Recently, the construction of cryptographic schemes based on hard lattice problems has gained immense popularity. Apart from being quantum resistant, lattice-based cryptography allows a wide range of variations in the underlying hard problem. As cryptographic schemes can work in different environments under different operational constraints such as memory footprint, silicon area, efficiency, power requirement, etc., such variations in the underlying hard problem are very useful for designers...

Computationally hard problems based on coding theory, such as the syndrome decoding problem, have been used for constructing secure cryptographic schemes for a long time. Schemes based on these problems are also assumed to be secure against quantum computers. However, these schemes are often considered impractical for real-world deployment due to large key sizes and inefficient computation time. In the recent call for standardization of additional post-quantum digital signatures by the...

Zero-Knowledge (ZK) protocols have been a subject of intensive study due to their fundamental importance and versatility in modern cryptography. However, the inherently different nature of quantum information significantly alters the landscape, necessitating a re-examination of ZK designs. A crucial aspect of ZK protocols is their round complexity, intricately linked to $\textit{simulation}$, which forms the foundation of their formal definition and security proofs. In the...

Digital signature is a fundamental cryptographic primitive and is widely used in the real world. Unfortunately, the current digital signature standards like EC-DSA and RSA are not quantum-resistant. Among post-quantum cryptography (PQC), isogeny-based signatures preserve some advantages of elliptic curve cryptosystems, particularly offering small signature sizes. Currently, SQIsign and its variants are the most promising isogeny-based digital signature schemes. In this paper, we propose a...

In 2022, Wang et al. proposed the multivariate signature scheme SNOVA as a UOV variant over the non-commutative ring of $\ell \times \ell $ matrices over $\mathbb{F}_q$. This scheme has small public key and signature size and is a first round candidate of NIST PQC additional digital signature project. Recently, Ikematsu and Akiyama, and Li and Ding show that the core matrices of SNOVA with $v$ vinegar-variables and $o$ oil-variables are regarded as the representation matrices of UOV with...

Kyber was selected by NIST as a Post-Quantum Cryptography Key Encapsulation Mechanism standard. This means that the industry now needs to transition and adopt these new standards. One of the most demanding operations in Kyber is the modular arithmetic, making it a suitable target for optimization. This work offers a novel modular reduction design with the lowest area on Xilinx FPGA platforms. This novel design, through K-reduction and LUT-based reduction, utilizes 49 LUTs and 1 DSP...

Digital signatures are fundamental building blocks in various protocols to provide integrity and authenticity. The development of the quantum computing has raised concerns about the security guarantees afforded by classical signature schemes. CRYSTALS-Dilithium is an efficient post-quantum digital signature scheme based on lattice cryptography and has been selected as the primary algorithm for standardization by the National Institute of Standards and Technology. In this work, we present a...

In the post-quantum migration of TLS 1.3, an ephemeral Diffie-Hellman must be replaced with a post-quantum key encapsulation mechanism (KEM). At EUROCRYPT 2022, Huguenin-Dumittan and Vaudenay [EC:HugVau22] demonstrated that KEMs with standard CPA security are sufficient for the security of the TLS1.3 handshake. However, their result is only proven in the random oracle model (ROM), and as the authors comment, their reduction is very much non-tight and not sufficient to guarantee security in...

Embedded systems are flexible and cost-effective and thus have found a use case in almost every part of our daily lives. Due to their widespread use, they have also become valuable targets for cyber attacks. However, translating cutting-edge cyber security from servers and desktops to the embedded realm can be challenging due to the limited computational power and memory of embedded devices. Although quantum computing is still in early research and development, it threatens to break...

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.

Blind signatures represent a class of cryptographic primitives enabling privacy-preserving authentication with several applications such as e-cash or e-voting. It is still a very active area of research, in particular in the post-quantum setting where the history of blind signatures has been hectic. Although it started to shift very recently with the introduction of a few lattice-based constructions, all of the latter give up an important characteristic of blind signatures (size, efficiency,...

From 2022, Korean Post-Quantum Cryptography (KpqC) Competition has been held. Among the Round 1 algorithms of KpqC, eight algorithms were selected in December 2023. To evaluate the algorithms, the performance is critical factor. However, the performance of the algorithms submitted to KpqC was evaluated in different development environments. Consequently, it is difficult to compare the performance of each algorithm fairly, because the measurements were not conducted in the identical...

