A hybrid cryptosystem combines two systems that fulfill the same cryptographic functionality, and its security enjoys the security of the harder one. There are many proposals for hybrid public-key encryption (hybrid PKE), hybrid signature (hybrid SIG) and hybrid authenticated key exchange (hybrid AKE). In this paper, we fill the blank of Hybrid Password Authentication Key Exchange (hybrid PAKE). For constructing hybrid PAKE, we first define an important class of PAKE -- full DH-type...

This work proposes a new white-box attack technique called filtering, which can be combined with any other trace-based attack method. The idea is to filter the traces based on the value of an intermediate variable in the implementation, aiming to fix a share of a sensitive value and degrade the security of an involved masking scheme. Coupled with LDA (filtered LDA, FLDA), it leads to an attack defeating the state-of-the-art SEL masking scheme (CHES 2021) of arbitrary degree and number of...

Incremental Verifiable Computation (IVC) allows a prover to prove to a verifier the correct execution of a sequential computation. Recent works focus on improving the universality and efficiency of IVC Schemes, which can be categorized into Accumulation and Folding-based IVCs with Folding-based ones being more efficient (due to their deferred proof generation until the final step). Unfortunately, both approaches satisfy only heuristic security as they model the Random Oracle (RO) as a...

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...

Side-channel attacks are a fundamental threat to the security of cryptographic implementations. One of the most prominent countermeasures against side-channel attacks is masking, where each intermediate value of the computation is secret shared, thereby concealing the computation's sensitive information. An important security model to study the security of masking schemes is the random probing model, in which the adversary obtains each intermediate value of the computation with some...

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...

Hybrid post-quantum cryptography is a cautious approach that aims to guard against the threat posed by the quantum computer, through the simultaneous use of Post-Quantum (PQ) and classical (i.e. pre-quantum) cryptosystems, should the post-quantum schemes used prove insecure. Regarding the hybridization of Key Encapsulation Mechanisms (KEMs), most recent studies focus on safely combining the symmetric keys out- put by a parallel execution of classical and post-quantum KEMs. While this...

This draft presents work-in-progress concerning hybrid/composite signature schemes. More concretely, we give several tailored combinations of Fiat-Shamir based signature schemes (such as Dilithium) or Falcon with RSA or DSA. We observe that there are a number of signature hybridization goals, few of which are not achieved through parallel signing or concatenation approaches. These include proof composability (that the post-quantum hybrid signature security can easily be linked to the...

We present a new generic transform that takes a multi-round interactive proof for the membership of a language $\mathcal{L}$ and outputs a non-interactive zero-knowledge proof (not of knowledge) in the common reference string model. Similar to the Fiat-Shamir transform, it requires a hash function $\mathsf{H}$. However, in our transform the zero-knowledge property is in the standard model, and the adaptive soundness is in the non-programmable random oracle model ($\mathsf{NPROM}$). ...

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...

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,...

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...

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...

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...

A quantum bit commitment scheme is to realize bit (rather than qubit) commitment by exploiting quantum communication and quantum computation. In this work, we study the binding property of the quantum string commitment scheme obtained by composing a generic quantum perfectly(resp. statistically)-hiding computationally-binding bit commitment scheme (which can be realized based on quantum-secure one-way permutations(resp. functions)) in parallel. We show that the resulting scheme satisfies a...

While unconditionally-secure quantum bit commitment (allowing both quantum computation and communication) is impossible, researchers turn to study the complexity-based one. A complexity-based canonical (non-interactive) quantum bit commitment scheme refers to a kind of scheme such that the commitment consists of just a single (quantum) message from the sender to the receiver that can be opened later by uncomputing the commit stage. In this work, we study general properties of...

The standard model security of the Fiat-Shamir transform has been an active research area for many years. In breakthrough results, Canetti et al. (STOC'19) and Peikert-Shiehian (Crypto'19) showed that, under the Learning-With-Errors (LWE) assumption, it provides soundness by applying correlation-intractable (CI) hash functions to so-called trapdoor $\Sigma$-protocols. In order to be compatible with CI hash functions based on standard LWE assumptions with polynomial approximation factors,...

In most post-quantum signature protocols, the verification procedure leaks information about which signature is being verified, and/or which public key is being used to verify the signature, to timing and other side-channel attacks. In some applications, this information leak is a breach of user privacy or system security. One class of signature protocols, based on the parallel composition of many runs of one or more interactive cut-and-choose protocols, can be modified to enable...

