent class of CPU-efficient CPIR protocols where the query sent by the client contains a number of ciphertexts proportional to the size of the database. We show how to compresses this query,...
Actively Secure Garbled Circuits with Constant Communication Overhead in the Plain Model
Carmit Hazay, Yuval Ishai, Muthuramakrishnan Venkitasubramaniam
We consider the problem of constant-round secure two-party computation in the presence of active (malicious) adversaries. We present the first protocol that has only a constant multiplicative communication overhead compared to Yao's protocol for passive adversaries, and can be implemented in the plain model by only making a black-box use of (parallel) oblivious transfer and a pseudo-random generator. This improves over the polylogarithmic overhead of the previous best protocol. A similar...
Amortization with Fewer Equations for Proving Knowledge of Small Secrets
Rafael del Pino, Vadim Lyubashevsky
Cryptographic protocols
For a linear function $f$, a vector $\mathbf x$ with small coefficients, and a vector $y=f(\mathbf x)$, we would like to be able to give a zero-knowledge proof for the knowledge of an $\mathbf x'$ with small coefficients that satisfies $f(\mathbf x')=y$. This is a common scenario in lattice-based cryptography, and there is currently no satisfactory solution for this problem. All known protocols are built via the repetition a basic protocol that only has constant ($1/2$ or $2/3$) soundness...
Conditional Disclosure of Secrets: Amplification, Closure, Amortization, Lower-bounds, and Separations
Benny Applebaum, Barak Arkis, Pavel Raykov, Prashant Nalini Vasudevan
Foundations
In the \emph{conditional disclosure of secrets} problem (Gertner et al., J. Comput. Syst. Sci., 2000) Alice and Bob, who hold inputs $x$ and $y$ respectively, wish to release a common secret $s$ to Carol (who knows both $x$ and $y$) if only if the input $(x,y)$ satisfies some predefined predicate $f$. Alice and Bob are allowed to send a single message to Carol which may depend on their inputs and some joint randomness and the goal is to minimize the communication complexity while providing...
Sublinear Zero-Knowledge Arguments for RAM Programs
Payman Mohassel, Mike Rosulek, Alessandra Scafuro
We describe a new succinct zero-knowledge argument protocol with the following properties. The prover commits to a large data-set $M$, and can thereafter prove many statements of the form $\exists w : \mathcal{R}_i(M,w)=1$, where $\mathcal{R}_i$ is a public function. The protocol is {\em succinct} in the sense that the cost for the verifier (in computation \& communication) does not depend on $|M|$, not even in any initialization phase. In each proof, the computation/communication cost for...
Constant Round Maliciously Secure 2PC with Function-independent Preprocessing using LEGO
Jesper Buus Nielsen, Thomas Schneider, Roberto Trifiletti
Implementation
Secure two-party computation (S2PC) allows two parties to compute a function on their joint inputs while leaking only the output of the function. At TCC 2009 Orlandi and Nielsen proposed the LEGO protocol for maliciously secure 2PC based on cut-and-choose of Yao's garbled circuits at the gate level and showed that this is asymptotically more efficient than on the circuit level. Since then the LEGO approach has been improved upon in several theoretical works, but never implemented. In this...
Hash First, Argue Later: Adaptive Verifiable Computations on Outsourced Data
Dario Fiore, Cédric Fournet, Esha Ghosh, Markulf Kohlweiss, Olga Ohrimenko, Bryan Parno
Proof systems for verifiable computation (VC) have the potential to make cloud outsourcing more trustworthy. Recent schemes enable a verifier with limited resources to delegate large computations and verify their outcome based on succinct arguments: verification complexity is linear in the size of the inputs and outputs (not the size of the computation). However, cloud computing also often involves large amounts of data, which may exceed the local storage and I/O capabilities of the...
Depth-Robust Graphs and Their Cumulative Memory Complexity
Joël Alwen, Jeremiah Blocki, Krzysztof Pietrzak
Data-independent Memory Hard Functions (iMHFS) are finding a growing number of applications in security; especially in the domain of password hashing. An important property of a concrete iMHF is specified by fixing a directed acyclic graph (DAG) $G_n$ on $n$ nodes. The quality of that iMHF is then captured by the following two pebbling complexities of $G_n$:
\begin{itemize}
\item The parallel cumulative pebbling complexity $\Pi^{\parallel}_{cc}(G_n)$ must be as high as possible (to ensure...
Faster Malicious 2-party Secure Computation with Online/Ofine Dual Execution
Peter Rindal, Mike Rosulek
Cryptographic protocols
We describe a highly optimized protocol for general-purpose secure two-party computation (2PC) in the presence of malicious adversaries. Our starting point is a protocol of Kolesnikov \etal (TCC 2015). We adapt that protocol to the online/offline setting, where two parties repeatedly evaluate the same function (on possibly different inputs each time) and perform as much of the computation as possible in an offline preprocessing phase before their inputs are known. Along the way we develop...
Simple Proofs of Space-Time and Rational Proofs of Storage
Tal Moran, Ilan Orlov
Cryptographic protocols
We introduce a new cryptographic primitive: Proofs of Space-Time (PoSTs) and construct an extremely simple, practical protocol for implementing these proofs. A PoST allows a prover to convince a verifier that she spent a ``space-time'' resource (storing data---space---over a period of time).
Formally, we define the PoST resource as a trade-off between CPU work and space-time (under reasonable cost assumptions, a rational user will prefer to use the lower-cost space-time resource over CPU...
POPE: Partial Order Preserving Encoding
Daniel S. Roche, Daniel Apon, Seung Geol Choi, Arkady Yerukhimovich
Recently there has been much interest in performing search queries over encrypted data to enable functionality while protecting sensitive data. One particularly efficient mechanism for executing such queries is order-preserving encryption/encoding (OPE) which results in ciphertexts that preserve the relative order of the underlying plaintexts thus allowing range and comparison queries to be performed directly on ciphertexts. Recently, Popa et al. (S&P 2013) gave the first construction of...
Equihash: Asymmetric Proof-of-Work Based on the Generalized Birthday Problem
Alex Biryukov, Dmitry Khovratovich
Proof-of-work is a central concept in modern cryptocurrencies and denial-of-service protection tools, but the requirement for fast verification so
far made it an easy prey for GPU-, ASIC-, and botnet-equipped users. The attempts to rely on
memory-intensive computations in order to remedy the disparity between architectures have
resulted in slow or broken schemes.
