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...

In this work, we consider the setting where one or more users with low computational resources would lie to outsource the task of proof generation for SNARKs to one external entity, named Prover. We study the scenario in which Provers have access to all statements and witnesses to be proven beforehand. We take a different approach to proof aggregation and design a new protocol that reduces simultaneously proving time and communication complexity, without going through recursive proof...

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...

Order fairness in the context of distributed ledgers has received recently significant attention due to a range of attacks that exploit the reordering and adaptive injection of transactions (violating what is known as “input causality”). To address such concerns an array of definitions for order fairness has been put forth together with impossibility and feasibility results highlighting the difficulty and multifaceted nature of fairness in transaction serialization. Motivated by this we...

Several cryptographic primitives, especially succinct proofs of various forms, transform the satisfaction of high-level properties to the existence of a polynomial quotient between a polynomial that interpolates a set of values with a cleverly arranged divisor. Some examples are SNARKs, like Groth16, and polynomial commitments, such as KZG. Such a polynomial division naively takes $O(n \log n)$ time with Fast Fourier Transforms, and is usually the asymptotic bottleneck for these...

A security proof for a key exchange protocol requires writing down a security definition. Authors typically have a clear idea of the level of security they aim to achieve. Defining the model formally additionally requires making choices on games vs. simulation-based models, partnering, on having one or more Test queries and on adopting a style of avoiding trivial attacks: exclusion, penalizing or filtering. We elucidate the consequences, advantages and disadvantages of the different possible...

Oblivious Transfer (OT) is a fundamental cryptographic primitive, becoming a crucial component of a practical secure protocol. OT is typically implemented in software, and one way to accelerate its running time is by using hardware implementations. However, such implementations are vulnerable to side-channel attacks (SCAs). On the other hand, protecting interactive protocols against SCA is highly challenging because of their longer secrets (which include inputs and randomness), more...

Message Authentication Codes (MACs) are ubiquitous primitives deployed in multiple flavors through standards such as HMAC, CMAC, GMAC, LightMAC, and many others. Its versatility makes it an essential building block in applications necessitating message authentication and integrity checks, in authentication protocols, authenticated encryption schemes, or as a pseudorandom or key derivation function. Its usage in this variety of settings makes it susceptible to a broad range of attack...

The current cryptographic frameworks like RSA, ECC, and AES are potentially under quantum threat. Quantum cryptographic and post-quantum cryptography are being extensively researched for securing future information. The quantum computer and quantum algorithms are still in the early developmental stage and thus lack scalability for practical application. As a result of these challenges, most researched PQC methods are lattice-based, code-based, ECC isogeny, hash-based, and multivariate...

We present a new approach to garbling arithmetic circuits using techniques from homomorphic secret sharing, obtaining constructions with high rate that support free addition gates. In particular, we build upon non-interactive protocols for computing distributed discrete logarithms in groups with an easy discrete-log subgroup, further demonstrating the versatility of tools from homomorphic secret sharing. Relying on distributed discrete log for the Damgård-Jurik cryptosystem (Roy and Singh,...

This work introduces homomorphic secret sharing (HSS) with succinct share size. In HSS, private inputs are shared between parties, who can then homomorphically evaluate a function on their shares, obtaining a share of the function output. In succinct HSS, a portion of the inputs can be distributed using shares whose size is sublinear in the number of such inputs. The parties can then locally evaluate a function $f$ on the shares, with the restriction that $f$ must be linear in the succinctly...

We introduce a new cryptographic primitive called symmetric signcryption, which differs from traditional signcryption because the sender and recipient share a secret key. We prove that a natural composition of symmetric encryption and signatures achieves strong notions of security against attackers that can learn and control many keys. We then identify that the core encryption algorithm of the Keybase encrypted messaging protocol can be modeled as a symmetric signcryption scheme. We prove...

Asymmetric Password-Authenticated Key Exchange (aPAKE) protocols, particularly Strong aPAKE (saPAKE) have enjoyed significant attention, both from academia and industry, with the well-known OPAQUE protocol currently undergoing standardization. In (s)aPAKE, a client and a server collaboratively establish a high-entropy key, relying on a previously exchanged password for authentication. A main feature is its resilience against offline and precomputation (for saPAKE) attacks. OPAQUE, as well as...

In covert adversary model, the corrupted parties can behave in any possible way like active adversaries, but any party that attempts to cheat is guaranteed to get caught by the honest parties with a minimum fixed probability. That probability is called the deterrence factor of covert adversary model. Security-wise, covert adversary is stronger than passive adversary and weaker than active adversary. It is more realistic than passive adversary model. Protocols for covert adversaries are...

Time-lock puzzles are unique cryptographic primitives that use computational complexity to keep information secret for some period of time, after which security expires. Unfortunately, current analysis techniques of time-lock primitives provide no sound mechanism to build multi-party cryptographic protocols which use expiring security as a building block. We explain in this paper that all other attempts at this subtle problem lack either composability, a fully consistent analysis, or...