We propose a new NTRU-based Public-Key Encryption (PKE) scheme called $\mathsf{NTRU+}\mathsf{PKE}$, which effectively incorporates the Fujisaki-Okamoto transformation for PKE (denoted as $\mathsf{FO}_{\mathsf{PKE}}$) to achieve chosen-ciphertext security in the Quantum Random Oracle Model (QROM). While $\mathsf{NTRUEncrypt}$, a first-round candidate in the NIST PQC standardization process, was proven to be chosen-ciphertext secure in the Random Oracle Model (ROM), it lacked corresponding...

Verifiable Timed Signatures (VTS) are cryptographic constructs that enable obtaining a signature at a specific time in the future and provide evidence that the signature is legitimate. This framework particularly finds utility in applications such as payment channel networks, multiparty signing operations, or multiparty computation, especially within blockchain architectures. Currently, VTS schemes are based on signature algorithms such as BLS signature, Schnorr signature, and ECDSA. These...

With the potential arrival of quantum computers, it is essential to build cryptosystems resistant to attackers with the computing power of a quantum computer. With Shor's algorithm, cryptosystems based on discrete logarithms and factorization become obsolete. Reason why NIST has launching two competitions in 2016 and 2023 to standardize post-quantum cryptosystems (such as KEM and signature ) based on problems supposed to resist attacks using quantum computers. EagleSign was prosed to NIT...

Lattice cryptography schemes based on the learning with errors (LWE) hardness assumption have been standardized by NIST for use as post-quantum cryptosystems, and by HomomorphicEncryption.org for encrypted compute on sensitive data. Thus, understanding their concrete security is critical. Most work on LWE security focuses on theoretical estimates of attack performance, which is important but may overlook attack nuances arising in real-world implementations. The sole existing concrete...

For more than two decades, pairings have been a fundamental tool for designing elegant cryptosystems, varying from digital signature schemes to more complex privacy-preserving constructions. However, the advancement of quantum computing threatens to undermine public-key cryptography. Concretely, it is widely accepted that a future large-scale quantum computer would be capable to break any public-key cryptosystem used today, rendering today's public-key cryptography obsolete and mandating the...

The progression of quantum computing is considered a potential threat to traditional cryptography system, highlighting the significance of post-quantum security in cryptographic systems. Regarding symmetric key encryption, the Grover algorithm can approximately halve the search complexity. Despite the absence of fully operational quantum computers at present, the necessity of assessing the security of symmetric key encryption against quantum computing continues to grow. In this paper, we...

A prominent countermeasure against side channel attacks, the hiding countermeasure, typically involves shuffling operations using a permutation algorithm. Especially in the era of Post-Quantum Cryptography, the importance of the hiding coun- termeasure is emphasized due to computational characteristics like those of lattice and code-based cryptography. In this context, swiftly and securely generating permutations has a critical impact on an algorithm’s security and efficiency. The widely...

This article presents an innovative project for a Central Bank Digital Currency (CBDC) infrastructure. Focusing on security and reliability, the proposed architecture: (1) employs post-quantum cryptography (PQC) algorithms for long-term security, even against attackers with access to cryptographically-relevant quantum computers; (2) can be integrated with a Trusted Execution Environment (TEE) to safeguard the confidentiality of transaction contents as they are processed by third-parties; and...

The field of post-quantum cryptography (PQC) is continuously evolving. Many researchers are exploring efficient PQC implementation on various platforms, including x86, ARM, FPGA, GPU, etc. In this paper, we present an Efficient CryptOgraphy CRYSTALS (ECO-CRYSTALS) implementation on standard 64-bit RISC-V Instruction Set Architecture (ISA). The target schemes are two winners of the National Institute of Standards and Technology (NIST) PQC competition: CRYSTALS-Kyber and CRYSTALS-Dilithium,...

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...

This paper presents extensions to the OpenTitan hardware root of trust that aim at enabling high-performance lattice-based cryptography. We start by carefully optimizing ML-KEM and ML-DSA - the two primary algorithms selected by NIST for standardization - in software targeting the OTBN accelerator. Based on profiling results of these implementations, we propose tightly integrated extensions to OTBN, specifically an interface from OTBN to OpenTitan's Keccak accelerator (KMAC core) and...