This paper studies constructions of pseudorandom functions (PRFs) from non-adaptive PRFs (naPRFs), i.e., PRFs which are secure only against distinguishers issuing all of their queries at once. Berman and Haitner (Journal of Cryptology, '15) gave a one-call construction which, however, is not hardness preserving -- to obtain a secure PRF (against polynomial-time distinguishers), they need to rely on a naPRF secure against superpolynomial-time distinguishers; in contrast, all known...

Blockchain protocols based on variations of the longest-chain rule—whether following the proof-of-work paradigm or one of its alternatives—suffer from a fundamental latency barrier. This arises from the need to collect a sufficient number of blocks on top of a transaction-bearing block to guarantee the transaction’s stability while limiting the rate at which blocks can be created in order to prevent security-threatening forks. Our main result is a black-box security-amplifying combiner based...

Sidechains are an appealing innovation devised to enable blockchain scalability and extensibility. The basic idea is simple yet powerful: construct a parallel chain - sidechain - with desired features, and provide a way to transfer coins between the mainchain and the sidechain. In this paper, we introduce Zendoo, a construction for Bitcoin-like blockchain systems that allows the creation and communication with sidechains of different types without knowing their internal structure. We...

Many constructions based on multilinear maps require independent slots in the plaintext, so that multiple computations can be performed in parallel over the slots. Such constructions are usually based on CLT13 multilinear maps, since CLT13 inherently provides a composite encoding space. However, a vulnerability was identified at Crypto 2014 by Gentry, Lewko and Waters, with a lattice-based attack in dimension 2, and the authors have suggested a simple countermeasure. In this paper, we...

Two of the most significant challenges in the design of blockchain protocols is increasing their transaction processing throughput and minimising latency in terms of transaction settlement. In this work we put forth for the first time a formal execution model that enables to express transaction throughput while supporting formal security arguments regarding safety and liveness. We then introduce parallel-chains, a simple yet powerful non-black-box composition technique for blockchain...

In this paper, we present a low complexity bit-parallel Montgomery multiplier for $GF(2^m)$ generated with a special class of irreducible pentanomials $x^m+x^{m-1}+x^k+x+1$. Based on a combination of generalized polynomial basis (GPB) squarer and a newly proposed square-based divide and conquer approach, we can partition field multiplications into a composition of sub-polynomial multiplications and Montgomery/GPB squarings, which have simpler architecture and thus can be implemented...

An important benchmark for multi-party computation protocols (MPC) is their round complexity. For several important MPC tasks, such as broadcast, (tight) lower bounds on the round complexity are known. However, some of these lower bounds can be circumvented when the termination round of every party is not a priori known, and simultaneous termination is not guaranteed. Protocols with this property are called \emph{probabilistic-termination (PT)} protocols. Running PT protocols in parallel...

Verifiable encryption allows one to prove properties about encrypted data and is an important building block in the design of cryptographic protocols, e.g., group signatures, key escrow, fair exchange protocols, etc. Existing lattice-based verifiable encryption schemes, and even just proofs of knowledge of the encrypted data, require parallel composition of proofs to reduce the soundness error, resulting in proof sizes that are only truly practical when amortized over a large number of...

When analyzing the round complexity of multi-party protocols, one often overlooks the fact that underlying resources, such as a broadcast channel, can by themselves be expensive to implement. For example, it is well known that it is impossible to implement a broadcast channel by a (deterministic) protocol in a sub-linear (in the number of corrupted parties) number of rounds. The seminal works of Rabin and Ben-Or from the early 80's demonstrated that limitations as the above can be overcome...

Large computations, when amenable to distributed parallel execution, are often executed on computer clusters, for scalability and cost reasons. Such computations are used in many applications, including, to name but a few, machine learning, webgraph mining, and statistical machine translation. Oftentimes, though, the input data is private and only the result of the computation can be published. Zero-knowledge proofs would allow, in such settings, to verify correctness of the output without...

Network firewalls are a standard security measure in computer networks that connect to the Internet. Often, ready-to-use firewall appliances are trusted to protect the network from malicious Internet traffic. However, because of their black-box nature, no one can be sure of their exact functionality. We address the possibility of actively compromised firewalls. That is, we consider the possibility that a network firewall might collaborate with an outside adversary to attack the network. To...