Foreign field arithmetic often creates significant additional overheads in zero-knowledge proof circuits. Previous work has offloaded foreign arithmetic from proof circuits by using effective and often simple primitives such as Sigma protocols. While these successfully move the foreign field work outside of the circuit, the costs for the Sigma protocol’s verifier still remains high. In use cases where the verifier is constrained computationally this poses a major challenge. One such use case...

In this paper we explore efficient ways to prove correctness of elliptic curve pairing relations. Pairing-based cryptographic protocols such as the Groth16 and Plonk SNARKs and the BLS signature scheme are used extensively in public blockchains such as Ethereum due in large part to their small size. However the relatively high cost of pairing computation remains a practical problem for many use cases such as verification ``in circuit" inside a SNARK. This naturally arises in recursive SNARK...

Fischlin's transform (CRYPTO 2005) is an alternative to the Fiat-Shamir transform that enables straight-line extraction when proving knowledge. In this work we focus on the problem of using the Fischlin transform to construct UC-secure zero-knowledge from Sigma protocols, since UC security -- that guarantees security under general concurrent composition -- requires straight-line (non-rewinding) simulators. We provide a slightly simplified transform that is much easier to understand, and...

A Password-Authenticated Key Exchange (PAKE) protocol allows two parties to agree upon a cryptographic key, in the setting where the only secret shared in advance is a low-entropy password. The standard security notion for PAKE is in the Universal Composability (UC) framework. In recent years there have been a large number of works analyzing the UC-security of Encrypted Key Exchange (EKE), the very first PAKE protocol, and its One-encryption variant (OEKE), both of which compile an...

We suggest the family of ciphers s^E^n, n=2,3,.... with the space of plaintexts (Z*_{2^s})^n, s >1 such that the encryption map is the composition of kind G=G_1A_1G_2A_2 where A_i are the affine transformations from AGL_n(Z_{2^s}) preserving the variety (Z*_{2^s)}^n , Eulerian endomorphism G_i , i=1,2 of K[x_1, x_2,...., x_n] moves x_i to monomial term ϻ(x_1)^{d(1)}(x_2)^{d(2)}...(x_n)^{d(n)} , ϻϵ Z*_{2^s} and act on (Z*_{2^s})^n as bijective transformations. The cipher is...

Cleve's celebrated result (STOC'86) showed that a strongly fair multi-party coin-toss is impossible in the presence of majority-sized coalitions. Recently, however, a fascinating line of work studied a relaxed fairness notion called \emph{game-theoretic fairness}, which guarantees that no coalition should be incentivized to deviate from the prescribed protocol. A sequence of works has explored the feasibility of game-theoretic fairness for \emph{two-sided} coin-toss, and indeed...

Typical results in multi-party computation (in short, MPC) capture faulty parties by assuming a threshold adversary corrupting parties actively and/or fail-corrupting. These corruption types are, however, inadequate for capturing correct parties that might suffer temporary network failures and/or localized faults - these are particularly relevant for MPC over large, global scale networks. Omission faults and general adversary structures have been proposed as more suitable alternatives....

In this paper, we propose a novel bi-primality test to determine whether $N=pq$ is the product of two primes on any RSA modulus in which we relaxed the restriction, $p\equiv q \equiv 3 \Mod{4}$, that was assumed in most of current bi-primality tests. Our bi-primality test is generalized from Lucas primality test to the bi-prime case. Our test always accepts when $p$ and $q$ are both prime, and otherwise accepts with probability at most $1/2$. In addition, we also prove that the...

The use of zero-knowledge Succinct Non-Interactive Arguments of Knowledge (zk-SNARK) and similar types of proofs has become increasingly popular as a solution for improving scalability, privacy, and interoperability of blockchain systems. However, even with the most advanced proving systems, verifying a single SNARK proof can require a significant amount of computational resources making it expensive to be performed on-chain. This becomes a noticeable bottleneck in scaling SNARK-based...

Let n stands for the length of digital signatures with quadratic multivariate public rule in n variables. We construct postquantum secure procedure to sign O(n^t), t ≥1 digital documents with the signature of size n in time O(n^{3+t}). It allows to sign O(n^t), t <1 in time O(n^4). The procedure is defined in terms of Algebraic Cryptography. Its security rests on the semigroup based protocol of Noncommutative Cryptography referring to complexity of the decomposition of the collision...

While many modern cryptographic primitives have stood the test of time, attacker have already begun to expand their attacks beyond classical cryptanalysis by specifically targeting implementations. One of the most well-documented classes of such attacks are subversion (or substitution) attacks, where the attacker replaces the Implementation of the cryptographic primitive in an undetectable way such that the subverted implementation leaks sensitive information of the user during a protocol...