We construct two efficient post-quantum ring signatures with anonymity against full key exposure from isogenies, addressing limitations of existing isogeny-based ring signatures. First, we present an efficient concrete distinguisher for the SQIsign simulator when the signing key is provided using one transcript. This shows that turning SQIsign into an efficient full anonymous ring signature requires some new ideas. Second, we propose a variant of SQIsign that is resistant to the...

Blockchain technology ensures accountability, transparency, and redundancy in critical applications, includ- ing IoT with embedded systems. However, the reliance on public-key cryptography (PKC) makes blockchain vulnerable to quantum computing threats. This paper addresses the urgent need for quantum-safe blockchain solutions by integrating Post- Quantum Cryptography (PQC) into blockchain frameworks. Utilizing algorithms from the NIST PQC standardization pro- cess, we aim to fortify...

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...

Resource-constrained devices such as wireless sensors and Internet of Things (IoT) devices have become ubiquitous in our digital ecosystem. These devices generate and handle a major part of our digital data. In the face of the impending threat of quantum computers on our public-key infrastructure, it is impossible to imagine the security and privacy of our digital world without integrating post-quantum cryptography (PQC) into these devices. Usually, due to the resource constraints of these...

Isogeny-based schemes often come with special requirements on the field of definition of the involved elliptic curves. For instance, the efficiency of SQIsign, a promising candidate in the NIST signature standardisation process, requires a large power of two and a large smooth integer $T$ to divide $p^2-1$ for its prime parameter $p$. We present two new methods that combine previous techniques for finding suitable primes: sieve-and-boost and XGCD-and-boost. We use these methods to find...

The one-time pad cipher is renowned for its theoretical perfect security, yet its practical deployment is primarily hindered by the key-size and distribution challenge. This paper introduces a novel approach to key distribution called q-stream, designed to make symmetric-key cryptography, and the one-time pad cipher in particular, a viable option for contemporary secure communications, and specifically, post-quantum cryptography, leveraging quantum noise and combinatorics to ensure secure...

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...

Enhanced pqsigRM is a code-based hash-and-sign scheme proposed to the second National Institute of Standards and Technology call for post-quantum signatures. The scheme is based on the $(U,U+V)$-construction and it enjoys remarkably small signature lengths, about $1$KBytes for a security level of $128$ bits. Unfortunately we show that signatures leak information about the underlying $(U,U+V)$-structure. It allows to retrieve the private-key with~$100, 000$ signatures.

In 2018, Mouha et al. (IEEE Trans. Reliability, 2018) performed a post-mortem investigation of the correctness of reference implementations submitted to the SHA3 competition run by NIST, finding previously unidentified bugs in a significant portion of them, including two of the five finalists. Their innovative approach allowed them to identify the presence of such bugs in a black-box manner, by searching for counterexamples to expected cryptographic properties of the implementations under...

Oblivious transfer (OT) is a fundamental cryptographic protocol that plays a crucial role in secure multi-party computation (MPC). Most practical OT protocols by, e.g., Naor and Pinkas (SODA'01) or Chou and Orlandi (Latincrypt'15), are based on Diffie-Hellman (DH)-like assumptions and not post-quantum secure. In contrast, many other components of MPC protocols, including garbled circuits and secret sharings, are post-quantum secure. The reliance on non-post-quantum OT protocols presents a...

Anticipating the advent of large quantum computers, NIST started a worldwide competition in 2016 aiming to define the next cryptographic standards. HQC is one of these post-quantum schemes still in contention, with four others already in the process of being standardized. In 2022, Guo et al. introduced a timing attack that exploited an inconsistency in HQC rejection sampling function to recover its secret key in 866,000 calls to an oracle. The authors of HQC updated its specification by...

Oblivious Transfer (OT) is at the heart of secure computation and is a foundation for many applications in cryptography. Over two decades of work have led to extremely efficient protocols for evaluating OT instances in the preprocessing model, through a paradigm called OT extension. A few OT instances generated in an offline phase can be used to perform many OTs in an online phase efficiently, i.e., with very low communication and computational overheads. Specifically, traditional OT...

It is fundamental that executing cryptographic software must not leak secrets through side-channels. For software-visible side-channels, it was long believed that "constant-time" programming would be sufficient as a systematic countermeasure. However, this belief was shattered in 2018 by attacks exploiting speculative execution—so called Spectre attacks. Recent work shows that language support suffices to protect cryptographic code with minimal overhead against one class of such attacks,...