In this paper we solve this open problem and show how to construct an asymmetric proof-of-work (PoW) based on a computationally...
Very-efficient simulatable flipping of many coins into a well
Luís T. A. N. Brandão
Cryptographic protocols
Secure two-party parallel coin-flipping is a cryptographic functionality that allows two mutually distrustful parties to agree on a common random bit-string of a certain target length. In coin-flipping into-a-well, one party learns the bit-string and then decides whether to abort or to allow the other party to learn it. It is well known that this functionality can be securely achieved in the ideal/real simulation paradigm, using commitment schemes that are simultaneously extractable (X) and...
Efficient Zero-Knowledge Proofs of Non-Algebraic Statements with Sublinear Amortized Cost
Zhangxiang Hu, Payman Mohassel, Mike Rosulek
Cryptographic protocols
We describe a zero-knowledge proof system in which a prover holds a large dataset $M$ and can repeatedly prove NP relations about that dataset. That is, for any (public) relation $R$ and $x$, the prover can prove that $\exists w: R(M,x,w)=1$. After an initial setup phase (which depends only on $M$), each proof requires only a constant number of rounds and has communication/computation cost proportional to that of a {\em random-access machine (RAM)} implementation of $R$, up to...
Cut-and-Choose Based Two-Party Computation in the Online/Offline and Batch Settings
Yehuda Lindell, Ben Riva
Cryptographic protocols
Protocols for secure two-party computation enable a pair of mistrusting parties to compute a joint function of their private inputs without revealing anything but the output. One of the fundamental techniques for obtaining secure computation is that of Yao's garbled circuits. In the setting of malicious adversaries, where the corrupted party can follow any arbitrary (polynomial-time) strategy in an attempt to breach security, the cut-and-choose technique is used to ensure that the garbled...
FFS Factory: Adapting Coppersmith's "Factorization Factory" to the Function Field Sieve
Jérémie Detrey
Public-key cryptography
In 1993, Coppersmith introduced the "factorization factory" approach as a means to speed up the Number Field Sieve algorithm (NFS) when factoring batches of integers of similar size: at the expense of a large precomputation whose cost is amortized when considering sufficiently many integers to factor, the complexity of each individual factorization can then be lowered.
We suggest here to extend this idea to the computation of discrete logarithms in finite fields of small characteristic...
Compact VSS and Efficient Homomorphic UC Commitments
Ivan Damgård, Bernardo David, Irene Giacomelli, Jesper Buus Nielsen
Cryptographic protocols
We present a new compact verifiable secret sharing scheme, based on
this we present the first construction of a homomorphic UC commitment
scheme that requires only cheap symmetric cryptography, except for a
small number of seed OTs. To commit to a $k$-bit string, the amortized
communication cost is $O(k)$ bits. Assuming a sufficiently efficient
pseudorandom generator, the computational complexity is $O(k)$ for the
verifier and $O(k^{1+\epsilon})$ for the committer (where $\epsilon
<1$ is a...
High Parallel Complexity Graphs and Memory-Hard Functions
Joël Alwen, Vladimir Serbinenko
We develop new theoretical tools for proving lower-bounds on the (amortized) complexity of functions in a parallel setting. We demonstrate their use by constructing the first provably secure Memory-hard functions (MHF); a class of functions recently gaining acceptance in practice as an effective means to counter brute-force attacks on security relevant functions.
Pebbling games over graphs have proven to be a powerful abstraction for a wide variety of computational models. A dominant...
Bandwidth Efficient PIR from NTRU
Yarkın Doröz, Berk Sunar, Ghaith Hammouri
We present a private information retrieval (PIR) scheme based on a somewhat homomorphic encryption (SWHE). In particular, we customize an NTRU-based SWHE scheme in order to evaluate a specific class of fixed depth circuits relevant for PIR implementation, thus achieving a more practical implementation. In practice, a SWHE that can evaluate a depth 5 circuit is sufficient to construct a PIR capable of retrieving data from a database containing 4 billion rows. We leverage this property in...
Multi-user collisions: Applications to Discrete Logarithm, Even-Mansour and PRINCE
Pierre-Alain Fouque, Antoine Joux, Chrysanthi Mavromati
In this paper, we investigate the multi-user setting both in public and in secret-key cryptanalytic applications. In
this setting, the adversary tries to recover keys of many users in parallel more efficiently than with classical attacks, \textit{i.e.}, the number of recovered keys multiplied by the time complexity to find a single key, by
amortizing the cost among several users. One possible scenario is to recover a single key in a large set of users more efficiently than to recover a key...
Achieving malicious security with high efficiency in dishonest-majority secure multiparty computation is a formidable challenge. The milestone works SPDZ and TinyOT have spawn a large family of protocols in this direction. For boolean circuits, state-of-the-art works (Cascudo et. al, TCC 2020 and Escudero et. al, CRYPTO 2022) have proposed schemes based on reverse multiplication-friendly embedding (RMFE) to reduce the amortized cost. However, these protocols are theoretically described and...
We present an efficient zero-knowledge argument of knowledge system customized for the Paillier cryptosystem. Our system enjoys sublinear proof size, low verification cost, and acceptable proof generation effort, while also supporting batch proof generation/verification. Existing works specialized for Paillier cryptosystem feature linear proof size and verification time. Using existing sublinear argument systems for generic statements (e.g., zk-SNARK) results in unaffordable proof generation...
RAM (random access memory) is an important primitive in verifiable computation. In this paper, we focus on realizing RAM with efficient batching property, i.e, proving a batch of $m$ updates on a RAM of size $N$ while incurring a cost that is sublinear in $N$. Classical approaches based on Merkle-trees or address ordered transcripts to model RAM correctness are either concretely inefficient, or incur linear overhead in the size of the RAM. Recent works explore cryptographic accumulators...
We present two techniques to improve the computational and/or communication costs of STARK proofs: packing and modular split-and-pack. Packing allows to generate a single proof of the satisfiability of several constraints. We achieve this by packing the evaluations of all relevant polynomials in the same Merkle leaves, and combining all DEEP FRI functions into a single randomized validity function. Our benchmarks show that packing reduces the verification time and proof size compared...
Machine learning as a service requires the client to trust the server and provide its own private information to use this service. Usually, clients may worry that their private data is being collected by server without effective supervision, and the server also aims to ensure proper management of the user data to foster the advancement of its services. In this work, we focus on private decision tree evaluation (PDTE) which can alleviates such privacy concerns associated with classification...