This paper introduces LERNA, a new framework for single-server secure aggregation. Our protocols are tailored to the setting where multiple consecutive aggregation phases are performed with the same set of clients, a fraction of which can drop out in some of the phases. We rely on an initial secret sharing setup among the clients which is generated once-and-for-all, and reused in all following aggregation phases. Compared to prior works [Bonawitz et al. CCS’17, Bell et al. CCS’20], the...

Most existing MPC protocols consider the homogeneous setting, where all the MPC players are assumed to have identical communication and computation resources. In practice, the weakest player often becomes the bottleneck of the entire MPC protocol execution. In this work, we initiate the study of so-called load-balanced MPC in the heterogeneous computing. A load-balanced MPC protocol can adjust the workload of each player accordingly to maximize the overall resource utilization. In...

We present two new constructions for private information retrieval (PIR) in the classical setting where the clients do not need to do any preprocessing or store any database dependent information, and the server does not need to store any client-dependent information. Our first construction (HintlessPIR) eliminates the client preprocessing step from the recent LWE-based SimplePIR (Henzinger et. al., USENIX Security 2023) by outsourcing the "hint" related computation to the server,...

Many secure computation schemes and protocols (such as numerous variants of secure multi-party computation and homomorphic encryption) have favorable performance characteristics when they are used to evaluate addition and scalar multiplication operations on private values that can be represented as ring elements. A purely algebraic argument (with no references to any specific protocol or scheme) can be used to show that the ability to perform these operations is sufficient to implement any...

Computing the distance between two non-normalized vectors $\mathbfit{x}$ and $\mathbfit{y}$, represented by $\Delta(\mathbfit{x},\mathbfit{y})$ and comparing it to a predefined public threshold $\tau$ is an essential functionality used in privacy-sensitive applications such as biometric authentication, identification, machine learning algorithms ({\em e.g.,} linear regression, k-nearest neighbors, etc.), and typo-tolerant password-based authentication. Tackling a widely used distance...

In the traditional consensus problem (aka Byzantine agreement), parties are required to agree on a common value despite the malicious behavior of some of them, subject to the condition that if all the honest parties start the execution with the same value, then that should be the outcome. This problem has been extensively studied by both the distributed computing and cryptographic protocols communities. With the advent of blockchains, whose main application—a distributed ledger—essentially...

Isogeny computations in CSIDH (Asiacrypt 2018) are described using a commutative group G acting on the set of supersingular elliptic curves. The commutativity property gives CSIDH enough flexibility to allow the creation of many cryptographic primitives and protocols. Nevertheless, these operations are limited and more complex applications have not yet been proposed. When calling the composition of two group elements of G addition, our goal in this work is to explore exponentiation,...

Non-malleable cryptography, proposed by Dolev, Dwork, and Naor (SICOMP '00), has numerous applications in protocol composition. In the context of proofs, it guarantees that an adversary who receives a proof cannot maul it into another valid proof. However, non-malleable cryptography (particularly in the non-interactive setting) suffers from an important limitation: An attacker can always copy the proof and resubmit it to another verifier (or even multiple verifiers). In this work, we...

The recent devastating attacks on SIDH rely on the fact that the protocol reveals the images $\varphi(P)$ and $\varphi(Q)$ of the secret isogeny $\varphi : E_0 \rightarrow E$ on a basis $\{P, Q\}$ of the $N$-torsion subgroup $E_0[N]$ where $N^2 > \deg(\varphi)$. To thwart this attack, two recent proposals, M-SIDH and FESTA, proceed by only revealing the images upto unknown scalars $\lambda_1, \lambda_2 \in \mathbb{Z}_N^\times$, i.e., only $\lambda_1 \varphi(P)$ and $\lambda_2 \varphi(Q)$...

Von Ahn, Hopper and Langford introduced the notion of steganographic a.k.a. covert computation, to capture distributed computation where the attackers must not be able to distinguish honest parties from entities emitting random bitstrings. This indistinguishability should hold for the duration of the computation except for what is revealed by the intended outputs of the computed functionality. An important case of covert computation is mutually authenticated key exchange, a.k.a. mutual...

Data formats used for cryptographic inputs have historically been the source of many attacks on cryptographic protocols, but their security guarantees remain poorly studied. One reason is that, due to their low-level nature, formats often fall outside of the security model. Another reason is that studying all of the uses of all of the formats within one protocol is too difficult to do by hand, and requires a comprehensive, automated framework. We propose a new framework, “Comparse”, that...

Sigma protocols are one of the most common and efficient zero-knowledge proofs (ZKPs). Over the decades, a large number of Sigma protocols are proposed, yet few works pay attention to the common design principal. In this work, we propose a generic framework of Sigma protocols for algebraic statements from verifiable secret sharing (VSS) schemes. Our framework provides a general and unified approach to understanding Sigma protocols. It not only neatly explains the classic protocols such as...

