NTRU-like constructions are among the most studied lattice-based schemes. The freedom of design of NTRU resulted in many variants in literature motivated by faster computations or more resistance against lattice attacks by changing the underlying algebra. To the best of our knowledge, BQTRU (DCC 2017), a noncommutative NTRU-like cryptosystem, is the fastest claimed variant of NTRU built over the quaternion algebra of the bivariate ring of polynomials. The key generation and the encryption of...

We present the protected hardware implementation of the Module-Lattice-Based Digital Signature Standard (ML-DSA). ML-DSA is an extension of Dilithium 3.1, which is the winner of the Post Quantum Cryptography (PQC) competition in the digital signature category. The proposed design is based on the existing high-performance Dilithium 3.1 design. We implemented existing Dilithium masking gadgets in hardware, which were only implemented in software. The masking gadgets are integrated with the...

Discrete Gaussian sampling on lattices is a fundamental problem in lattice-based cryptography. In this paper, we revisit the Markov chain Monte Carlo (MCMC)-based Metropolis-Hastings-Klein (MHK) algorithm proposed by Wang and Ling and study its complexity under the Geometric Series Assuption (GSA) when the given basis is BKZ-reduced. We give experimental evidence that the GSA is accurate in this context, and we give a very simple approximate formula for the complexity of the sampler that is...

Digital signature schemes based on multivariate- and code-based hard problems are promising alternatives for lattice-based signature schemes, due to their smaller signature size. Hence, several candidates in the ongoing additional standardization for quantum secure digital signature (DS) schemes by the National Institute of Standards and Technology (NIST) rely on such alternate hard problems. Gaussian Elimination (GE) is a critical component in the signing procedure of these schemes. In this...

We present an efficient Publicly Verifiable Fully Homomorphic Encryption scheme that, along with being able to evaluate arbitrary boolean circuits over ciphertexts, also generates a succinct proof of correct homomorphic computation. Our scheme is based on FHEW proposed by Ducas and Micciancio (Eurocrypt'15), and we incorporate the GINX homomorphic accumulator (Eurocrypt'16) for improved bootstrapping efficiency. In order to generate the proof efficiently, we generalize the widely used Rank-1...

In parallel with the standardization of lattice-based cryptosystems, the research community in Post-quantum Cryptography focused on non-lattice-based hard problems for constructing public-key cryptographic primitives. The Linear Code Equivalence (LCE) Problem has gained attention regarding its practical applications and cryptanalysis. Recent advancements, including the LESS signature scheme and its candidacy in the NIST standardization for additional signatures, supported LCE as a...

NTRU is one of the most extensively studied lattice-based schemes. Its flexible design has inspired different proposals constructed over different rings, with some aiming to enhance security and others focusing on improving performance. The literature has introduced a line of noncommutative NTRU-like designs that claim to offer greater resistance to existing attacks. However, most of these proposals are either theoretical or fall short in terms of time and memory requirements when compared...

This work conducts a comprehensive investigation on determining the entropic hardness of (R/M)LWR under polynomial modulus. Particularly, we establish the hardness of (M)LWR for general entropic secret distributions from (Module) LWE assumptions based on a new conceptually simple framework called rounding lossiness. By combining this hardness result and a trapdoor inversion algorithm with asymptotically the most compact parameters, we obtain a compact lossy trapdoor function (LTF) with...

One of the main candidates of post-quantum cryptography is lattice-based cryptography. Its cryptographic security against quantum attackers is based on the worst-case hardness of lattice problems like the shortest vector problem (SVP), which asks to find the shortest non-zero vector in an integer lattice. Asymptotic quantum speedups for solving SVP are known and rely on Grover's search. However, to assess the security of lattice-based cryptography against these Grover-like quantum speedups,...

Masking schemes are key in thwarting side-channel attacks due to their robust theoretical foundation. Transitioning from Boolean to arithmetic (B2A) masking is a necessary step in various cryptography schemes, including hash functions, ARX-based ciphers, and lattice-based cryptography. While there exists a significant body of research focusing on B2A software implementations, studies pertaining to hardware implementations are quite limited, with the majority dedicated solely to creating...

Speed efficiency, memory optimization, and quantum resistance are essential for safeguarding the performance and security of cloud computing environments. Fully Homomorphic Encryption (FHE) addresses this need by enabling computations on encrypted data without requiring decryption, thereby maintaining data privacy. Additionally, lattice-based FHE is quantum secure, providing defense against potential quantum computer attacks. However, the performance of current FHE schemes remains...

Post-quantum cryptography has gained attention due to the need for secure cryptographic systems in the face of quantum computing. Code-based and lattice-based cryptography are two promi- nent approaches, both heavily studied within the NIST standardization project. Code-based cryptography—most prominently exemplified by the McEliece cryptosystem—is based on the hardness of decoding random linear error-correcting codes. Despite the McEliece cryptosystem having been unbroken for several...

In this article, we propose a generic hybrid encryption scheme providing entity authentication. The scheme is based on lossy trapdoor functions relying on the hardness of the Learning With Errors problem. The construction can be used on a number of different security requirements with minimal reconfiguration. It ensures entity authentication and ciphertext integrity while providing security against adaptive chosen ciphertext attacks in the standard model. As a desired characteristic of...