In this paper, we introduce a new framework for constructing linkable ring signatures (LRS). Our framework is based purely on signatures of knowledge (SoK) which allows one to issue signatures on behalf of any NP-statement using the corresponding witness. Our framework enjoys the following advantages: (1) the security of the resulting LRS depends only on the security of the underlying SoK; (2) the resulting LRS naturally supports online/offline signing (resp. verification), where the output...
Consider the task of secure multiparty computation (MPC) among $n$ parties with perfect security and guaranteed output delivery, supporting $t<n/3$ active corruptions. Suppose the arithmetic circuit $C$ to be computed is defined over a finite ring $\mathbb{Z}/q\mathbb{Z}$, for an arbitrary $q\in\mathbb{Z}$. It is known that this type of MPC over such ring is possible, with communication that scales as $O(n|C|)$, assuming that $q$ scales as $\Omega(n)$. However, for constant-size rings...
Asynchronous complete secret sharing (ACSS) is a foundational primitive in the design of distributed algorithms and cryptosystems that require secrecy. Dual-threshold ACSS permits a dealer to distribute a secret to a collection of $n$ servers so that everyone holds shares of a polynomial containing the dealer's secret. This work contributes a new ACSS protocol, called Haven++, that uses packing and batching to make asymptotic and concrete advances in the design and application of ACSS for...
Threshold variants of the Schnorr signature scheme have recently been at the center of attention due to their applications to Bitcoin, Ethereum, and other cryptocurrencies. However, existing constructions for threshold Schnorr signatures among a set of $n$ parties with corruption threshold $t_c$ suffer from at least one of the following drawbacks: (i) security only against static (i.e., non-adaptive) adversaries, (ii) cubic or higher communication cost to generate a single signature, (iii)...
Secure transformer inference has emerged as a prominent research topic following the proliferation of ChatGPT. Existing solutions are typically interactive, involving substantial communication load and numerous interaction rounds between the client and the server. In this paper, we propose NEXUS, the first non-interactive protocol for secure transformer inference, using which the client is only required to perform one round of communication with the server throughout the evaluation...
The security of lattice-based crytography (LWE, NTRU, and FHE) depends on the hardness of the shortest-vector problem (SVP). Sieving algorithms give the lowest asymptotic runtime to solve SVP, but depend on exponential memory. Memory access costs much more in reality than in the RAM model, so we consider a computational model where processors, memory, and meters of wire are in constant proportions to each other. While this adds substantial costs to route data during lattice sieving, we...
Through tremendous efforts, the communication cost of secure multi-party computation (MPC) in the honest-majority setting has been significantly improved. In particular, the state-of-the-art honest-majority MPC protocol by Escudero et al. (CCS'22) takes 12 field elements in total per multiplication gate for arithmetic circuits in the online phase. However, it still requires $12 \log(5n/4)$ bits of online communication per AND gate for Boolean circuits. That is, for Boolean circuits, no...
Classically, Private Information Retrieval (PIR) was studied in a setting without any pre-processing. In this setting, it is well-known that 1) public-key cryptography is necessary to achieve non-trivial (i.e., sublinear) communication efficiency in the single-server setting, and 2) the total server computation per query must be linear in the size of the database, no matter in the single-server or multi-server setting. Recent works have shown that both of these barriers can be overcome...
On-chain mixers, such as Tornado Cash (TC), have become a popular privacy solution for many non-privacy-preserving blockchain users. These mixers enable users to deposit a fixed amount of coins and withdraw them to another address, while effectively reducing the linkability between these addresses and securely obscuring their transaction history. However, the high cost of interacting with existing on-chain mixer smart contracts prohibits standard users from using the mixer, mainly due to the...
The recent technological advances in Post-Quantum Cryptography (PQC) raise the questions of robust implementations of new asymmetric cryptographic primitives in today’s technology. This is the case for the lattice-based Module Lattice-Key Encapsulation Mechanism (ML-KEM) algorithm which is proposed by the NIST as the first standard for Key Encapsulation Mechanism (KEM), taking inspiration from CRYSTALS-Kyber. We have notably to make sure the ML-KEM implementation is resilient against...
We present new protocols for threshold Schnorr signatures that work in an asynchronous communication setting, providing robustness and optimal resilience. These protocols provide unprecedented performance in terms of communication and computational complexity. In terms of communication complexity, for each signature, a single party must transmit a few dozen group elements and scalars across the network (independent of the size of the signing committee). In terms of computational...
Amortized bootstrapping offers a way to refresh multiple ciphertexts of a fully homomorphic encryption scheme in parallel more efficiently than refreshing a single ciphertext at a time. Micciancio and Sorrell (ICALP 2018) first proposed the technique to bootstrap $n$ LWE ciphertexts simultaneously, reducing the total cost from $\tilde{O}(n^2)$ to $\tilde{O}(3^\epsilon n^{1+\frac{1}{\epsilon}})$ for arbitrary $\epsilon > 0$. Several recent works have further improved the asymptotic cost....
In this work, we focus on maliciously secure 3PC for binary circuits with honest majority. While the state-of-the-art (Boyle et al. CCS 2019) has already achieved the same amortized communication as the best-known semi-honest protocol (Araki et al. CCS 2016), they suffer from a large computation overhead: when comparing with the best-known implementation result (Furukawa et al. Eurocrypt 2017) which requires $9\times$ communication cost of Araki et al., the protocol by Boyle et al. is around...
Secure Machine Learning as a Service is a viable solution where clients seek secure delegation of the ML computation while protecting their sensitive data. We propose an efficient method to securely evaluate deep standard convolutional neural networks based on CKKS fully homomorphic encryption, in the manner of batch inference. In this paper, we introduce a packing method called Channel-by-Channel Packing that maximizes the slot compactness and single-instruction-multipledata capabilities in...
We prove that perfectly-secure optimally-resilient secure Multi-Party Computation (MPC) for a circuit with $C$ gates and depth $D$ can be obtained in $O((Cn+n^4 + Dn^2)\log n)$ communication complexity and $O(D)$ expected time. For $D \ll n$ and $C\geq n^3$, this is the first perfectly-secure optimal-resilient MPC protocol with linear communication complexity per gate and constant expected time complexity per layer. Compared to state-of-the-art MPC protocols in the player elimination...