While cryptographic protocols are often analyzed in isolation, they are typically deployed within a stack of protocols, where each layer relies on the security guarantees provided by the protocol layer below it, and in turn provides its own security functionality to the layer above. Formally analyzing the whole stack in one go is infeasible even for semi-automated verification tools, and impossible for pen-and-paper proofs. The DY$^\star$ protocol verification framework offers a modular and...

We present TVA, a multi-party computation (MPC) system for secure analytics on secret-shared time series data. TVA achieves strong security guarantees in the semi-honest and malicious settings, and high expressivity by enabling complex analytics on inputs with unordered and irregular timestamps. TVA is the first system to support arbitrary composition of oblivious window operators, keyed aggregations, and multiple filter predicates, while keeping all data attributes private, including record...

It is well known that without randomization, Byzantine agreement (BA) requires a linear number of rounds in the synchronous setting, while it is flat out impossible in the asynchronous setting. The primitive which allows to bypass the above limitation is known as oblivious common coin (OCC). It allows parties to agree with constant probability on a random coin, where agreement is oblivious, i.e., players are not aware whether or not agreement has been achieved. The starting point of our...

In the threshold version of Paillier's encryption scheme, a set of parties collectively holds the secret decryption key through a secret sharing scheme. Whenever a ciphertext is to be decrypted, the parties send their decryption shares, which are then verified for correctness and combined into the plaintext. The scheme has been widely adopted in various applications, from secure voting to general purpose MPC protocols. However, among the handful existing proposals for a maliciously...

Proofs for machine computation allow for proving the correct execution of arbitrary programs that operate over fixed instruction sets (e.g., RISC-V, EVM, Wasm). A standard approach for proving machine computation is to prove a universal set of constraints that encode the full instruction set at each step of program execution. This approach incurs prover cost per execution step on the order of the sum of instruction constraints for instructions in the set despite only a single instruction...

We propose UniPlonK, a modification of the PlonK protocol that uniformizes the Verifier’s work for families of circuits. Specifically, a single fixed-cost “Universal Verifier” can check proofs for circuits of different: sizes, public input lengths, selector polynomials, copy constraints, and even different custom gate sets. UniPlonK therefore extends the universality of PlonK beyond the SRS; it enables a single “Universal Verifier Circuit” capable of verifying proofs from different PlonK...

Pairings are useful tools in isogeny-based cryptography and have been used in SIDH/SIKE and other protocols. As a general technique, pairings can be used to move problems about points on curves to elements in finite fields. However, until now, their applicability was limited to curves over fields with primes of a specific shape and pairings seemed too costly for the type of primes that are nowadays often used in isogeny-based cryptography. We remove this roadblock by optimizing pairings for...

Differential obliviousness (DO) is a privacy notion which mandates that the access patterns of a program satisfy differential privacy. Earlier works have shown that in numerous applications, differential obliviousness allows us to circumvent fundamental barriers pertaining to fully oblivious algorithms, resulting in asymptotical (and sometimes even polynomial) performance improvements. Although DO has been applied to various contexts, including the design of algorithms, data structures, and...

Accumulation is a simple yet powerful primitive that enables incrementally verifiable computation (IVC) without the need for recursive SNARKs. We provide a generic, efficient accumulation (or folding) scheme for any $(2k-1)$-move special-sound protocol with a verifier that checks $\ell$ degree-$d$ equations. The accumulation verifier only performs $k+2$ elliptic curve multiplications and $k+d+O(1)$ field/hash operations. Using the compiler from BCLMS21 (Crypto 21), this enables building...

In this paper we introduce a novel version of the Joye-Libert cryptosystem that allows users to decrypt without knowing the factorisation of the composite modulus. Then we use our construction as a building block for a threshold decryption protocol of the homomorphic Joye-Libert encryption scheme. Finally, we present several extensions of the threshold cryptosystem.

Central Bank Digital Currency (CBDC) is in the phase of discussion in most of countries. In this paper, we consider the security issues of centralized retail CBDC. Our focus is on the design and analysis of the underlying cryptographic protocol. The main security requirements against the protocol are transaction anonymity and protection against tax evasion. The protocol provides security guarantees in case of the strongest model of an execution environment which is the general concurrent...

Computationally sound protocol verification tools promise to deliver full-strength cryptographic proofs for security protocols. Unfortunately, current tools lack either modularity or automation. We propose a new approach based on a novel use of information flow and refinement types for sound cryptographic proofs. Our framework, Owl, allows type-based modular descriptions of security protocols, wherein disjoint subprotocols can be programmed and automatically proved secure separately....

Wireless-channel key exchange (WiKE) protocols that leverage Physical Layer Security (PLS) techniques could become an alternative solution for secure communication establishment, such as vehicular ad-hoc networks, wireless IoT networks, or cross-layer protocols. In this paper, we provide a novel abstraction of WiKE protocols and present the first game-based security model for WiKE. Our result enables the analysis of security guarantees offered by these cross-layer protocols and allows the...