$SPHINCS^+$, one of the Post-Quantum Cryptography Digital Signature Algorithms (PQC-DSA) selected by NIST in the third round, features very short public and private key lengths but faces significant performance challenges compared to other post-quantum cryptographic schemes, limiting its suitability for real-world applications. To address these challenges, we propose the GPU-based paRallel Accelerated $SPHINCS^+$ (GRASP), which leverages GPU technology to enhance the efficiency of...

Oblivious Transfer (OT) is a fundamental cryptographic protocol with applications in secure Multi-Party Computation, Federated Learning, and Private Set Intersection. With the advent of quantum computing, it is crucial to develop unconditionally secure core primitives like OT to ensure their continued security in the post-quantum era. Despite over four decades since OT's introduction, the literature has predominantly relied on computational assumptions, except in cases using unconventional...

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...

This work expands the machinery we have for isogeny-based cryptography in genus 2 by developing a toolbox of several essential algorithms for Kummer surfaces, the dimension-2 analogue of $x$-only arithmetic on elliptic curves. Kummer surfaces have been suggested in hyper-elliptic curve cryptography since at least the 1980s and recently these surfaces have reappeared to efficiently compute $(2,2)$-isogenies. We construct several essential analogues of techniques used in one-dimensional...

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...

$\mathrm{SPHINCS^{+}}$ is a post-quantum signature scheme that, at the time of writing, is being standardized as $\mathrm{SLH\text{-}DSA}$. It is the most conservative option for post-quantum signatures, but the original tight proofs of security were flawed—as reported by Kudinov, Kiktenko and Fedorov in 2020. In this work, we formally prove a tight security bound for $\mathrm{SPHINCS^{+}}$ using the EasyCrypt proof assistant, establishing greater confidence in the general security of the...

We present an efficient quantum algorithm for solving the semidirect discrete logarithm problem (SDLP) in any finite group. The believed hardness of the semidirect discrete logarithm problem underlies more than a decade of works constructing candidate post-quantum cryptographic algorithms from nonabelian groups. We use a series of reduction results to show that it suffices to consider SDLP in finite simple groups. We then apply the celebrated Classification of Finite Simple Groups to...

A popular way to build post-quantum signature schemes is by first constructing an identification scheme (IDS) and applying the Fiat-Shamir transform to it. In this work we tackle two open questions related to the general applicability of techniques around this approach that together allow for efficient post-quantum signatures with optimal security bounds in the QROM. First we consider a recent work by Aguilar-Melchor, Hülsing, Joseph, Majenz, Ronen, and Yue (Asiacrypt'23) that showed...

Interactive proofs are a cornerstone of modern cryptography and as such used in many areas, from digital signatures to multy-party computation. Often the knowledge error $\kappa$ of an interactive proof is not small enough, and thus needs to be reduced. This is usually achieved by repeating the interactive proof in parallel t times. Recently, it was shown that parallel repetition of any $(k_1, \ldots , k_\mu)$-special-sound multi-round public-coin interactive proof reduces the knowledge...

We provide explicit radical $N$-isogeny formulae for all odd integers $N$. The formulae are compact closed-form expressions which require one $N$th root computation and $\mathcal{O}(N)$ basic field operations. The formulae are highly efficient to compute a long chain of $N$-isogenies, and have the potential to be extremely beneficial for speeding up certain cryptographic protocols such as CSIDH. Unfortunately, the formulae are conjectured, but we provide ample supporting evidence which...

Direct Anonymous Attestation (DAA) allows a (host) device with a Trusted Platform Module (TPM) to prove that it has a certified configuration of hardware and software whilst preserving the privacy of the device. All deployed DAA schemes are based on classical security assumptions. Despite a long line of works proposing post-quantum designs, the vast majority give only theoretical schemes and where concrete parameters are computed, their efficiency is far from practical. Our first...

Multivariate Cryptography is one of the main candidates for Post-quantum Cryptography. Multivariate schemes are usually constructed by applying two secret affine invertible transformations $\mathcal S,\mathcal T$ to a set of multivariate polynomials $\mathcal{F}$ (often quadratic). The secret polynomials $\mathcal{F}$ posses a trapdoor that allows the legitimate user to find a solution of the corresponding system, while the public polynomials $\mathcal G=\mathcal S\circ\mathcal...