Sieving using near-neighbor search techniques is a well-known method in lattice-based cryptanalysis, yielding the current best runtime for the shortest vector problem in both the classical [BDGL16] and quantum [BCSS23] setting. Recently, sieving has also become an important tool in code-based cryptanalysis. Specifically, using a sieving subroutine, [GJN23, DEEK24] presented a variant of the information-set decoding (ISD) framework, which is commonly used for attacking cryptographically...

Let $N=pq$ be the product of two balanced prime numbers $p$ and $q$. In 2002, Elkamchouchi, Elshenawy, and Shaban introduced an interesting RSA-like cryptosystem that, unlike the classical RSA key equation $ed - k (p-1)(q-1) = 1$, uses the key equation $ed - k (p^2-1)(q^2-1) = 1$. The scheme was further extended by Cotan and Te\c seleanu to a variant that uses the key equation $ed - k (p^n-1)(q^n-1) = 1$, where $n \geq 1$. Furthermore, they provide a continued fractions attack that recovers...

We propose Scloud+, a lattice-based key encapsulation mechanism (KEM) scheme. The design of Scloud+ is informed by the following two aspects. Firstly, Scloud+ is based on the hardness of algebraic-structure-free lattice problems, which avoids potential attacks brought by the algebraic structures. Secondly, Scloud+ provides sets of light weight parameters, which greatly reduce the complexity of computation and communication complexity while maintaining the required level of security.

This paper presents Raccoon, a lattice-based signature scheme submitted to the NIST 2022 call for additional post-quantum signatures. Raccoon has the specificity of always being masked. Concretely, all sensitive intermediate values are shared into 𝑑 parts. The main design rationale of Raccoon is to be easy to mask at high orders, and this dictated most of its design choices, such as the introduction of new algorithmic techniques for sampling small errors. As a result, Raccoon achieves a...

Lyubashevsky’s signature can be viewed as a lattice-based adapation of the Schnorr signature, with the core difference being the use of aborts during signature generation process. Since the proposal of Lyubashevsky’s signature, a number of other variants of Schnorr-type signatures with aborts have been proposed, both in lattice-based and code-based setting. In this paper, we examine the security of Schnorr-type signature schemes with aborts. We give a detailed analysis of when the expected...

HAWK is a lattice-based signature scheme candidate to the fourth call of the NIST's Post-Quantum standardization campaign. Considered as a cousin of Falcon (one of the future NIST post-quantum standards) one can wonder whether HAWK shares the same drawbacks as Falcon in terms of side-channel attacks. Indeed, Falcon signature algorithm and particularly its Gaussian sampler, has shown to be highly vulnerable to power-analysis attacks. Besides, efficiently protecting Falcon's signature...

Lattice-based cryptography is in the process of being standardized. Several proposals to deal with side-channel information using lattice reduction exist. However, it has been shown that algorithms based on Bayesian updating are often more favorable in practice. In this work, we define distribution hints; a type of hint that allows modelling probabilistic information. These hints generalize most previously defined hints and the information obtained in several attacks. We define two...

The rapid evolution of post-quantum cryptography, spurred by standardization efforts such as those led by NIST, has highlighted the prominence of lattice-based cryptography, notably exemplified by CRYSTALS-Kyber. However, concerns persist regarding the security of cryptographic implementations, particularly in the face of Side-Channel Attacks (SCA). The usage of operations like the Number Theoretic Transform (NTT) in CRYSTALS-Kyber introduces vulnerabilities to SCA, especially single-trace...

As the use of the internet and digital devices has grown rapidly, keeping digital communications secure has become very important. Authenticated Key Agreement (AKA) protocols play a vital role in securing digital communications. These protocols enable the communicating parties to mutually authenticate and securely establish a shared secret key. The emergence of quantum computers makes many existing AKA protocols vulnerable to their immense computational power. Consequently, designing new...

As a prominent category of side-channel attacks (SCAs), plaintext-checking (PC) oracle-based SCAs offer the advantages of generality and operational simplicity on a targeted device. At TCHES 2023, Rajendran et al. and Tanaka et al. independently proposed the multiple-valued (MV) PC oracle, significantly reducing the required number of queries (a.k.a., traces) in the PC oracle. However, in practice, when dealing with environmental noise or inaccuracies in the waveform classifier, they...

Private Stream Aggregation (PSA) allows clients to send encryptions of their private values to an aggregator that is then able to learn the sum of these values but nothing else. It has since found many applications in practice, e.g. for smart metering or federated learning. In 2018, Becker et al. proposed the first lattice-based PSA scheme LaPS (NDSS 2018), with putative post-quantum security, which has subsequently been patented. In this paper, we describe two attacks on LaPS that break the...

EagleSign is one of the 40 “Round 1 Additional Signatures” that is accepted for consideration in the supplementary round of the Post-Quantum Cryptography standardization process, organized by NIST. Its design is based on structured lattices, and it boasts greater simplicity and performance compared to the two lattice signatures already selected for standardization: Falcon and Dilithium. In this paper, we show that those claimed advantages come at the cost of security. More precisely, we...