The introduction of time-lock puzzles initiated the study of publicly “sending information into the future.” For time-lock puzzles, the underlying security-enabling mechanism is the computational complexity of the operations needed to solve the puzzle, which must be tunable to reveal the solution after a predetermined time, and not before that time. Time-lock puzzles are typically constructed via a commitment to a secret, paired with a reveal algorithm that sequentially iterates a basic...

OPAQUE is an Asymmetric Password-Authenticated Key Exchange (aPAKE) protocol being standardized by the IETF (Internet Engineering Task Force) as a more secure alternative to the traditional ``password-over-TLS'' mechanism prevalent in current practice. OPAQUE defends against a variety of vulnerabilities of password-over-TLS by dispensing with reliance on PKI and TLS security, and ensuring that the password is never visible to servers or anyone other than the client machine where the password...

Recently, SIDH was broken by a series of attacks. To avoid the attacks, several new countermeasures, such as M-SIDH and binSIDH, have been developed. Different from SIDH, the new SIDH-like schemes have relatively large public key sizes. Besides, the orders of the torsion groups considered in new SIDH-like schemes are the products of many primes. Therefore, the key compression techniques in SIDH can not be directly applied to these schemes. It remains an open problem to compress the public...

Non-interactive zero-knowledge proofs (NIZKs) and in particular succinct NIZK arguments of knowledge (zk-SNARKs) increasingly see real-world adoption in large and complex systems. Many zk-SNARKs require a trusted setup, i.e., a common reference string (CRS), and for practical use it is desirable to reduce the trust in the CRS generation. The latter can be achieved via the notions of subversion or updatable CRS. Another important property when deployed in large systems is the ability to...

An important research direction in secure multi-party computation (MPC) is to improve the efficiency of the protocol. One idea that has recently received attention is to consider a slightly weaker security model than full malicious security -- the so-called setting of $\textit{covert security}$. In covert security, the adversary may cheat but only is detected with certain probability. Several works in covert security consider the offline/online approach, where during a costly offline phase...

Distributed key generation (DKG) allows bootstrapping threshold cryptosystems without relying on a trusted party, nowadays enabling fully decentralized applications in blockchains and multiparty computation (MPC). While we have recently seen new advancements for asynchronous DKG (ADKG) protocols, their performance remains the bottleneck for many applications, with only one protocol being implemented (DYX+ ADKG, IEEE S&P 2022). DYX+ ADKG relies on the Decisional Composite Residuosity...

This paper presents a code-based signature scheme based on the well-known syndrome decoding (SD) problem. The scheme builds upon a recent line of research which uses the Multi-Party-Computation-in-the-Head (MPCitH) approach to construct efficient zero-knowledge proofs, such as Syndrome Decoding in the Head (SDitH), and builds signature schemes from them using the Fiat-Shamir transform. At the heart of our proposal is a new approach, Hypercube-MPCitH, to amplify the soundness of any MPC...

Accountability is a well-established and widely used security concept that allows for obtaining undeniable cryptographic proof of misbehavior, thereby incentivizing honest behavior. There already exist several general purpose accountability frameworks for formal game-based security analyses. Unfortunately, such game-based frameworks do not support modular security analyses, which is an important tool to handle the complexity of modern protocols. Universal composability (UC) models...

Post-Compromise Security (PCS) is a property of secure-channel establishment schemes, which limits the security breach of an adversary that has compromised one of the endpoint to a certain number of messages, after which the channel heals. An attractive property, especially in view of Snowden's revelation of mass-surveillance, PCS was pioneered by the Signal messaging protocol, and is present in OTR. In this paper, we introduce a framework for quantifying and comparing PCS security, with...

SNARK is a well-known family of cryptographic tools that is increasingly used in the field of computation integrity at scale. In this area, multiple works have introduced SNARK-friendly cryptographic primitives: hashing, but also encryption and signature verification. Despite all the efforts to create cryptographic primitives that can be proved faster, it remains a major performance hole in practice. In this paper, we present a recursive technique that can improve the efficiency of the...

Verifiable random functions (Micali et al., FOCS'99) allow a key-pair holder to verifiably evaluate a pseudorandom function under that particular key pair. These primitives enable fair and verifiable pseudorandom lotteries, essential in proof-of-stake blockchains such as Algorand and Cardano, and are being used to secure billions of dollars of capital. As a result, there is an ongoing IRTF effort to standardize VRFs, with a proposed ECVRF based on elliptic-curve cryptography appearing as the...

Zero-knowledge proof is a powerful cryptographic primitive that has found various applications in the real world. However, existing schemes with succinct proof size suffer from a high overhead on the proof generation time that is super-linear in the size of the statement represented as an arithmetic circuit, limiting their efficiency and scalability in practice. In this paper, we present Orion, a new zero-knowledge argument system that achieves $O(N)$ prover time of field operations and hash...