In this paper we propose verifiable secret sharing (VSS) schemes secure for any honest majority in the synchronous model, and that only use symmetric-key cryptographic tools, therefore having plausibly post-quantum security. Compared to the state-of-the-art scheme with these features (Atapoor et al., Asiacrypt `23), our main improvement lies on the complexity of the ``optimistic'' scenario where the dealer and all but a small number of receivers behave honestly in the sharing phase: in this...

Extensible Markup Language (XML) is one of the most popular serialization languages. Since many security protocols are built using XML, it also provides cryptographic functionality. A central framework in this area is the Security Assertion Markup Language (SAML). This standard is one of the most widely used options for implementing Single Sign-On (SSO), which allows users to authenticate to different service providers using the credentials from a single identity provider. Like all other...

In this paper, we present three types of variations of the ALTEQ cryptosystem, a recent submission to the NIST's additional call for signatures. We name these Dangerous Variations of ALTEQ (DVA), as there is always a certain danger in stepping out of usual constructions, although we attempt to maintain heuristic security. First, we present DVA-GG (Graph Generalization), that can be seen as a more abstract point-of-view on the operations done in ALTEQ and encourages more research on the...

In this paper, we introduce a new probability function parameter in the instantiations of the Goldreich-Micali-Wigderson with Fiat-Shamir and unbalanced challenges used in ALTEQ, a recent NIST PQC candidate in the call for additional signatures. This probability set at 100% does not bring any changes in the scheme, but modifies the public challenge generation process when below 100%, by injecting potential rejections in otherwise completely valid inputs. From a theoretical point of view,...

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...

An important proof technique in the random oracle model involves reprogramming it on hard to predict inputs and arguing that an attacker cannot detect that this occurred. In the quantum setting, a particularly challenging version of this considers adaptive reprogramming wherein the points to be reprogrammed (or output values they should be programmed to) are dependent on choices made by the adversary. Frameworks for analyzing adaptive reprogramming were given by, e.g., by Unruh (CRYPTO...

The BUFF transform, due to Cremers et al. (S&P'21), is a generic transformation for digital signature scheme, with the purpose of obtaining additional security guarantees beyond unforgeability: exclusive ownership, message-bound signatures, and non-resignability. Non-resignability (which essentially challenges an adversary to re-sign an unknown message for which it only obtains the signature) turned out to be a delicate matter, as recently Don et al. (CRYPTO'24) showed that the initial...

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...

The Deuring correspondence is a correspondence between supersingular elliptic curves and quaternion orders. Under this correspondence, an isogeny between elliptic curves corresponds to a quaternion ideal. This correspondence plays an important role in isogeny-based cryptography and several algorithms to compute an isogeny corresponding to a quaternion ideal (ideal-to-isogeny algorithms) have been proposed. In particular, SQIsign is a signature scheme based on the Deuring correspondence and...

We introduce SQIPrime, a post-quantum digital signature scheme based on the Deuring correspondence and Kani's Lemma. Compared to its predecessors that are SQISign and especially SQISignHD, SQIPrime further expands the use of high dimensional isogenies, already in use in the verification in SQISignHD, to both key generation and commitment. In doing so, it no longer relies on smooth degree isogenies (of dimension 1). SQIPrime operates with a prime number of the form $p = 2^\alpha f-1$, as...

Isogeny-based cryptography is cryptographic schemes whose security is based on the hardness of a mathematical problem called the isogeny problem, and is attracting attention as one of the candidates for post-quantum cryptography. A representative isogeny-based cryptography is the signature scheme called SQIsign, which was submitted to the NIST PQC standardization competition. SQIsign has attracted much attention because of its very short signature and key size among the candidates for the...

Multivariate public key cryptography (MPKC) is one of the most promising alternatives to build quantum-resistant signature schemes, as evidenced in NIST's call for additional post-quantum signature schemes. The main assumption in MPKC is the hardness of the Multivariate Quadratic (MQ) problem, which seeks for a common root to a system of quadratic polynomials over a finite field. Although the Crossbred algorithm is among the most efficient algorithm to solve MQ over small fields, its...

In this work we introduce PERK a compact digital signature scheme based on the hardness of a new variant of the Permuted Kernel Problem (PKP). PERK achieves the smallest signature sizes for any PKP-based scheme for NIST category I security with 6 kB, while obtaining competitive signing and verification timings. PERK also compares well with the general state-of-the-art. To substantiate those claims we provide an optimized constant-time AVX2 implementation, a detailed performance analysis and...