Anonymous message delivery, as in private communication and privacy-preserving blockchain applications, ought to protect recipient metadata: a message should not be inadvertently linkable to its destination. But how can messages then be delivered to each recipient, without each recipient scanning all messages? Recent work constructed Oblivious Message Retrieval (OMR) protocols that outsource this job to untrusted servers in a privacy-preserving manner. We consider the case of group...
The implementation of cryptographic algorithms must be protected against physical attacks. Side-channel and fault injection analyses are two prominent such implem\-entation-level attacks. Protections against either do exist; they are characterized by security orders: the higher the order, the more difficult the attack. In this paper, we leverage fast discrete Fourier transform to reduce the complexity of high-order masking, and extend it to allow for fault detection and/or correction. The...
Oblivious RAM (ORAM) allows a client to outsource storage to a remote server while hiding the data access pattern from the server. Many ORAM designs have been proposed to reduce the computational overhead and bandwidth blowup for the client. A recent work, Onion Ring ORAM (CCS'19), is able to achieve $O(1)$ bandwidth blowup in the online phase using fully homomorphic encryption (FHE) techniques, at the cost of a computationally expensive client-side offline phase. Furthermore, such a scheme...
We study the complexity of two-party secure arithmetic computation where the goal is to evaluate an arithmetic circuit over a finite field $F$ in the presence of an active (aka malicious) adversary. In the passive setting, Applebaum et al. (Crypto 2017) constructed a protocol that only makes a *constant* (amortized) number of field operations per gate. This protocol uses the underlying field $F$ as a black box, makes black-box use of (standard) oblivious transfer, and its security is based...
Amortized bootstrapping offers a way to simultaneously refresh many ciphertexts of a fully homomorphic encryption scheme, at a total cost comparable to that of refreshing a single ciphertext. An amortization method for FHEW-style cryptosystems was first proposed by (Micciancio and Sorrell, ICALP 2018), who showed that the amortized cost of bootstrapping n FHEW-style ciphertexts can be reduced from $O(n)$ basic cryptographic operations to just $O(n^{\epsilon})$, for any constant...
Designing an efficient solution for Byzantine broadcast is an important problem for many distributed computing and cryptographic tasks. There have been many attempts to achieve sub-quadratic communication complexity in several directions, both in theory and practice, all with pros and cons. This paper initiates the study of another attempt: improving the amortized communication complexity of multi-shot Byzantine broadcast. Namely, we try to improve the average cost when we have sequential...
Micciancio and Sorrel (ICALP 2018) proposed a bootstrapping algorithm that can refresh many messages at once with sublinearly many homomorphic operations per message. However, despite the attractive asymptotic cost, it is unclear if their algorithm could ever be practical, which reduces the impact of their results. In this work, we follow their general framework, but propose an amortized bootstrapping that is conceptually simpler and asymptotically cheaper. We reduce the number of...
Non-interactive batch arguments for $\mathsf{NP}$ provide a way to amortize the cost of $\mathsf{NP}$ verification across multiple instances. In particular, they allow a prover to convince a verifier of multiple $\mathsf{NP}$ statements with communication that scales sublinearly in the number of instances. In this work, we study fully succinct batch arguments for $\mathsf{NP}$ in the common reference string (CRS) model where the length of the proof scales not only sublinearly in the...
Function Secret Sharing (FSS; Eurocrypt 2015) allows a dealer to share a function f with two or more evaluators. Given secret shares of a function f, the evaluators can locally compute secret shares of f(x) on an input x, without learning information about f. In this paper, we initiate the study of access control for FSS. Given the shares of f, the evaluators can ensure that the dealer is authorized to share the provided function. For a function family F and an access control list defined...
The classical (parallel) black pebbling game is a useful abstraction which allows us to analyze the resources (space, space-time, cumulative space) necessary to evaluate a function $f$ with a static data-dependency graph $G$. Of particular interest in the field of cryptography are data-independent memory-hard functions $f_{G,H}$ which are defined by a directed acyclic graph (DAG) $G$ and a cryptographic hash function $H$. The pebbling complexity of the graph $G$ characterizes the amortized...
The MPC-in-the-Head paradigm is a popular framework to build zero-knowledge proof systems using techniques from secure multi-party computation (MPC). While this paradigm is not restricted to a particular secret sharing scheme, all the efficient instantiations for small circuits proposed so far rely on additive secret sharing. In this work, we show how applying a threshold linear secret sharing scheme (threshold LSSS) can be beneficial to the MPC-in-the-Head paradigm. For a general...
This paper studies Batch Private Information Retrieval (BatchPIR), a variant of private information retrieval (PIR) where the client wants to retrieve multiple entries from the server in one batch. BatchPIR matches the use case of many practical applications and holds the potential for substantial efficiency improvements over PIR in terms of amortized cost per query. Existing BatchPIR schemes have achieved decent computation efficiency but have not been able to improve communication...
Memory-hard functions (MHFs) are a useful cryptographic primitive which can be used to design egalitarian proof of work puzzles and to protect low entropy secrets like passwords against brute-force attackers. Intuitively, a memory-hard function is a function whose evaluation costs are dominated by memory costs even if the attacker uses specialized hardware (FPGAs/ASICs), and several cost metrics have been proposed to quantify this intuition. For example, space-time cost looks at the product...
In this work we present a novel actively secure multiparty computation protocol in the dishonest majority setting, where the computation domain is a ring of the type $\mathbb{Z}_{2^k}$. Instead of considering an "extension ring" of the form $\mathbb{Z}_{2^{k+\kappa}}$ as in SPD$\mathbb{Z}_{2^k}$ (Cramer et al, CRYPTO 2018) and its derivatives, we make use of an actual ring extension, or more precisely, a Galois ring extension $\mathbb{Z}_{p^k}[\mathtt{X}]/(h(\mathtt{X}))$ of large enough...
The SPDZ multiparty computation protocol allows $n$ parties to securely compute arithmetic circuits over a finite field, while tolerating up to $n − 1$ active corruptions. A line of work building upon SPDZ have made considerable improvements to the protocol’s performance, typically focusing on concrete efficiency. However, the communication complexity of each of these protocols is $\Omega(n^2 |C|)$. In this paper, we present a protocol that achieves $O(n|C|)$ communication. Our...
We introduce a new MPC protocol to securely compute any functionality over an arbitrary black-box finite ring (which may not be commutative), tolerating $t<n/3$ active corruptions while \textit{guaranteeing output delivery} (G.O.D.). Our protocol is based on replicated secret-sharing, whose share size is known to grow exponentially with the number of parties $n$. However, even though the internal storage and computation in our protocol remains exponential, the communication complexity of our...