Coin mixing services allow users to mix their cryptocurrency coins and thus enable unlinkable payments in a way that prevents tracking of honest users' coins by both the service provider and the users themselves. The easy bootstrapping of new users and backwards compatibility with cryptocurrencies (such as Bitcoin) with limited support for scripts are attractive features of this architecture, which has recently gained considerable attention in both academia and industry. A recent work...

We formalize security properties of zero-knowledge protocols and their proofs in EasyCrypt. Specifically, we focus on sigma-protocols (three-round protocols). Most importantly, we also cover properties whose security proofs require the use of rewinding; prior work has focused on properties that do not need this more advanced technique. On our way we give generic definitions of the main properties associated with sigma protocols, both in the computational and ...

Secure multi-party computation (MPC) protocols that are resilient to a dishonest majority allow the adversary to get the output of the computation while, at the same time, forcing the honest parties to abort. Aumann and Lindell introduced the enhanced notion of security with identifiable abort, which still allows the adversary to trigger an abort but, at the same time, it enables the honest parties to agree on the identity of the party that led to the abort. More recently, in Eurocrypt 2016,...

Zero Knowledge proofs of Elliptic Curve Inner Products (ECIPs) and elliptic curve operations more generally are an increasingly important part of zero knowledge protocols and a significant bottle neck in recursive proof composition over amicable cycles of elliptic curves. To prove ECIPs more efficiently, I represent a collection of points that sum to zero using a polynomial element of the function field and evaluate this function at a random principal divisor. By Weil reciprocity, this is...

One of the most successful applications of peer-to-peer communication networks is in the context of blockchain protocols, which—in Satoshi Nakamoto's own words—rely on the "nature of information being easy to spread and hard to stifle." Significant efforts were invested in the last decade into analyzing the security of these protocols, and invariably the security arguments known for longest-chain Nakamoto-style consensus use an idealization of this tenet. Unfortunately, the real-world...

We show that for $\mathbf{x}\gets [0,2^\lambda)^\mu$ and any integer $N$ the probability that $f(\mathbf{x})\equiv 0 \bmod N$ for any non-zero multilinear polynomial $f\in \mathbb{Z}[X_1, \dots,X_\mu]$, co-prime to $N$ is inversely proportional to $N$. As a corollary we show that if $\log_2 N\geq \log_2(2\mu)\lambda+8\mu^2 $ then the probability is bounded by $\frac{\mu+1}{2^\lambda}$. We also give tighter numerically derived bounds, showing that if $\log_2 N\geq {418}$, and $\mu\leq 20$ the...

The goal of this paper is to improve the efficiency and applicability of straightline extraction techniques in the random oracle model. Straightline extraction in the random oracle model refers to the existence of an extractor, which given the random oracle queries made by a prover $P^*(x)$ on some theorem $x$, is able to produce a witness $w$ for $x$ with roughly the same probability that $P^*$ produces a verifying proof. This notion applies to both zero-knowledge protocols and verifiable...

We model and analyze the Signal end-to-end secure messaging protocol within the Universal Composability (UC) framework. Specifically: (1) We formulate an ideal functionality that captures end-to-end secure messaging in a setting with Public Key Infrastructure (PKI) and an untrusted server, against an adversary that has full control over the network and can adaptively and momentarily compromise parties at any time, obtaining their entire internal states. Our analysis captures the forward...

In a multiparty signing protocol, also known as a threshold signature scheme, the private signing key is shared amongst a set of parties and only a quorum of those parties can generate a signature. Research on multiparty signing has been growing in popularity recently due to its application to cryptocurrencies. Most work has focused on reducing the number of rounds to two, and as a result: (a) are not fully simulatable in the sense of MPC real/ideal security definitions, and/or (b) are not...

We introduce the Spiral family of single-server private information retrieval (PIR) protocols. Spiral relies on a composition of two lattice-based homomorphic encryption schemes: the Regev encryption scheme and the Gentry-Sahai-Waters encryption scheme. We introduce new ciphertext translation techniques to convert between these two schemes and in doing so, enable new trade-offs in communication and computation. Across a broad range of database configurations, the basic version of Spiral...

Numerous cryptographic applications require efficient non-interactive zero-knowledge proofs of knowledge (NIZKPoK) as a building block. Typically they rely on the Fiat-Shamir heuristic to do so, as security in the random-oracle model is considered good enough in practice. However, there is a troubling disconnect between the stand-alone security of such a protocol and its security as part of a larger, more complex system where several protocols may be running at the same time. Provable...

Subversion attacks undermine security of cryptographic protocols by replacing a legitimate honest party's implementation with one that leaks information in an undetectable manner. An important limitation of all currently known techniques for designing cryptographic protocols with security against subversion attacks is that they do not automatically guarantee security in the realistic setting where a protocol session may run concurrently with other protocols. We remedy this situation by...