In 2017, Petzoldt, Szepieniec, and Mohamed proposed a blind signature scheme, based on multivariate cryptography. This construction has been expanded on by several other works. This short paper shows that their construction is susceptible to an efficient polynomial-time attack. The problem is that the authors implicitly assumed that for a random multivariate quadratic map $\mathcal{R}:\mathbb{F}_q^m \rightarrow \mathbb{F}_q^m$ and a collision-resistant hash function $H: \{0,1\}^* \rightarrow...

The advent of quantum computing technology will compromise many of the current cryptographic algorithms, especially public-key cryptography, which is widely used to protect digital information. Most algorithms on which we depend are used worldwide in components of many different communications, processing, and storage systems. Once access to practical quantum computers becomes available, all public-key algorithms and associated protocols will be vulnerable to criminals, competitors, 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...

This work shows how FALCON can achieve the Beyond UnForgeability Features (BUFF) introduced by Cremers et al. (S&P'21) more efficiently than by applying the generic BUFF transform. Specifically, we show that applying a transform of Pornin and Stern (ACNS'05), dubbed PS-3 transform, already suffices for FALCON to achieve BUFF security. For FALCON, this merely means to include the public key in the hashing step in signature generation and verification, instead of hashing only the nonce and the...

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...

In white-box cryptography, early protection techniques have fallen to the automated Differential Computation Analysis attack (DCA), leading to new countermeasures and attacks. A standard side-channel countermeasure, Ishai-Sahai-Wagner's masking scheme (ISW, CRYPTO 2003) prevents Differential Computation Analysis but was shown to be vulnerable in the white-box context to the Linear Decoding Analysis attack (LDA). However, recent quadratic and cubic masking schemes by Biryukov-Udovenko...

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...

WebAuthn is a passwordless authentication protocol which allows users to authenticate to online services using public-key cryptography. Users prove their identity by signing a challenge with a private key, which is stored on a device such as a cell phone or a USB security token. This approach avoids many of the common security problems with password-based authentication. WebAuthn's reliance on proof-of-possession leads to a usability issue, however: a user who loses access to their...

Byzantine consensus is a fundamental building block in distributed cryptographic problems. Despite decades of research, most existing asynchronous consensus protocols require a strong trusted setup and expensive public-key cryptography. In this paper, we study asynchronous Byzantine consensus protocols that do not rely on a trusted setup and do not use public-key cryptography such as digital signatures. We give an Asynchronous Common Subset (ACS) protocol whose security is only based on...

To introduce a post-quantum-secure encryption scheme specifically for use in flight-computers, we used avionics’ module-isolation methods to wrap a recent encryption standard (HPKE – Hybrid Public Key Encryption) within a software partition. This solution proposes an upgrade to HPKE, using quantum-resistant ciphers (Kyber/ML-KEM and Dilithium/ML-DSA) redundantly alongside well-established ciphers, to achieve post-quantum security. Because cryptographic technology can suddenly become...

This paper presents a comprehensive security analysis of the Adh zero-knowledge proof system, a novel lattice-based, quantum-resistant proof of possession system. The Adh system offers compact key and proof sizes, making it suitable for real-world digital signature and public key agreement protocols. We explore its security by reducing it to the hardness of the Module-ISIS problem and introduce three new variants: Module-ISIS+, Module-ISIS*, and Module-ISIS**. These constructions enhance...

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...

Group signatures and their variants have been widely used in privacy-sensitive scenarios such as anonymous authentication and attestation. In this paper, we present a new post-quantum group signature scheme from symmetric primitives. Using only symmetric primitives makes the scheme less prone to unknown attacks than basing the design on newly proposed hard problems whose security is less well-understood. However, symmetric primitives do not have rich algebraic properties, and this makes it...

This paper defines a post-quantum encryption scheme based on discussion cryptography by introducing a new post-quantum hard problem called Q-Problem. The idea behind this scheme is to hide the keys of each entity, and the encryption process is based on secret message holders using only random private keys.

Machine-learning systems continue to advance at a rapid pace, demonstrating remarkable utility in various fields and disciplines. As these systems continue to grow in size and complexity, a nascent industry is emerging which aims to bring machine-learning-as-a-service (MLaaS) to market. Outsourcing the operation and training of these systems to powerful hardware carries numerous advantages, but challenges arise when needing to ensure privacy and the correctness of work carried out by a...