Most cryptographic security proofs require showing that two systems are indistinguishable. A central tool in such proofs is that of a game, where winning the game means provoking a certain condition, and it is shown that the two systems considered cannot be distinguished unless this condition is provoked. Upper bounding the probability of winning such a game, i.e., provoking this condition, for an arbitrary strategy is usually hard, except in the special case where the best strategy for...

In this paper, a new bit-parallel Montgomery multiplier for $GF(2^m)$ is presented, where the field is generated with an irreducible trinomial. We first present a slightly generalized version of a newly proposed divide and conquer approach. Then, by combining this approach and a carefully chosen Montgomery factor, the Montgomery multiplication can be transformed into a composition of small polynomial multiplications and Montgomery squarings, which are simpler and more efficient. Explicit...

We consider the client-server setting for the concurrent composition of secure protocols: in this setting, a single server interacts with multiple clients concurrently, executing with each client a specified protocol where only the client should receive any nontrivial output. Such a setting is easily motivated from an application standpoint. There are important special cases for which positive results are known – such as concurrent zero knowledge protocols – and it has been an open question...

In implementation of elliptic curve cryptography, three kinds of finite fields have been widely studied, i.e. prime field, binary field and optimal extension field. In pairing-based cryptography, however, pairing-friendly curves are usually chosen among ordinary curves over prime fields and supersingular curves over extension fields with small characteristics. In this paper, we study pairings on elliptic curves over extension fields from the point of view of accelerating the Miller's...

In [DNRS99, DNRS03], Dwork et al. opened the fundamental question of existence of commitment schemes that are secure against selective opening attacks (SOA, for short). In [BHY09] Bellare, Hofheinz, and Yilek, and Hofheinz in [Hof11] solved this problem positively by presenting a scheme which is based on non-black-box use of a one-way permutation and which has super- constant number of rounds. The achieved solution however opened other challenging questions on improvements of round...

Recently, composite-order bilinear pairing has been shown to be useful in many cryptographic constructions. However, it is time-costly to evaluate. This is because the composite order should be at least 1024bit and, hence, the elliptic curve group order $n$ and base field become too large, rendering the bilinear pairing algorithm itself too slow to be practical (e.g., the Miller loop is $\Omega(n)$). Thus, composite-order computation easily becomes the bottleneck of a cryptographic...

We present a modular iterated block cipher suitable for 32-bit parallel computing environments. The cipher implements a Substitution Permutation Network (SPN) on 128-bit blocks using 128-bit keys.

A fundamental question in leakage-resilient cryptography is: can leakage resilience always be amplified by parallel repetition? It is natural to expect that if we have a leakage-resilient primitive tolerating $\ell$ bits of leakage, we can take $n$ copies of it to form a system tolerating $n\ell$ bits of leakage. In this paper, we show that this is not always true. We construct a public key encryption system which is secure when at most $\ell$ bits are leaked, but if we take $n$ copies of...

We revisit the composability of different forms of zero-knowledge proofs when the honest prover strategy is restricted to be polynomial time (given an appropriate auxiliary input). Our results are: \begin{enumerate} \item When restricted to efficient provers, the original Goldwasser--Micali--Rackoff (GMR) definition of zero knowledge (STOC `85), here called \emph{plain zero knowledge}, is closed under a constant number of sequential compositions (on the same input). This contrasts with the...

Selective opening attacks against commitment schemes occur when the commitment scheme is repeated in parallel and an adversary can choose depending on the commit-phase transcript to see the values and openings to some subset of the committed bits. Commitments are secure under such attacks if one can prove that the remaining, unopened commitments stay secret. We prove the following black-box constructions and black-box lower bounds for commitments secure against selective opening attacks...

For many cryptographic protocols, security relies on the assumption that adversarial entities have limited computational power. This type of security degrades progressively over the lifetime of a protocol. However, some cryptographic services, such as timestamping services or digital archives, are long-lived in nature; they are expected to be secure and operational for a very long time (i.e. super-polynomial). In such cases, security cannot be guaranteed in the traditional sense: a...

The *selective decommitment problem* can be described as follows: assume an adversary receives a number of commitments and then may request openings of, say, half of them. Do the unopened commitments remain secure? Although this question arose more than twenty years ago, no satisfactory answer could be presented so far. We answer the question in several ways: - If simulation-based security is desired (i.e., if we demand that the adversary's output can be simulated by a machine that does not...