Universal Composability is a widely used concept for the design and analysis of protocols. Since Canetti's original UC model and the model by Pfitzmann and Waidner several different models for universal composability have been proposed, including, for example, the IITM model, GNUC, CC, but also extensions and restrictions of the UC model, such as JUC, GUC, and SUC. These were motivated by the lack of expressivity of existing models, ease of use, or flaws in previous models. Cryptographers...

We describe a technique to backdoor a prime factor of a composite odd integer $N$, so that an attacker knowing a possibly secret factor base $\mathcal{B}$, can efficiently retrieve it from $N$. Such method builds upon Complex Multiplication theory for elliptic curves, by generating primes $p$ associated to $\mathcal{B}$-smooth order elliptic curves over $\mathbb{F}_p$. When such primes $p$ divide an integer $N$, the latter can be efficiently factored using a generalization of Lenstra's...

Secure multiparty computation enables mutually distrusting parties to compute a public function of their secret inputs. One of the main approaches for designing MPC protocols are garbled circuits whose core component is usually referred to as a garbling scheme. In this work, we revisit the security of Yao’s garbling scheme and provide a modular security proof which composes the security of multiple layer garblings to prove security of the full circuit garbling. We perform our security proof...

Most existing work on secure multi-party computation (MPC) ignores a key idiosyncrasy of modern communication networks, that there are a limited number of communication paths between any two nodes, many of which might even be corrupted. The problem becomes particularly acute in the information-theoretic setting, where the lack of trusted setups (and the cryptographic primitives they enable) makes communication over sparse networks more challenging. The work by Garay and Ostrovsky...

We consider the task of designing secure computation protocols in an unstable network where honest parties can drop out at any time, according to a schedule provided by the adversary. This type of setting, where even honest parties are prone to failures, is more realistic than traditional models, and has therefore gained a lot of attention recently. Our model, Phoenix, enables a new approach to secure multiparty computation with dropouts, allowing parties to drop out and re-enter the...

The algebraic-group model (AGM), which lies between the generic group model and the standard model of computation, provides a means by which to analyze the security of cryptosystems against so-called algebraic adversaries. We formalize the AGM within the framework of universal composability, providing formal definitions for this setting and proving an appropriate composition theorem. This extends the applicability of the AGM to more-complex protocols, and lays the foundations for analyzing...

We advance the state-of-the art for zero-knowledge commit-and-prove SNARKs (CP-SNARKs). CP-SNARKs are an important class of SNARKs which, using commitments as ``glue'', allow to efficiently combine proof systems---e.g., general-purpose SNARKs (an efficient way to prove statements about circuits) and $\Sigma$-protocols (an efficient way to prove statements about group operations). Thus, CP-SNARKs allow to efficiently provide zero-knowledge proofs for composite statements such as $h=H(g^{x})$...

We present probabilistic dynamic I/O automata, a framework to model dynamic probabilistic systems. Our work extends dynamic I/O Automata formalism of Attie & Lynch to probabilistic setting. The original dynamic I/O Automata formalism included operators for parallel composition, action hiding, action renaming, automaton creation, and behavioral sub-typing by means of trace inclusion. They can model mobility by using signature modification. They are also hierarchical: a dynamically changing...

Multi-party computation (MPC) allows two or more parties to jointly and securely compute functions over private inputs. Cryptographic protocols that realize MPC require functions to be expressed as Boolean or arithmetic circuits. Deriving such circuits is either done manually, or with hardware synthesis tools and specialized MPC compilers. Unfortunately, such existing tools compile only from a single front-end language and neglect decades of research for optimizing regular compilers. In...

The advent of blockchain protocols has reignited the interest in adaptively secure broadcast, as it is by now well understood that broadcasting over a diffusion network allows an adaptive adversary to corrupt the sender depending on the message it attempts to send and change it. Hirt and Zikas [Eurocrypt '10] proved that this is an inherent limitation of broadcast in the simulation-based setting---i.e., that this task is impossible against an adaptive adversary corrupting a strict majority...

A dominant approach towards the solution of the scalability problem in blockchain systems has been the development of layer 2 protocols and specifically payment channel networks (PCNs) such as the Lightning Network (LN) over Bitcoin. Routing payments over LN requires the coordination of all path intermediaries in a multi-hop round trip that encumbers the layer 2 solution both in terms of responsiveness as well as privacy. The issue is resolved by “virtual channel” protocols that,...

Consider a server with a large set $S$ of strings $\{x_1,x_2, \dots,x_N\}$ that would like to publish a small hash $h$ of its set $S$ such that any client with a string $y$ can send the server a short message allowing it to learn $y$ if $y \in S$ and nothing otherwise. In this work, we study this problem of two-round private set intersection (PSI) with low (asymptotically optimal) communication cost, or what we call laconic private set intersection ($\ell$PSI) and its extensions. This...