Public key cryptography is used to asymmetrically establish keys, authenticate or encrypt data between communicating parties at a relatively high performance cost. To reduce computational overhead, modern network protocols combine asymmetric primitives for key establishment and authentication with symmetric ones. Similarly, Hybrid Public Key Encryption, a relatively new scheme, uses public key cryptography for key derivation and symmetric key cryptography for data encryption. In this paper,...
Non-interactive batch arguments for NP provide a way to amortize the cost of NP verification across multiple instances. They enable a prover to convince a verifier of multiple NP statements with communication much smaller than the total witness length and verification time much smaller than individually checking each instance. In this work, we give the first construction of a non-interactive batch argument for NP from standard assumptions on groups with bilinear maps (specifically, from...
We show a compiler that allows to prove the correct execution of RAM programs using any zero-knowledge system for circuit satisfiability. At the core of this work is an arithmetic circuit which verifies the consistency of a list of memory access tuples in zero-knowledge. Using such a circuit, we obtain the first constant-round and concretely efficient zero-knowledge proof protocol for RAM programs using any stateless zero-knowledge proof system for Boolean or arithmetic circuits. Both the...
We propose a new garbled RAM construction called NanoGRAM, which achieves an amortized cost of $\widetilde{O}(\lambda \cdot (W \log N + \log^3 N))$ bits per memory access, where $\lambda$ is the security parameter, $W$ is the block size, and $N$ is the total number of blocks, and $\widetilde{O}(\cdot)$ hides $poly\log\log$ factors. For sufficiently large blocks where $W = \Omega(\log^2 N)$, our scheme achieves $\widetilde{O}(\lambda \cdot W \log N)$ cost per memory access, where the...
We construct new private-information-retrieval protocols in the single-server setting. Our schemes allow a client to privately fetch a sequence of database records from a server, while the server answers each query in average time sublinear in the database size. Specifically, we introduce the first single-server private-information-retrieval schemes that have sublinear amortized server time, require sublinear additional storage, and allow the client to make her queries adaptively. Our...
In this work we present a direct construction for verifiable decryption for the BGV encryption scheme by combining existing zero-knowledge proofs for linear relations and bounded values. This is one of the first constructions of verifiable decryption protocols for lattice-based cryptography, and we give a protocol that is simpler and at least as efficient as the state of the art when amortizing over many ciphertexts. To prove its practicality we provide concrete parameters, resulting in...
A homomorphic secret sharing (HSS) scheme is a secret sharing scheme that supports evaluating functions on shared secrets by means of a local mapping from input shares to output shares. We initiate the study of the download rate of HSS, namely, the achievable ratio between the length of the output shares and the output length when amortized over $\ell$ function evaluations. We obtain the following results. * In the case of linear information-theoretic HSS schemes for degree-$d$...
Recent new constructions of rate-1 OT [Döttling, Garg, Ishai, Malavolta, Mour, and Ostrovsky, CRYPTO 2019] have brought this primitive under the spotlight and the techniques have led to new feasibility results for private-information retrieval, and homomorphic encryption for branching programs. The receiver communication of this construction consists of a quadratic (in the sender's input size) number of group elements for a single instance of rate-1 OT. Recently [Garg, Hajiabadi, Ostrovsky,...
Garbled RAM (GRAM) is a powerful technique introduced by Lu and Ostrovsky that equips Garbled Circuit (GC) with a sublinear cost RAM without adding rounds of interaction. While multiple GRAM constructions are known, none are suitable for practice, due to costs that have high constants and poor scaling. We present the first GRAM suitable for practice. For computational security parameter $\kappa$ and for a size-$n$ RAM that stores blocks of size $w = \Omega(\log^2 n)$ bits, our GRAM incurs...
A $(1,n)$-robust combiner combines $n$ cryptography primitives to construct a new primitive of the same type, and guarantees that if any of the ingredient primitive is secure, then the resulting primitive is secure. In recent two decades, robust combiners for various crypto primitives (e.g. public key encryption, oblivious transfer) have been proposed. Very recently, more works on robust combiners for post-quantum key encapsulation mechanism appear to achieve multi-layer of defence, to...
Due to its amazing speed and multiplicative properties the Legendre PRF recently finds widespread applications e.g. in Ethereum 2.0, multiparty computation and in the quantum-secure signature proposal LegRoast. However, its security is not yet extensively studied. The Legendre PRF computes for a key $k$ on input $x$ the Legendre symbol $L_k(x) = \left( \frac {x+k} {p} \right)$ in some finite field $\F_p$. As standard notion, PRF security is analysed by giving an attacker oracle access to...
Fully Homomorphic encryption (FHE) has been gaining popularity as an emerging way of enabling an unlimited number of operations on the encrypted message without decryption. A major drawback of FHE is its high computational cost. Especially, a bootstrapping that refreshes the noise accumulated through consequent FHE operations on the ciphertext is even taking minutes. This significantly limits the practical use of FHE in numerous real applications. By exploiting massive parallelism available...
The safety of the Bitcoin blockchain relies on strong network synchrony. Therefore, violating the blockchain safety requires strong adversaries who control a mining pool with 51% hash rate. In this paper, we show that the network synchrony does not hold in the real world Bitcoin network, which can be exploited to amortize the cost of various attacks. Towards that, first we construct the Bitcoin ideal world functionality to formally specify its ideal execution model in a synchronous network....
Having shared access to high-quality random numbers is essential in many important applications. Yet, existing constructions of distributed random beacons still have limitations such as imperfect security guarantees, strong setup or network assumptions, or high costs. In this paper, we present SPURT, an efficient distributed randomness beacon protocol that does not require any trusted or expensive setup and is secure against a malicious adversary that controls up to one-third of the nodes in...
We propose a smart contract that allows two mutually distrusting parties to transact any non-digital good or service on a blockchain. The contract acts as an escrow and settles disputes by letting parties wager that they can convince an arbiter they were the honest party. We analyze the contract as an extensive-form game and prove that the contract is secure in a strong game-theoretic sense if and only if the arbiter is biased in favor of honest parties. We show this is inherent to any...
In this work we introduce Banquet, a digital signature scheme with post-quantum security, constructed using only symmetric-key primitives. The design is based on the MPC-in-head paradigm also used by Picnic (CCS 2017) and BBQ (SAC 2019). Like BBQ, Banquet uses only standardized primitives, namely AES and SHA-3, but signatures are more than 50% shorter, making them competitive with Picnic (which uses a non-standard block cipher to improve performance). The MPC protocol in Banquet uses a new...