In this work, we use some recent developments in lattice-based cryptanalytic tools to revisit a fault attack on RSA-CRT signatures based on the Partial Approximate Common Divisor (PACD) problem. By reducing the PACD to a Hidden Number Problem (HNP) instance, we decrease the number of required faulted bits from 32 to 7 in the case of a 1024-bit RSA. We successfully apply the attack to RSA instances up to 8192-bit and present an enhanced analysis of the error-tolerance in the Bounded Distance...

A threshold signature scheme distributes the ability to generate signatures through distributed key generation and signing protocols. A threshold signature scheme should be functionally interchangeable, meaning that a signature produced by a threshold scheme should be verifiable by the same algorithm used for non-threshold signatures. To resist future attacks from quantum adversaries, lattice-based threshold signatures are desirable. However, the performance of existing lattice-based...

The field of Fully Homomorphic Encryption (FHE) has seen many theoretical and computational advances in recent years, bringing the technology closer to practicality than ever before. For this reason, practitioners from neighbouring fields such as machine learning have sought to understand FHE to provide privacy to their work. Unfortunately, selecting secure and efficient parameters in FHE is a daunting task due to the many interdependencies between the parameters involved. In this work, we...

Internet of Medical Things (IoMT) has gained significant research focus in both academic and medical institutions. Nevertheless, the sensitive data involved in IoMT raises concerns regarding user validation and data privacy. To address these concerns, certificateless signcryption (CLSC) has emerged as a promising solution, offering authenticity, confidentiality, and unforgeability. Unfortunately, most existing CLSC schemes are impractical for IoMT due to their heavy computational and storage...

ECMQV is a standardized key agreement protocol based on ECC with an additional implicit signature authentication. In this paper we investigate the vulnerability of ECMQV against fault attacks and propose two efficient lattice-based fault attacks. In our attacks, by inducing a storage fault to the ECC parameter $a$ before the execution of ECMQV, we can construct two kinds of weak curves and successfully pass the public-key validation step in the protocol. Then, by solving ECDLP and using a...

In this paper, we study the robustness of Kyber, the Learning With Errors (LWE)-based Key Encapsulation Mechanism (KEM) chosen for standardization by NIST, against key mismatch attacks. We demonstrate that Kyber's security levels can be compromised with a few mismatch queries by striking a balance between the parallelization level and the cost of lattice reduction for post-processing. This highlights the imperative need to strictly prohibit key reuse in CPA-secure Kyber. We further...

NTRU-like cryptosystems are among the most studied lattice-based post-quantum candidates. While most NTRU proposals have been introduced over a commutative ring of quotient polynomials, other rings can be used. Noncommutative algebra has been endorsed as a direction to build new variants of NTRU a long time ago. The first attempt to construct a noncommutative variant was due to Hoffstein and Silverman motivated by more resistance to lattice attack. The scheme has been built over the group...

In computer arithmetic operations, the Number Theoretic Transform (NTT) plays a significant role in the efficient implementation of cyclic and nega-cyclic convolutions with the application of multiplying large integers and large degree polynomials. Multiplying polynomials is a common operation in lattice-based cryptography. Hence, the NTT is a core component of several lattice-based cryptographic algorithms. Two well-known examples are the key encapsulation mechanism Kyber and the...

With the rise of quantum computing, the security of traditional cryptographic systems, especially those vulnerable to quantum attacks, is under threat. While public key cryptography has been widely studied in post-quantum security, symmetric-key cryptography has received less attention. This paper explores using the Ajtai-Micciancio hash function, based on the Short Integer Solution (SIS) problem, as a pseudorandom function in the Luby-Rackoff cipher. Since lattice-based problems like SIS...

For security issue, data in cloud is encrypted. Searching encrypted data (without decryption) is a practical and important problem. Public key authenticated encryption with keyword search (PAEKS) enables the retrieval of encrypted data, while resisting the insider keyword guessing attacks (IKGAs). Most PAEKS schemes only work with single-receiver model, exhibiting very limited applicability. To address this concern, there have been researches on broadcast authenticated encryption with...

The Module-NTRU problem, introduced by Cheon, Kim, Kim, Son (IACR ePrint 2019/1468), and Chuengsatiansup, Prest, Stehlé, Wallet, Xagawa (ASIACCS ’20), generalizes the versatile NTRU assump- tion. One of its main advantages lies in its ability to offer greater flexibil- ity on parameters, such as the underlying ring dimension. In this work, we present several lattice-based encryption schemes, which are IND-CPA (or OW-CPA) secure in the standard model based on the Module-NTRU and...

Quantum computers can efficiently model and solve several challenging problems for classical computers, raising concerns about potential security reductions in cryptography. NIST is already considering potential quantum attacks in the development of post-quantum cryptography by estimating the quantum resources required for such quantum attacks. In this paper, we present quantum circuits for the NV sieve algorithm to solve the Shortest Vector Problem (SVP), which serves as the security...

FALCON is candidate for standardization of the new Post Quantum Cryptography (PQC) primitives by the National Institute of Standards and Technology (NIST). However, it remains a challenge to define efficient countermeasures against side-channel attacks (SCA) for this algorithm. FALCON is a lattice-based signature that relies on rational numbers which is unusual in the cryptography field. While recent work proposed a solution to mask the addition and the multiplication, some roadblocks...