Elliptic curve cryptography (ECC), independently introduced by Koblitz and Miller in the 80's, has attracted increasing attention in recent years due to its shorter key length requirement in comparison with other public-key cryptosystems such as RSA. Shorter key length means reduced power consumption and computing effort, and less storage requirement, factors that are fundamental in ubiquitous portable devices such as PDAs, cellphones, smartcards, and many others. To that end, a lot of...

For many cryptographic protocols, security relies on the assumption that adversarial entities have limited computational power. This type of security degrades progressively over the lifetime of a protocol. However, some cryptographic services, such as timestamping services or digital archives, are long-lived in nature; they are expected to be secure and operational for a very long time (i.e., super-polynomial). In such cases, security cannot be guaranteed in the traditional sense: a...

A random system is the abstraction of the input-output behavior of any kind of discrete system, in particular cryptographic systems. Many aspects of cryptographic security analyses and proofs can be seen as the proof that a certain random system (e.g. a block cipher) is indistinguishable from an ideal system (e.g. a random permutation), for different types of distinguishers. This paper presents a new generic approach to proving upper bounds on the distinguishing advantage of a combined...

In [3] the authors give the first mathematical formalization of an unconditionally secure commitment scheme. Their construction has some similarities to one used to build authentication codes, so they raise the question whether there is some relation between commitment schemes and authentication schemes. They conjecture that authentication schemes with arbitration can be used, but they stress that the information flows are different. In this paper, we show that there is indeed a relation...

A fundamental problem of distributed computing is that of simulating a secure broadcast channel, within the setting of a point-to-point network. This problem is known as Byzantine Agreement (or Generals) and has been the focus of much research. Lamport et al. showed that in order to achieve Byzantine Agreement in the standard model, more than 2/3 of the participating parties must be honest. They further showed that by augmenting the network with a public-key infrastructure for digital...

We study the problem of securely extending the domain of a collision resistant compression function. A new construction based on directed acyclic graphs is described. This generalizes the usual iterated hashing constructions. Our main contribution is to introduce a new technique for hashing arbitrary length strings. Combined with DAG based hashing, this technique gives a new hashing algorithm. The amount of padding and the number of invocations of the compression function required by the new...

We present a new, elegant composition method for joint signature and encryption, also referred to as signcryption. The new method, which we call *Padding-based Parallel Signcryption* (PbPS), builds an efficient signcryption scheme from any family of trapdoor permutations, such as RSA. Each user U generates a single public/secret key pair f_U/f^{-1}_U used for both sending and receiving the data. To signcrypt a message m to a recipient with key f_{rcv}, a sender with key f_{snd} efficiently...

Cryptographic schemes are often designed as a combination of multiple component cryptographic modules. Such a combiner design is {\em robust} for a (security) specification if it meets the specification, provided that a sufficient subset of the components meet their specifications. A folklore combiner for encryption is {\em cascade}, i.e. $c={\cal E}''_{e''}({\cal E}'_{e'}(m))$. We show that cascade is a robust combiner for cryptosystems, under three important indistinguishability...

We formally study the notion of a joint signature and encryption in the public-key setting. We refer to this primitive as {\em signcryption}, adapting the terminology of Zheng [Zhe97]. We present wo definitions for the security of signcryption depending on whether the adversary is an outsider or a legal user of the system. We then examine generic sequential composition methods of building signcryption from a signature and encryption scheme. Contrary to what recent results in the symmetric...

It has recently been shown that authenticated Byzantine agreement, in which more than a third of the parties are corrupted, cannot be securely realized under concurrent or parallel (stateless) composition. This result puts into question any usage of authenticated Byzantine agreement in a setting where many executions take place. In particular, this is true for the whole body of work of secure multi-party protocols in the case that a third or more of the parties are corrupted. This is because...

Following Dwork, Naor, and Sahai (30th STOC, 1998), we consider concurrent execution of protocols in a semi-synchronized network. Specifically, we assume that each party holds a local clock such that a constant bound on the relative rates of these clocks is a-priori known, and consider protocols that employ time-driven operations (i.e., time-out in-coming messages and delay out-going messages). We show that the constant-round zero-knowledge proof for NP of Goldreich and Kahan (Jour. of...

We present efficient zero-knowledge proof systems for quasi-safe prime products and other related languages. Quasi-safe primes are a relaxation of safe primes, a class of prime numbers useful in many cryptographic applications. Our proof systems achieve higher security and better efficiency than all previously known ones. In particular, all our proof systems are perfect or statistical zero-knowledge, meaning that even a computationally unbounded adversary cannot extract any...