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...
MPC functionalities are increasingly specified in high-level languages, where control-flow constructions such as conditional statements are extensively used. Today, concretely efficient MPC protocols are circuit-based and must evaluate all conditional branches at high cost to hide the taken branch. The Goldreich-Micali-Wigderson, or GMW, protocol is a foundational circuit-based technique that realizes MPC for p players and is secure against up to p - 1 semi-honest corruptions. While GMW...
Higher-order masking countermeasures provide strong provable security against side-channel attacks at the cost of incurring significant overheads, which largely hinders its applicability. Previous works towards remedying cost mostly concentrated on ``local'' calculations, i.e., optimizing the cost of computation units such as a single AND gate or a field multiplication. This paper explores a complementary ``global'' approach, i.e., considering multiple operations in the masked domain as a...
At CRYPTO 2018, Cascudo et al. introduced Reverse Multiplication Friendly Embeddings (RMFEs). These are a mechanism to compute $\delta$ parallel evaluations of the same arithmetic circuit over a field $\mathbb{F}_q$ at the cost of a single evaluation of that circuit in $\mathbb{F}_{q^d}$, where $\delta < d$. Due to this inequality, RMFEs are a useful tool when protocols require to work over $\mathbb{F}_{q^d}$ but one is only interested in computing over $\mathbb{F}_q$. In this work we...
The private join and compute (PJC) functionality enables secure computation over data distributed across different databases, which is a functionality with a wide range of applications, many of which address settings where the input databases are of significantly different sizes. We introduce the notion of private information retrieval (PIR) with default, which enables two-party PJC functionalities in a way that hides the size of the intersection of the two databases and incurs sublinear...
In this paper we present ALBATROSS, a family of multiparty randomness generation protocols with guaranteed output delivery and public verification that allows to trade off corruption tolerance for a much improved amortized computational complexity. Our basic stand alone protocol is based on publicly verifiable secret sharing (PVSS) and is secure under in the random oracle model under the decisional Diffie-Hellman (DDH) hardness assumption. We also address the important issue of constructing...
Private set intersection and related functionalities are among the most prominent real-world applications of secure multiparty computation. While such protocols have attracted significant attention from the research community, other functionalities are often required to support a PSI application in practice. For example, in order for two parties to run a PSI over the unique users contained in their databases, they might first invoke on a support functionality to agree on the primary keys to...
The theoretical idea of using FHE to realize MPC has been therefor over a decade. Existing threshold (and multi-key) FHE schemes were constructed by modifying and analyzing a traditional single-keyFHE in a case-by-case manner, thus technically highly-demanding.This work explores a new approach to build threshold FHE (therebyMPC schemes) through tailoring generic MPC protocols to the base FHE scheme while requiring no effort in FHE redesign. We applied our approach to two representative...
In this work, we design and implement the first protocol for RSA modulus construction that can support thousands of parties and offers security against an arbitrary number of corrupted parties. In a nutshell, we design the ``best'' protocol for this scale that is secure against passive corruption, then amplify it to obtain active security using efficient non-interactive zero-knowledge arguments. Our protocol satisfies a stronger security guarantee where a deviating party can be identified...
We present a new secure multiparty computation protocol in the preprocessing model that allows for the evaluation of a number of instances of a boolean circuit in parallel, with a small online communication complexity per instance of 10 bits per party and multiplication gate. Our protocol is secure against an active dishonest majority, and can be also transformed, via known techniques, into a protocol for the evaluation of a single “well-formed” boolean circuit with the same complexity per...
Byzantine agreement (BA), the task of $n$ parties to agree on one of their input bits in the face of malicious agents, is a powerful primitive that lies at the core of a vast range of distributed protocols. Interestingly, in protocols with the best overall communication, the demands of the parties are highly unbalanced: the amortized cost is $\tilde O(1)$ bits per party, but some parties must send $\Omega(n)$ bits. In best known balanced protocols, the overall communication is sub-optimal,...
We revisit the framework of Commodity-based Cryptography presented by Beaver (STOC'97) with a focus on updating the framework to fit with modern multiparty computation (MPC) protocols. We study the possibility of replacing the well-known preprocessing model with a commodity-based setting, where a set of independent servers (some of which may be corrupt) provide clients with correlated randomness. From this, the clients then distill correct and secure correlated randomness that they can use...
We present a fully homomorphic encryption scheme continuing the line of works of Ducas and Micciancio (2015, [DM15]), Chillotti et al. (2016, [CGGI16a]; 2017, [CGGI17]; 2018, [CGGI18a]), and Gao (2018,[Gao18]). Ducas and Micciancio (2015) show that homomorphic computation of one bit operation on LWE ciphers can be done in less than a second, which is then reduced by Chillotti et al. (2016, 2017, 2018) to 13ms. According to Chillotti et al. (2018, [CGGI18b]), the cipher expansion for TFHE is...
To achieve security and privacy for data stored on the cloud, we need the ability to secure data in compute. Equality comparisons, ``$x=y, x\neq y$'', have been widely studied with many proposals but there is much room for improvement for order comparisons, ``$x < y,~x \leq y, x > y$ and $x \geq y$''. Most protocols for order comparisons have some limitation, either leaking some information about the data or requiring several rounds of communication between client and server. In addition,...
Oblivious linear-function evaluation (OLE) is a secure two-party protocol allowing a receiver to learn a secret linear combination of a pair of field elements held by a sender. OLE serves as a common building block for secure computation of arithmetic circuits, analogously to the role of oblivious transfer (OT) for boolean circuits. A useful extension of OLE is vector OLE (VOLE), allowing the receiver to learn a linear combination of two vectors held by the sender. In several applications of...
We present a new protocol for computing a circuit which implements the private set intersection functionality (PSI). Using circuits for this task is advantageous over the usage of specific protocols for PSI, since many applications of PSI do not need to compute the intersection itself but rather functions based on the items in the intersection. Our protocol is the first circuit-based PSI protocol to achieve linear communication complexity. It is also concretely more efficient than all...
We introduce and study the notion of fully linear probabilistically checkable proof systems. In such a proof system, the verifier can make a small number of linear queries that apply jointly to the input and a proof vector. Our new type of proof system is motivated by applications in which the input statement is not fully available to any single verifier, but can still be efficiently accessed via linear queries. This situation arises in scenarios where the input is partitioned or...