Introduced as a new protocol implemented in “Chrome Canary” for the Google Inc. Chrome browser, “New Hope” is engineered as a post-quantum key exchange for the TLS 1.2 protocol. The structure of the exchange is revised lattice-based cryptography. New Hope incorporates the key-encapsulation mechanism of Peikert which itself is a modified Ring-LWE scheme. The search space used to introduce the closest-vector problem is generated by an intersection of a tesseract and hexadecachoron, or the...

We construct an efficient proxy re-encryption (PRE) scheme secure against honest re-encryption attacks (HRA-secure) with precise concrete security estimates. To get these precise concrete security estimates, we introduce the tight, fine-grained noise-flooding techniques of Li et al. (CRYPTO'22) to RLWE-based (homomorphic) PRE schemes, as well as a mixed statistical-computational security to HRA security analysis. Our solution also supports homomorphic operations on the ciphertexts. Such...

The elliptic curve-based Enhanced Privacy ID (EPID) signature scheme is broadly used for hardware enclave attestation by many platforms that implement Intel Software Guard Extensions (SGX) and other devices. This scheme has also been included in the Trusted Platform Module (TPM) specifications and ISO/IEC standards. However, it is insecure against quantum attackers. While research into quantum-resistant EPID has resulted in several lattice-based schemes, Boneh et al. have initiated the study...

Direct Anonymous Attestation (DAA) was designed for the Trusted Platform Module (TPM) and versions using RSA and elliptic curve cryptography have been included in the TPM specifications and in ISO/IEC standards. These standardised DAA schemes have their security based on the factoring or discrete logarithm problems and are therefore insecure against quantum attackers. Research into quantum-resistant DAA has resulted in several lattice-based schemes. Now in this paper, we propose the first...

Vector commitments (VC) have gained significant attention due to their extensive use in applications such as blockchain and accumulators. Mercurial vector commitments (MVC) and mercurial functional commitments (MFC), as variants of VC, are central techniques for constructing more advanced cryptographic primitives, such as zero-knowledge sets and zero-knowledge functional elementary databases (ZK-FEDB). However, existing MFCs $\textit{only support linear functions}$, which limits their...

Lattice-based cryptography typically uses lattices with special properties to improve efficiency. We show how blockwise reduction can exploit lattices with special geometric properties, effectively reducing the required blocksize to solve the shortest vector problem to half of the lattice's rank, and in the case of the hypercubic lattice $\mathbb{Z}^n$, further relaxing the approximation factor of blocks to $\sqrt{2}$. We study both provable algorithms and the heuristic well-known primal...

Many proposals of lattice-based cryptosystems estimate security levels by following a recipe introduced in the New Hope proposal. This recipe, given a lattice dimension n, modulus q, and standard deviation s, outputs a "primal block size" β and a security level growing linearly with β. This β is minimal such that some κ satisfies ((n+κ)s^2+1)^{1/2} < (d/β)^{1/2} δ^{2β−d−1} q^{κ/d}, where d = n + κ + 1 and δ = (β(πβ)^{1/β}/(2π exp 1))^{1/2(β−1)}. This paper identifies how β grows with n,...

Fault attacks that exploit the propagation of effective/ineffective faults present a richer attack surface than Differential Fault Attacks, in the sense that the adversary depends on a single bit of information to eventually leak secret cryptographic material. In the recent past, a number of propagation-based fault attacks on Lattice-based Key Encapsulation Mechanisms have been proposed; many of which have no known countermeasures. In this work, we propose an orthogonal countermeasure...

As we enter 2024, the post-quantum cryptographic algorithm Dilithium, which emerged from the National Institute of Standards and Technology post-quantum cryptography competition, has now reached the deployment stage. This paper focuses on the practical security of Dilithium. We performed practical attacks on Dilithium2 on an STM32F4 platform. Our results indicate that an attack can be executed with just two signatures within five minutes, with a single signature offering a 60% probability of...

Oblivious message retrieval (OMR) allows resource-limited recipients to outsource the message retrieval process without revealing which messages are pertinent to which recipient. Its realizations in recent works leave an open problem: can an OMR scheme be both practical and provably secure against spamming attacks from malicious senders (i.e., DoS-resistant) under standard assumptions? In this paper, we first prove that a prior construction $\mathsf{OMRp2}$ is DoS-resistant under a...

Direct Anonymous Attestation (DAA) is a cryptographic protocol that enables users with a Trusted Platform Module (TPM) to authenticate without revealing their identity. Thus, DAA emerged as a good privacy-enhancing solution. Current standards have security based on factorization and discrete logarithm problem making them vulnerable to quantum computer attacks. Recently, a number of lattice-based DAA has been propose in the literature to start transition to quantum-resistant cryptography. In...

Lattice-based cryptography has emerged as a promising new candidate to build cryptographic primitives. It offers resilience against quantum attacks, enables fully homomorphic encryption, and relies on robust theoretical foundations. Zero-knowledge proofs (ZKPs) are an essential primitive for various privacy-preserving applications. For example, anonymous credentials, group signatures, and verifiable oblivious pseudorandom functions all require ZKPs. Currently, the majority of ZKP systems are...