Restricted syndrome decoding problems (R-SDP and R-SDP($G$)) provide an interesting basis for post-quantum cryptography. Indeed, they feature in CROSS, a submission in the ongoing process for standardizing post-quantum signatures. This work improves our understanding of the security of both problems. Firstly, we propose and implement a novel collision attack on R-SDP($G$) that provides the best attack under realistic restrictions on memory. Secondly, we derive precise complexity...

Hash-and-Sign with Retry is a popular technique to design efficient signature schemes from code-based or multivariate assumptions. Contrary to Hash-and-Sign signatures based on preimage-sampleable functions as defined by Gentry, Peikert and Vaikuntanathan (STOC 2008), trapdoor functions in code-based and multivariate schemes are not surjective. Therefore, the standard approach uses random trials. Kosuge and Xagawa (PKC 2024) coined it the Hash-and-Sign with Retry paradigm. As many attacks...

Cumplido, María et al. have recently shown that the Wang-Hu digital signature is not secure and has presented a potential attack on the root extraction problem. The effectiveness of generic attacks on solving this problem for braids is still uncertain and it is unknown if it is possible to create braids that require exponential time to solve these problems. In 2023, Lin and al. has proposed a post-quantum signature scheme similar to the Wang-Hu scheme that is proven to be able to withstand...

The Number Theoretic Transform (NTT) is a powerful mathematical tool that has become increasingly important in developing Post Quantum Cryptography (PQC) and Homomorphic Encryption (HE). Its ability to efficiently calculate polynomial multiplication using the convolution theorem with a quasi-linear complexity $O(n \log{n})$ instead of $O(n^2)$ when implemented with Fast Fourier Transform-style algorithms has made it a key component in modern cryptography. FFT-style NTT algorithm or fast-NTT...

We revisit the alternating-moduli paradigm for constructing symmetric-key primitives with a focus on constructing efficient protocols to evaluate them using secure multi-party computation (MPC). The alternating-moduli paradigm of Boneh, Ishai, Passelègue, Sahai, and Wu (TCC 2018) enables the construction of various symmetric-key primitives with the common characteristic that the inputs are multiplied by two linear maps over different moduli. The first contribution focuses on...

In this paper, we introduce the first fault attack on SQIsign. By injecting a fault into the ideal generator during the commitment phase, we demonstrate a meaningful probability of inducing the generation of order $\mathcal{O}_0$. The probability is bounded by one parameter, the degree of commitment isogeny. We also show that the probability can be reasonably estimated by assuming uniform randomness of a random variable, and provide empirical evidence supporting the validity of this...

Adaptor signatures can be viewed as a generalized form of the standard digital signature schemes where a secret randomness is hidden within a signature. Adaptor signatures are a recent cryptographic primitive and are becoming an important tool for blockchain applications such as cryptocurrencies to reduce on-chain costs, improve fungibility, and contribute to off-chain forms of payment in payment-channel networks, payment-channel hubs, and atomic swaps. However, currently used adaptor...

In this paper, we introduce a new framework for constructing linkable ring signatures (LRS). Our framework is based purely on signatures of knowledge (SoK) which allows one to issue signatures on behalf of any NP-statement using the corresponding witness. Our framework enjoys the following advantages: (1) the security of the resulting LRS depends only on the security of the underlying SoK; (2) the resulting LRS naturally supports online/offline signing (resp. verification), where the output...

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...

We present a solution to the open problem of designing a linear-time, unbiased and timing attack-resistant shuffling algorithm for fixed-weight sampling. Although it can be implemented without timing leakages of secret data in any architecture, we illustrate with ARMv7-M and ARMv8-A implementations; for the latter, we take advantage of architectural features such as NEON and conditional instructions, which are representative of features available on architectures targeting similar systems,...

In 2021, Sterner proposed a commitment scheme based on supersingular isogenies. For this scheme to be binding, one relies on a trusted party to generate a starting supersingular elliptic curve of unknown endomorphism ring. In fact, the knowledge of the endomorphism ring allows one to compute an endomorphism of degree a power of a given small prime. Such an endomorphism can then be split into two to obtain two different messages with the same commitment. This is the reason why one needs a...