Homomorphic universally composable (UC) commitments allow for the sender to reveal the result of additions and multiplications of values contained in commitments without revealing the values themselves while assuring the receiver of the correctness of such computation on committed values. In this work, we construct essentially optimal additively homomorphic UC commitments from any (not necessarily UC or homomorphic) extractable commitment. We obtain amortized linear computational complexity...
Memory-hard functions (MHFs) are a key cryptographic primitive underlying the design of moderately expensive password hashing algorithms and egalitarian proofs of work. Over the past few years several increasingly stringent goals for an MHF have been proposed including the requirement that the MHF have high sequential space-time (ST) complexity, parallel space-time complexity, amortized area-time (aAT) complexity and sustained space complexity. Data-Independent Memory Hard Functions (iMHFs)...
Optimizing performance of Fully Homomorphic Encryption (FHE) is nowadays an active trend of research in cryptography. One way of improvement is to use a hybrid construction with a classical symmetric encryption scheme to transfer encrypted data to the Cloud. This allows to reduce the bandwidth since the expansion factor of symmetric schemes (the ratio between the ciphertext and the plaintext length) is close to one, whereas for FHE schemes it is in the order of 1,000 to 1,000,000. However,...
The FHEW fully homomorphic encryption scheme (Ducas and Micciancio, Eurocrypt 2015) offers very fast homomorphic NAND-gate computations (on encrypted data) and a relatively fast refreshing procedure that allows to homomorphically evaluate arbitrary NAND boolean circuits. Unfortunately, the refreshing procedure needs to be executed after every single NAND computation, and each refreshing operates on a single encrypted bit, greatly decreasing the overall throughput of the scheme. We give a new...
A fundamental and widely-applied paradigm due to Franklin and Yung (STOC 1992) on Shamir-secret-sharing based general $n$-player MPC shows how one may trade the adversary threshold $t$ against amortized communication complexity, by using a so-called packed version of Shamir's scheme. For e.g.~the BGW-protocol (with active security), this trade-off means that if $t + 2k -2 < n/3$, then $k$ parallel evaluations of the same arithmetic circuit on different inputs can be performed at the...
We present PanORAMa, the first Oblivious RAM construction that achieves communication overhead $O(\log N \cdot \log \log N)$ for a database of $N$ blocks and for any block size $B=\Omega(\log N)$ while requiring client memory of only a constant number of memory blocks. Our scheme can be instantiated in the ``balls and bins" model in which Goldreich and Ostrovsky [JACM 96] showed an $\Omega(\log N)$ lower bound for ORAM communication. Our construction follows the hierarchical approach to...
Oblivious RAM (ORAM) has established itself as a fundamental cryptographic building block. Understanding which bandwidth overheads are possible under which assumptions has been the topic of a vast amount of previous works. In this work, we focus on perfectly secure ORAM and we present the first construction with sublinear bandwidth overhead in the worst-case. All prior constructions with perfect security require linear communication overhead in the worst-case and only achieve sublinear...
Memory Hard Functions (MHFs) have been proposed as an answer to the growing inequality between the computational speed of general purpose CPUs and Application Specific Integrated Circuits (ASICs). MHFs have seen widespread applications including password hashing, key stretching and proofs of work. Several metrics have been proposed to quantify the ``memory hardness'' of a function. Cumulative memory complexity (CMC) (Alwen and Serbinenko, STOC 2015) (or amortized Area $\times$ Time...
This paper extends the leveled homomorphic encryption scheme for an approximate arithmetic of Cheon et al. (ASIACRYPT 2017) to a fully homomorphic encryption, i.e., we propose a new technique to refresh low-level ciphertexts based on Gentry's bootstrapping procedure. The modular reduction operation is the main bottleneck in the homomorphic evaluation of the decryption circuit. We exploit a scaled sine function as an approximation of the modular reduction operation and present an efficient...
Memory-hard functions (MHF) are functions whose evaluation cost is dominated by memory cost. MHFs are egalitarian, in the sense that evaluating them on dedicated hardware (like FPGAs or ASICs) is not much cheaper than on off-the-shelf hardware (like x86 CPUs). MHFs have interesting cryptographic applications, most notably to password hashing and securing blockchains. Alwen and Serbinenko [STOC'15] define the cumulative memory complexity (cmc) of a function as the sum (over all time-steps)...
Adaptive security embodies one of the strongest notions of security that allows an adversary to corrupt parties at any point during protocol execution and gain access to its internal state. Since it models real-life situations such as ``hacking", efficient adaptively-secure multiparty computation (MPC) protocols are desirable. Such protocols demand primitives such as oblivious transfer (OT) and commitment schemes that are adaptively-secure as building blocks. Efficient realizations of these...
Private information retrieval (PIR) is a key building block in many privacy-preserving systems. Unfortunately, existing constructions remain very expensive. This paper introduces two techniques that make the computational variant of PIR (CPIR) more efficient in practice. The first technique targets a recent class of CPU-efficient CPIR protocols where the query sent by the client contains a number of ciphertexts proportional to the size of the database. We show how to compresses this query,...
We consider the problem of constant-round secure two-party computation in the presence of active (malicious) adversaries. We present the first protocol that has only a constant multiplicative communication overhead compared to Yao's protocol for passive adversaries, and can be implemented in the plain model by only making a black-box use of (parallel) oblivious transfer and a pseudo-random generator. This improves over the polylogarithmic overhead of the previous best protocol. A similar...
For a linear function $f$, a vector $\mathbf x$ with small coefficients, and a vector $y=f(\mathbf x)$, we would like to be able to give a zero-knowledge proof for the knowledge of an $\mathbf x'$ with small coefficients that satisfies $f(\mathbf x')=y$. This is a common scenario in lattice-based cryptography, and there is currently no satisfactory solution for this problem. All known protocols are built via the repetition a basic protocol that only has constant ($1/2$ or $2/3$) soundness...
In the \emph{conditional disclosure of secrets} problem (Gertner et al., J. Comput. Syst. Sci., 2000) Alice and Bob, who hold inputs $x$ and $y$ respectively, wish to release a common secret $s$ to Carol (who knows both $x$ and $y$) if only if the input $(x,y)$ satisfies some predefined predicate $f$. Alice and Bob are allowed to send a single message to Carol which may depend on their inputs and some joint randomness and the goal is to minimize the communication complexity while providing...