The Partial Vandermonde (PV) Knapsack problem is an algebraic variant of the low-density inhomogeneous SIS problem. The problem has been used as a building block for various lattice-based constructions, including signatures (ACNS'14, ACISP'18), encryptions (DCC'15,DCC'20), and signature aggregation (Eprint'20). At Crypto'22, Boudgoust, Gachon, and Pellet-Mary proposed a key distinguishing attack on the PV Knapsack exploiting algebraic properties of the problem. Unfortunately, their attack...

FuLeeca is a signature scheme submitted to the recent NIST call for additional signatures. It is an efficient hash-and-sign scheme based on quasi-cyclic codes in the Lee metric and resembles the lattice-based signature Falcon. FuLeeca proposes a so-called concentration step within the signing procedure to avoid leakage of secret-key information from the signatures. However, FuLeeca is still vulnerable to learning attacks, which were first observed for lattice-based schemes. We present three...

The Hidden Number Problem (HNP) has found extensive applications in side-channel attacks against cryptographic schemes, such as ECDSA and Diffie-Hellman. There are two primary algorithmic approaches to solving the HNP: lattice-based attacks and Fourier analysis-based attacks. Lattice-based attacks exhibit better efficiency and require fewer samples when sufficiently long substrings of the nonces are known. However, they face significant challenges when only a small fraction of the nonce is...

Kyber KEM, the NIST selected PQC standard for Public Key Encryption and Key Encapsulation Mechanisms (KEMs) has been subjected to a variety of side-channel attacks, through the course of the NIST PQC standardization process. However, all these attacks targeting the decapsulation procedure of Kyber KEM either require knowledge of the ciphertexts or require to control the value of ciphertexts for key recovery. However, there are no known attacks in a blind setting, where the attacker does not...

Learning with Errors (LWE) is a hard math problem underlying post-quantum cryptography (PQC) systems for key exchange and digital signatures, recently standardized by NIST. Prior work [Wenger et al., 2022; Li et al., 2023a;b] proposed new machine learning (ML)-based attacks on LWE problems with small, sparse secrets, but these attacks require millions of LWE samples to train on and take days to recover secrets. We propose three key methods—better pre-processing, angular embeddings and model...

The conversion between arithmetic and Boolean masking representations (A2B \& B2A) is a crucial component for side-channel resistant implementations of lattice-based (post-quantum) cryptography. In this paper, we first propose novel $d$-order algorithms for the secure addition (SecADDChain$_q$) and B2A (B2X2A). Our secure adder is well-suited for repeated ('chained') executions, achieved through an improved method for repeated masked modular reduction. The optimized B2X2A gadget removes a...

Number Theoretic Transform (NTT) has been widely used in accelerating computations in lattice-based cryptography. However, attackers can potentially launch power analysis targeting NTT because it is usually the most time-consuming part of the implementation. This extended time frame provides a natural window of opportunity for attackers. In this paper, we investigate the first CPU frequency leakage (Hertzbleed-like) attacks against NTT in lattice-based KEMs. Our key observation is that...

This paper questions the side-channel security of central reduction technique, which is widely adapted in efficient implementations of Lattice-Based Cryptography (LBC). We show that the central reduction leads to a vulnerability by creating a strong dependency between the power consumption and the sign of sensitive intermediate values. We exploit this dependency by introducing the novel absolute value prediction function, which can be employed in higher-order non-profiled multi-query...

In this paper, we focus on the common prime RSA variant and introduces a novel investigation into the partial key exposure attack targeting it. We explore the vulnerability of this RSA variant, which employs two common primes $p$ and $q$ defined as $p=2ga+1$ and $q=2gb+1$ for a large prime $g$. Previous cryptanalysis of common prime RSA has primarily focused on the small private key attack. In our work, we delve deeper into the realm of partial key exposure attacks by categorizing them into...

As the message recovery-based attack poses a serious threat to lattice-based schemes, we conducted a study on the side-channel secu- rity of parallel implementations of lattice-based key encapsulation mech- anisms. Initially, we developed a power model to describe the power leakage during message encoding. Utilizing this power model, we pro- pose a multi-ciphertext message recovery attack, which can retrieve the required messages for a chosen ciphertext attack through a suitable mes- sage...

The Learning With Errors ($\mathsf{LWE}$) problem asks to find $\mathbf{s}$ from an input of the form $(\mathbf{A}, \mathbf{b} = \mathbf{A}\mathbf{s}+\mathbf{e}) \in (\mathbb{Z}/q\mathbb{Z})^{m \times n} \times (\mathbb{Z}/q\mathbb{Z})^{m}$, for a vector $\mathbf{e}$ that has small-magnitude entries. In this work, we do not focus on solving $\mathsf{LWE}$ but on the task of sampling instances. As these are extremely sparse in their range, it may seem plausible that the only way to proceed...

A functional commitment allows a user to commit to an input $\mathbf{x} \in \{0,1\}^\ell$ and later open up the commitment to a value $y = f(\mathbf{x})$ with respect to some function $f$. In this work, we focus on schemes that support fast verification. Specifically, after a preprocessing step that depends only on $f$, the verification time as well as the size of the commitment and opening should be sublinear in the input length $\ell$, We also consider the dual setting where the user...