Given the widespread use of cryptography in Enterprise IT, migration to post-quantum cryptography (PQC) is not drop-in replacement at all. Cryptographic agility, or crypto-agility, is a design feature that enables seamless updates to new cryptographic algorithms and standards without the need to modify or replace the surrounding infrastructure. This paper introduces a notion of software-defined cryptography as the desired design feature for crypto-agility, emphasizing the role of software...

Quantum computers have the potential to solve hard problems that are nearly impossible to solve by classical computers, this has sparked a surge of research to apply quantum technology and algorithm against the cryptographic systems to evaluate for its quantum resistance. In the process of selecting post-quantum standards, NIST categorizes security levels based on the complexity that quantum computers would require to crack AES encryption (levels 1, 3 and 5) and SHA-2 or SHA-3 (levels 2 and...

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...

This paper shows novel techniques to reduce the signature size of the code-based signature schemes MEDS and ALTEQ, by a large factor. For both schemes, the signature size is dominated by the responses for rounds with nonzero challenges, and we reduce the signature size by reducing the size of these responses. For MEDS, each of the responses consists of $m^2 + n^2$ field elements,while in our new protocol each response consists of only $2k$ ($k$ is usually chosen to be close to $m$ and $n$)...

SHA2 is widely used in various traditional public key ryptosystems, post-quantum cryptography, personal identification, and network communication protocols. Therefore, ensuring its robust security is of critical importance. Several differential fault attacks based on random word fault have targeted SHA1 and SHACAL-2. However, extending such random word-based fault attacks to SHA2 proves to be much more difficult due to the increased complexity of the Boolean functions in SHA2. In this...

The VOLE-in-the-Head paradigm, recently introduced by Baum et al. (Crypto 2023), is a compiler that uses SoftspokenOT (Crypto 2022) to transfer any VOLE-based designated verifier zero-knowledge protocol into a publicly verifiable zero-knowledge protocol. Together with the Fiat-Shamir transformation, a new digital signature scheme FAEST (faest.info) is proposed, and it outperforms all MPC-in-the-Head signatures. We propose a new candidate post-quantum signature scheme from the Multivariate...

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...

Soft Analytical Side Channel Attacks (SASCA) are a powerful family of Side Channel Attacks (SCA) that allows the recovery of secret values with only a small number of traces. Their effectiveness lies in the Belief Propagation (BP) algorithm, which enables efficient computation of the marginal distributions of intermediate values. Post-quantum schemes such as Kyber, and more recently, Hamming Quasi-Cyclic (HQC), have been targets of SASCA. Previous SASCA on HQC focused on Reed-Solomon (RS)...

A ranking function for permutations maps every permutation of length $n$ to a unique integer between $0$ and $n!-1$. For permutations of size that are of interest in cryptographic applications, evaluating such a function requires multiple-precision arithmetic. This work introduces a quasi-optimal ranking technique that allows us to rank a permutation efficiently without needing a multiple-precision arithmetic library. We present experiments that show the computational advantage of our method...

We present a new post-quantum Public Key Encryption scheme (PKE) named Supersingular Isogeny Lollipop Based Encryption or SILBE. SILBE is obtained by leveraging the generalised lollipop attack of Castryck and Vercauteren on the M-SIDH Key exchange by Fouotsa, Moriya and Petit. Doing so, we can in fact make SILBE a post-quantum secure Updatable Public Key Encryption scheme (UPKE). SILBE is in fact the first isogeny-based UPKE which is not based on group actions. Hence, SILBE overcomes the...

We devise algorithms for finding equivalences of trilinear forms over finite fields modulo linear group actions. Our focus is on two problems under this umbrella, Matrix Code Equivalence (MCE) and Alternating Trilinear Form Equivalence (ATFE), since their hardness is the foundation of the NIST round-$1$ signature candidates MEDS and ALTEQ respectively. We present new algorithms for MCE and ATFE, which are further developments of the algorithms for polynomial isomorphism and alternating...

The Alternating Trilinear Form Equivalence (ATFE) problem was recently used by Tang et al. as a hardness assumption in the design of a Fiat-Shamir digital signature scheme ALTEQ. The scheme was submitted to the additional round for digital signatures of the NIST standardization process for post-quantum cryptography. ATFE is a hard equivalence problem known to be in the class of equivalence problems that includes, for instance, the Tensor Isomorphism (TI), Quadratic Maps Linear...