We consider threshold public-key encryption, where the decryption servers distributively hold the private key shares, and we need a threshold of these servers to decrypt the message (while the system remains secure when less than the threshold is corrupt). We investigate the notion of chosen-ciphertext secure threshold systems which has been historically hard to achieve. We further require the systems to be, both, adaptively secure (i.e., secure against a strong adversary making corruption...

We analyze the security of the TLS 1.3 key establishment protocol, as specified at the end of its rigorous standardization process. We define a core key-schedule and reduce its security to concrete assumptions against an adversary that controls client and server configurations and adaptively chooses some of their keys. Our model supports all key derivations featured in the standard, including its negotiated modes and algorithms that combine an optional Diffie-Hellman exchange for...

Proofs of partial knowledge demonstrate the possession of certain subsets of witnesses for a given collection of statements $x_1,\dots,x_n$. Cramer, Damgård, and Schoenmakers (CDS), built proofs of partial knowledge, given ``atomic'' protocols for individual statements $x_i$, by having the prover randomly secret share the verifier's challenge and using the shares as challenges for the atomic protocols. This simple and highly-influential transformation has been used in numerous applications,...

Large semigroups and groups of transformations of finite affine space of dimension n with the option of computability of the composition of n arbitrarily chosen elements in polynomial time are described in the paper. Constructions of such families are given together with effectively computed homomorphisms between members of the family. These algebraic platforms allow us to define protocols for several generators of subsemigroup of affine Cremona semigroups with several outputs. Security of...

The high demand for customer-centric applications such as secure cloud storage laid the foundation for the development of user-centric security protocols with multiple security features in recent years. But, the current state-of-art techniques primarily emphasized only one type of security feature i.e., either homomorphism or non-malleability. In order to fill this gap and provide a common platform for both homomorphic and non-malleable cloud applications, we have introduced a new public key...

Trusted execution enviroments (TEEs) enable secure execution of program on untrusted hosts and cryptographically attest the correctness of outputs. As these are complex systems, it is hard to capture the exact security achieved by protocols employing TEEs. Crucially TEEs are typically employed in multiple protocols at the same time, thus composable security (with global subroutines) is a natural goal for such systems. We show that under an attested execution setup $G_\mathsf{att}$ we can...

We describe a simple method for solving the distributed discrete logarithm problem in Paillier groups, allowing two parties to locally convert multiplicative shares of a secret (in the exponent) into additive shares. Our algorithm is perfectly correct, unlike previous methods with an inverse polynomial error probability. We obtain the following applications and further results. - Homomorphic secret sharing. We construct homomorphic secret sharing for branching programs with *negligible*...

Blockchain technologies have received a great amount of attention, and its immutability is paramount to facilitate certain applications requiring persistent records. However, in many other use-cases, tremendous real-world incidents have exposed the harm of strict immutability. For example, illicit data stored in immutable blockchain poses numerous challenges for law enforcement agencies such as Interpol, and millions of dollars are lost due to the vulnerabilities of immutable smart contract....

Sharding is an emerging technique to overcome scalability issues on blockchain based public ledgers. Without sharding, every node in the network has to listen to and process all ledger protocol messages. The basic idea of sharding is to parallelize the ledger protocol: the nodes are divided into smaller subsets that each take care of a fraction of the original load by executing lighter instances of the ledger protocol, also called shards. The smaller the shards, the higher the efficiency, as...

Zero-knowledge succinct non-interactive arguments (zk-SNARKs) rely on knowledge assumptions for their security. Meanwhile, as the complexity and scale of cryptographic systems continues to grow, the composition of secure protocols is of vital importance. The current gold standards of composable security, the Universal Composability and Constructive Cryptography frameworks cannot capture knowledge assumptions, as their core proofs of composition prohibit white-box extraction. In this paper,...

Cryptographic communication protocols provide confidentiality, integrity and authentication properties for end-to- end communication under strong corruption attacks, including, notably, post-compromise security (PCS). Most protocols are designed for one-to-one communication. Protocols for group communication are less common, less efficient, and tend to provide weaker security guarantees. This is because group communication poses unique challenges, such as coordinated key updates, changes to...

Multi-Party Non-Interactive Key Exchange (MP-NIKE) is a fundamental cryptographic primitive in which users register into a key generation centre and receive a public/private key pair each. After that, any subset of these users can compute a shared key without any interaction. Nowadays, IoT devices suffer from a high number and large size of messages exchanged in the Key Management Protocol (KMP). To overcome this, an MP-NIKE scheme can eliminate the airtime and latency of messages...

This paper describes a non-interactive process allowing a prover to convince a verifier that a modulus $n$ is the product of two primes ($p,q$) of about the same size. A further heuristic argument conjectures that $p-1$ and $q-1$ have sufficiently large prime factors for cryptographic applications. The new protocol relies upon elementary number-theoretic properties and can be implemented efficiently using very few operations. This contrasts with state-of-the-art zero-knowledge protocols for...