This paper reviews common attacks in classical cryptography and plausible attacks in the post-quantum era targeted at CRYSTALS-Kyber. Kyber is a recently standardized post-quantum cryptography scheme that relies on the hardness of lattice problems. Although it has undergone rigorous testing by the National Institute of Standards and Technology (NIST), there have recently been studies that have successfully executed attacks against Kyber while showing their applicability outside of controlled...

This work *completely breaks* the sequentiality assumption (and broad generalizations thereof) underlying the candidate lattice-based proof of sequential work (PoSW) recently proposed by Lai and Malavolta at CRYPTO 2023. In addition, it breaks an essentially identical variant of the PoSW, which differs from the original in only an arbitrary choice that is immaterial to the design and security proof (under the falsified assumption). This suggests that whatever security the original PoSW may...

zkSNARK is a cryptographic primitive that allows a prover to prove to a resource constrained verifier, that it has indeed performed a specified non-deterministic computation correctly, while hiding private witnesses. In this work we focus on lattice based zkSNARK, as this serves two important design goals. Firstly, we get post-quantum zkSNARK schemes with $O(\log (\mbox{Circuit size}))$ sized proofs (without random oracles) and secondly, the easy verifier circuit allows further...

The security of code-based cryptography relies primarily on the hardness of decoding generic linear codes. Until very recently, all the best algorithms for solving the decoding problem were information set decoders ($\mathsf{ISD}$). However, recently a new algorithm called RLPN-decoding which relies on a completely different approach was introduced and it has been shown that RLPN outperforms significantly $\mathsf{ISD}$ decoders for a rather large range of rates. This RLPN decoder relies on...

The Dual-Sieve Attack on Learning with Errors (LWE), or more generally Bounded Distance Decoding (BDD), has seen many improvements in the recent years, and ultimately led to claims that it outperforms the primal attack against certain lattice-based schemes in the PQC standardization process organised by NIST. However, the work of Ducas--Pulles (Crypto '23) revealed that the so-called "Independence Heuristic", which all recent dual attacks used, leads to wrong predictions in a contradictory...

In recent years, quantum computers and Shor’s quantum algorithm have been able to effectively solve NP (Non-deterministic Polynomial-time) problems such as prime factorization and discrete logarithm problems, posing a threat to current mainstream asymmetric cryptography, including RSA and Elliptic Curve Cryptography (ECC). As a result, the National Institute of Standards and Technology (NIST) in the United States call for Post-Quantum Cryptography (PQC) methods that include lattice-based...

Multi-signatures allow for compressing many signatures for the same message that were generated under independent keys into one small aggregated signature. This primitive is particularly useful for proof-of-stake blockchains, like Ethereum, where the same block is signed by many signers, who vouch for the block's validity. Being able to compress all signatures for the same block into a short string significantly reduces the on-chain storage costs, which is an important efficiency metric...

This paper presents a comprehensive analysis of the verification algorithm of the CRYSTALS-Dilithium, focusing on a C reference implementation. Limited research has been conducted on its susceptibility to fault attacks, despite its critical role in ensuring the scheme’s security. To fill this gap, we investigate three distinct fault models - randomizing faults, zeroizing faults, and skipping faults - to identify vulnerabilities within the verification process. Based on our analysis, we...

CRYSTALS-Kyber is a key-encapsulation mechanism, whose security is based on the hardness of solving the learning-with-errors (LWE) problem over module lattices. As in its specification, Kyber prescribes the usage of the Number Theoretic Transform (NTT) for efficient polynomial multiplication. Side-channel assisted attacks against Post-Quantum Cryptography (PQC) algorithms like Kyber remain a concern in the ongoing standardization process of quantum-computer-resistant cryptosystems. Among the...

The Snowden's revelations kick-started a community-wide effort to develop cryptographic tools against mass surveillance. In this work, we propose to add another primitive to that toolbox: Fail-Stop Signatures (FSS) [EC'89]. FSS are digital signatures enhanced with a forgery-detection mechanism that can protect a PPT signer from more powerful attackers. Despite the fascinating concept, research in this area stalled after the '90s. However, the ongoing transition to post-quantum...

Masking is a well-known and provably secure countermeasure against side-channel attacks. However, due to additional redundant computations, integrating masking schemes is expensive in terms of performance. The performance overhead of integrating masking countermeasures is heavily influenced by the design choices of a cryptographic algorithm and is often not considered during the design phase. In this work, we deliberate on the effect of design choices on integrating masking techniques into...

Physical attacks are serious threats to cryptosystems deployed in the real world. In this work, we propose a microarchitectural end-to-end attack methodology on generic lattice-based post-quantum key encapsulation mechanisms to recover the long-term secret key. Our attack targets a critical component of a Fujisaki-Okamoto transform that is used in the construction of almost all lattice-based key encapsulation mechanisms. We demonstrate our attack model on practical schemes such as Kyber and...

Public key encryption with keyword search (PEKS), formalized by Boneh et al. [EUROCRYPT' 04], enables secure searching for specific keywords in the ciphertext. Nevertheless, in certain scenarios, varying user tiers are granted disparate data searching privileges, and administrators need to restrict the searchability of ciphertexts to select users exclusively. To address this concern, Jiang et al. [ACISP' 16] devised a variant of PEKS, namely public key encryption with authorized keyword...