We describe a new succinct zero-knowledge argument protocol with the following properties. The prover commits to a large data-set $M$, and can thereafter prove many statements of the form $\exists w : \mathcal{R}_i(M,w)=1$, where $\mathcal{R}_i$ is a public function. The protocol is {\em succinct} in the sense that the cost for the verifier (in computation \& communication) does not depend on $|M|$, not even in any initialization phase. In each proof, the computation/communication cost for...
Secure two-party computation (S2PC) allows two parties to compute a function on their joint inputs while leaking only the output of the function. At TCC 2009 Orlandi and Nielsen proposed the LEGO protocol for maliciously secure 2PC based on cut-and-choose of Yao's garbled circuits at the gate level and showed that this is asymptotically more efficient than on the circuit level. Since then the LEGO approach has been improved upon in several theoretical works, but never implemented. In this...
Proof systems for verifiable computation (VC) have the potential to make cloud outsourcing more trustworthy. Recent schemes enable a verifier with limited resources to delegate large computations and verify their outcome based on succinct arguments: verification complexity is linear in the size of the inputs and outputs (not the size of the computation). However, cloud computing also often involves large amounts of data, which may exceed the local storage and I/O capabilities of the...
Data-independent Memory Hard Functions (iMHFS) are finding a growing number of applications in security; especially in the domain of password hashing. An important property of a concrete iMHF is specified by fixing a directed acyclic graph (DAG) $G_n$ on $n$ nodes. The quality of that iMHF is then captured by the following two pebbling complexities of $G_n$: \begin{itemize} \item The parallel cumulative pebbling complexity $\Pi^{\parallel}_{cc}(G_n)$ must be as high as possible (to ensure...
We describe a highly optimized protocol for general-purpose secure two-party computation (2PC) in the presence of malicious adversaries. Our starting point is a protocol of Kolesnikov \etal (TCC 2015). We adapt that protocol to the online/offline setting, where two parties repeatedly evaluate the same function (on possibly different inputs each time) and perform as much of the computation as possible in an offline preprocessing phase before their inputs are known. Along the way we develop...
We introduce a new cryptographic primitive: Proofs of Space-Time (PoSTs) and construct an extremely simple, practical protocol for implementing these proofs. A PoST allows a prover to convince a verifier that she spent a ``space-time'' resource (storing data---space---over a period of time). Formally, we define the PoST resource as a trade-off between CPU work and space-time (under reasonable cost assumptions, a rational user will prefer to use the lower-cost space-time resource over CPU...
Recently there has been much interest in performing search queries over encrypted data to enable functionality while protecting sensitive data. One particularly efficient mechanism for executing such queries is order-preserving encryption/encoding (OPE) which results in ciphertexts that preserve the relative order of the underlying plaintexts thus allowing range and comparison queries to be performed directly on ciphertexts. Recently, Popa et al. (S&P 2013) gave the first construction of...
Proof-of-work is a central concept in modern cryptocurrencies and denial-of-service protection tools, but the requirement for fast verification so far made it an easy prey for GPU-, ASIC-, and botnet-equipped users. The attempts to rely on memory-intensive computations in order to remedy the disparity between architectures have resulted in slow or broken schemes. In this paper we solve this open problem and show how to construct an asymmetric proof-of-work (PoW) based on a computationally...
Secure two-party parallel coin-flipping is a cryptographic functionality that allows two mutually distrustful parties to agree on a common random bit-string of a certain target length. In coin-flipping into-a-well, one party learns the bit-string and then decides whether to abort or to allow the other party to learn it. It is well known that this functionality can be securely achieved in the ideal/real simulation paradigm, using commitment schemes that are simultaneously extractable (X) and...
We describe a zero-knowledge proof system in which a prover holds a large dataset $M$ and can repeatedly prove NP relations about that dataset. That is, for any (public) relation $R$ and $x$, the prover can prove that $\exists w: R(M,x,w)=1$. After an initial setup phase (which depends only on $M$), each proof requires only a constant number of rounds and has communication/computation cost proportional to that of a {\em random-access machine (RAM)} implementation of $R$, up to...
Protocols for secure two-party computation enable a pair of mistrusting parties to compute a joint function of their private inputs without revealing anything but the output. One of the fundamental techniques for obtaining secure computation is that of Yao's garbled circuits. In the setting of malicious adversaries, where the corrupted party can follow any arbitrary (polynomial-time) strategy in an attempt to breach security, the cut-and-choose technique is used to ensure that the garbled...
In 1993, Coppersmith introduced the "factorization factory" approach as a means to speed up the Number Field Sieve algorithm (NFS) when factoring batches of integers of similar size: at the expense of a large precomputation whose cost is amortized when considering sufficiently many integers to factor, the complexity of each individual factorization can then be lowered. We suggest here to extend this idea to the computation of discrete logarithms in finite fields of small characteristic...
We present a new compact verifiable secret sharing scheme, based on this we present the first construction of a homomorphic UC commitment scheme that requires only cheap symmetric cryptography, except for a small number of seed OTs. To commit to a $k$-bit string, the amortized communication cost is $O(k)$ bits. Assuming a sufficiently efficient pseudorandom generator, the computational complexity is $O(k)$ for the verifier and $O(k^{1+\epsilon})$ for the committer (where $\epsilon <1$ is a...
We develop new theoretical tools for proving lower-bounds on the (amortized) complexity of functions in a parallel setting. We demonstrate their use by constructing the first provably secure Memory-hard functions (MHF); a class of functions recently gaining acceptance in practice as an effective means to counter brute-force attacks on security relevant functions. Pebbling games over graphs have proven to be a powerful abstraction for a wide variety of computational models. A dominant...
We present a private information retrieval (PIR) scheme based on a somewhat homomorphic encryption (SWHE). In particular, we customize an NTRU-based SWHE scheme in order to evaluate a specific class of fixed depth circuits relevant for PIR implementation, thus achieving a more practical implementation. In practice, a SWHE that can evaluate a depth 5 circuit is sufficient to construct a PIR capable of retrieving data from a database containing 4 billion rows. We leverage this property in...
In this paper, we investigate the multi-user setting both in public and in secret-key cryptanalytic applications. In this setting, the adversary tries to recover keys of many users in parallel more efficiently than with classical attacks, \textit{i.e.}, the number of recovered keys multiplied by the time complexity to find a single key, by amortizing the cost among several users. One possible scenario is to recover a single key in a large set of users more efficiently than to recover a key...