In recent years, the elliptic curve Qu-Vanstone (ECQV) implicit certificate scheme has found application in security credential management systems (SCMS) and secure vehicle-to-everything (V2X) communication to issue pseudonymous certificates. However, the vulnerability of elliptic-curve cryptography (ECC) to polynomial-time attacks posed by quantum computing raises concerns. In order to enhance resistance against quantum computing threats, various post-quantum cryptography methods have been...

The Peregrine signature scheme is one of the candidates in the ongoing Korean post-quantum cryptography competition. It is proposed as a high-speed variant of Falcon, which is a hash-and-sign signature scheme over NTRU lattices and one of the schemes selected by NIST for standardization. To this end, Peregrine replaces the lattice Gaussian sampler in the Falcon signing procedure with a new sampler based on the centered binomial distribution. While this modification offers significant...

In an effort to circumvent the high cost of standard countermeasures against side-channel attacks in post-quantum cryptography, some works have developed low-cost detection-based countermeasures. These countermeasures try to detect maliciously generated input ciphertexts and react to them by discarding the ciphertext or secret key. In this work, we take a look at two previously proposed low-cost countermeasures: the ciphertext sanity check and the decapsulation failure check, and demonstrate...

Many of the three-round blind signatures based on identification protocols are only proven to be $\ell$-concurrently unforgeable for $\ell = \mathsf{polylog}(\lambda)$. It was only recently shown in a seminal work by Benhamouda et al. (EUROCRYPT'21) that this is not just a limitation of the proof technique. They proposed an elegant polynomial time attack against the $\ell$-concurrently unforgeability of the classical blind Schnorr protocol for $\ell = \mathsf{poly}(\lambda)$. However,...

Quantum computers, especially those with over 10,000 qubits, pose a potential threat to current public key cryptography systems like RSA and ECC due to Shor's algorithms. Grover's search algorithm is another quantum algorithm that could significantly impact current cryptography, offering a quantum advantage in searching unsorted data. Therefore, with the advancement of quantum computers, it is crucial to analyze potential quantum threats. While many works focus on Grover’s attacks in...

In post-quantum cryptography, Learning With Errors (LWE) is one of the dominant underlying mathematical problems. The dual attack is one of the main strategies for solving the LWE problem, and it has recently gathered significant attention within the research community. The attack strategy consists of a lattice reduction part and a distinguishing part. The latter includes an enumeration subroutine over a certain number of positions of the secret key. Our contribution consists of giving a...

Learning with Errors (LWE) is an important problem for post-quantum cryptography (PQC) that underlines the security of several NIST PQC selected algorithms. Several recent papers have claimed improvements on the complexity of so-called dual attacks on LWE. These improvements make dual attacks comparable to or even better than primal attacks in certain parameter regimes. Unfortunately, those improvements rely on a number of untested and hard-to-test statistical assumptions. Furthermore, a...

Dual attacks aiming at decoding generic linear codes have been found recently to outperform for certain parameters information set decoding techniques which have been for $60$ years the dominant tool for solving this problem and choosing the parameters of code-based cryptosystems. However, the analysis of the complexity of these dual attacks relies on some unproven assumptions that are not even fully backed up with experimental evidence. These dual attacks can actually be viewed as the...

Succinct non-interactive zero-knowledge arguments of knowledge (zk-SNARKs) are a type of non-interactive proof system enabling efficient privacy-preserving proofs of membership for NP languages. A great deal of works has studied candidate constructions that are secure against quantum attackers, which are based on either lattice assumptions, or post-quantum collision-resistant hash functions. In this paper, we propose a code-based zk-SNARK scheme, whose security is based on the rank support...

We propose a generic construction of password-based authenticated key exchange (PAKE) from key encapsulation mechanisms (KEM). Assuming that the KEM is oneway secure against plaintext-checkable attacks (OW-PCA), we prove that our PAKE protocol is \textit{tightly secure} in the Bellare-Pointcheval-Rogaway model (EUROCRYPT 2000). Our tight security proofs require ideal ciphers and random oracles. The OW-PCA security is relatively weak and can be implemented tightly with the Diffie-Hellman...

Location tracking accessories (or "tracking tags") such as those sold by Apple, Samsung, and Tile, allow owners to track the location of their property via offline finding networks. The tracking protocols were designed to ensure that no entity (including the vendor) can use a tag's broadcasts to surveil its owner. These privacy guarantees, however, seem to be at odds with the phenomenon of $\textit{tracker-based stalking}$, where attackers use these very tags to monitor a target's...

We point out critical deficiencies in lattice-based cryptanalysis of common prime RSA presented in ``Remarks on the cryptanalysis of common prime RSA for IoT constrained low power devices'' [Information Sciences, 538 (2020) 54--68]. To rectify these flaws, we carefully scrutinize the relevant parameters involved in the analysis during solving a specific trivariate integer polynomial equation. Additionally, we offer a synthesized attack illustration of small private key attacks on common prime RSA.

The recent technological advances in Post-Quantum Cryptography (PQC) raise the questions of robust implementations of new asymmetric cryptography 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 National Institute of Standards and Technology (NIST) as the first standard for Key Encapsulation Mechanism (KEM), taking inspiration from CRYSTALS-Kyber. We must ensure that the ML-KEM...

CRYSTALS-Kyber, as the only public key encryption (PKE) algorithm selected by the National Institute of Standards and Technology (NIST) in the third round, is considered one of the most promising post-quantum cryptography (PQC) schemes. Lattice-based cryptography uses complex discrete alogarithm problems on lattices to build secure encryption and decryption systems to resist attacks from quantum computing. Performance is an important bottleneck affecting the promotion of post quantum...

The KpqC competition has begun in 2022, that aims to standardize Post-Quantum Cryptography (PQC) in the Republic of Korea. Among the 16 submissions of the KpqC competition, the lattice-based schemes exhibit the most promising and balanced features in performance. In this paper, we propose an effective classical CCA attack to recover the transmitted session key for NTRU+, one of the lattice-based Key Encapsulation Mechanisms (KEM) proposed in the KpqC competition, for the first time. With the...

Masking is a well-studied method for achieving provable security against side-channel attacks. In masking, each sensitive variable is split into $d$ randomized shares, and computations are performed with those shares. In addition to the computational overhead of masked arithmetic, masking also has a storage cost, increasing the requirements for working memory and secret key storage proportionally with $d$. In this work, we introduce mask compression. This conceptually simple technique is...

Lattice-based cryptographic schemes such as Crystals-Kyber and Dilithium are post-quantum algorithms selected to be standardized by NIST as they are considered to be secure against quantum computing attacks. The multiplication in polynomial rings is the most time-consuming operation in many lattice-based cryptographic schemes, which is also subject to side-channel attacks. While NTT-based polynomial multiplication is almost a norm in a wide range of implementations, a relatively new method,...

In public key encryption (PKE), anonymity is essential to ensure privacy by preventing the ciphertext from revealing the recipient’s identity. However, the literature has addressed the anonymity of PKE under different attack scenarios to a limited extent. Benhamouda et al. (TCC 2020) introduced the first formal definition of anonymity for PKE under corruption, and Huang et al. (ASIACRYPT 2022) made further extensions and provided a generic framework. In this paper, we introduce a new...

This work addresses the long quest for proving full (adaptive) security for attribute-based encryption (ABE). We show that in order to prove full security in a black-box manner, the scheme must be ``irregular'' in the sense that it is impossible to ``validate'' secret keys to ascertain consistent decryption of ciphertexts. This extends a result of Lewko and Waters (Eurocrypt 2014) that was only applicable to straight-line proofs (without rewinding). Our work, therefore, establishes that it...

Key mismatch attacks resilience is a great concern for KEMs in the NIST PQC standardization process. In key mismatch attacks, the adversary aims to recover the reused key by sending special form of ciphertexts to the target party and observing whether the shared key matches his guesses or not. In this paper, we propose pairwise-parallel key mismatch attacks on Kyber and other lattice-based KEMs. The strategy is to recover partial information about multiple secret key coefficient-pairs in...

We report on a new class of ECDSA signature vulnerability observed in the wild on the Bitcoin blockchain that results from a signature nonce generated by concatenating half of the bits of the message hash together with half of the bits of the secret signing key. We give a lattice-based attack for efficiently recovering the secret key from a single signature of this form. We then search the entire Bitcoin blockchain for such signatures, and identify and track the activities of an apparently...

We construct the first tightly secure authenticated key exchange (AKE) protocol from lattices. Known tight constructions are all based on Diffie-Hellman-like assumptions. Thus, our protocol is the first construction with tight security from a post-quantum assumption. Our AKE protocol is constructed tightly from a new security notion for key encapsulation mechanisms (KEMs), called one-way security against checkable chosen-ciphertext attacks (OW- ChCCA). We show how an OW-ChCCA secure KEM...

Historically, most cryptosystems chose their keys uniformly at random. This is in contrast to modern (lattice-based) schemes, which typically sample their keys from more complex distributions $\mathcal{D}$, such as the discrete Gaussian or centered binomial distribution. It is well-known that any key drawn from the uniform distribution $\mathcal{U}$ can be guessed using at most $2^{\operatorname{H}(\mathcal{U})}$ key guesses, where $\operatorname{H}(\mathcal{U})$ denotes the entropy of...

All modern lattice-based schemes build on variants of the LWE problem. Information leakage of the LWE secret $\mathbf{s} \in \mathbb{Z}_q^n$ is usually modeled via so-called hints, i.e., inner products of $\mathbf{s}$ with some known vector. At Crypto`20, Dachman-Soled, Ducas, Gong and Rossi (DDGR) defined among other so-called perfect hints and modular hints. The trailblazing DDGR framework allows to integrate and combine hints successively into lattices, and estimates the resulting LWE...

Recently, NIST has announced Kyber, a lattice-based key encapsulation mechanism (KEM), as a post-quantum standard. However, it is not the most efficient scheme among the NIST's KEM finalists. Saber enjoys more compact sizes and faster performance, and Mera et al. (TCHES '21) further pushed its efficiency, proposing a shorter KEM, Sable. As KEM are frequently used on the Internet, such as in TLS protocols, it is essential to achieve high efficiency while maintaining sufficient security....